OFDM AIR-INTERFACE DESIGN FOR MULTIMEDIA COMMUNICATIONS

Transcription

1 OFDM AIR-INTERFACE DESIGN FOR MULTIMEDIA COMMUNICATIONS

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3 OFDM AIR-INTERFACE DESIGN FOR MULTIMEDIA COMMUNICATIONS Proefschrft ter verkrjgng van de graad van doctor aan de Technsche Unverstet Delft, op gezag van de Rector Magnfcus Prof. dr. r. J. T. Fokkema voorztter van het College van Promotes, n het openbaar te verdedgen op dnsdag aprl om.3 uur door Klaus WITRISAL Dplomngeneur der Elektrotechnk, Technsche Unverstät Graz, geboren te Graz, Oostenrjk.

4 Dt proefschrft s goedgekeurd door de promotoren: Prof. dr. r. L. P. Lgthart Prof. dr. R. Prasad Toegevoegd promotor: Dr. r. G. J. M. Janssen Samenstellng promotecommsse: Rector Magnfcus voorztter Prof. dr. r. L. P. Lgthart Technsche Unverstet Delft, promotor Prof. dr. R. Prasad Aalborg Unversty, Denmark, promotor Dr. r. G. J. M. Janssen Technsche Unverstet Delft, toegevoegd promotor Prof. r. W. Dk Technsche Unverstet Delft Prof. dr. H. Rohlng Technsche Unverstät Hamburg-Harburg, Dutsland Prof. dr. r. W. C. van Etten Unverstet Twente Prof. dr. r. J. W. M. Bergmans Technsche Unverstet Endhoven ISBN: Copyrght Klaus Wtrsal All rghts reserved. No part of the materal protected by ths copyrght notce may be reproduced or utlzed n any form or by any means, electronc or mechancal, ncludng photocopyng, recordng or by any nformaton storage and retreval system, wthout permsson from the author Klaus Wtrsal. Cover Desgn by Arnold Zwanenburg ( Prnted n Austra

5 To Slke and my parents

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7 Summary The am of ths dssertaton s the nvestgaton of the key ssues encountered n the development of wdeband rado ar-nterfaces. Orthogonal frequency-dvson multplexng (OFDM) s consdered as the enablng technology for transmttng data at extremely hgh rates over tme-dspersve rado channels. OFDM s a transmsson scheme, whch splts up the data stream, sendng the data symbols smultaneously at a drastcally reduced symbol rate over a set of parallel sub-carrers. The frst part of ths thess deals wth the modelng of the tme-dspersve and frequency-selectve rado channel, utlzng second order Gaussan stochastc processes. A novel channel measurement technque s developed, n whch the RMS delay spread of the channel s estmated from the level-crossng rate of the frequency-selectve channel transfer functon. Ths method enables the emprcal channel characterzaton utlzng smplfed non-coherent measurements of the receved power versus frequency. Ar-nterface and multple access scheme of an OFDM-based communcatons system are proposed and nvestgated n part two of ths work. Cumulatve data rates up to 55 Mbt/s are reached under optmum channel condtons, n ndoor and short range outdoor scenaros at low moblty (pedestran speed). Wreless LANs (local area networks) are a typcal applcaton for the system. Synchronzaton and channel estmaton algorthms are developed and evaluated, utlzng a known tranng symbol, whch s perodcally transmtted n the begnnng of the fxed frame structure. It has been concluded that robust and effcent synchronzaton and channel estmaton schemes crtcal tasks for an OFDM recever are enabled by ths tranng symbol, at the cost of a very small overhead. Detaled topcs n synchronzaton nclude the analyss of a fne tmng-offset estmaton algorthm over multpath channels, and the analyss of the mpact of DC-offsets and carrer feed-through on a popular frequency-synchronzaton scheme. A remedy s found for the latter ssue. For the up-lnk, pre-equalzaton s suggested n a tme-dvson duplexng (TDD)

8 OFDM Ar-Interface Desgn for Multmeda Communcatons scheme to pre-compensate for the frequency-selectvty of the rado channel and thereby to smplfy the data detecton at the base staton. Synchronzaton s mostly done by the mobles, whch mples a dstrbuton of the hgh complexty nvolved. Concepts are presented for keepng the power of the up-lnk sgnal constant and for estmatng the remanng synchronzaton-offsets. The man sgnal processng algorthms for the OFDM transcevers have been mplemented and valdated on a DSP-based expermental platform, whch operates n realtme, however, at drastcally downscaled data rate. Forward error correcton codng s an essental part of OFDM schemes, because frequency-dversty s exploted by spreadng the coded data symbols over the large sgnal bandwdth. The performance of coded OFDM systems s evaluated, ndcatng that ncreased system bandwdth and channel delay spread (the latter under certan constrants) lead to enhanced performance. A novel antenna dversty technque s proposed, whch can mprove the performance at low computatonal complexty, f the system bandwdth and/or the channel s delay spread are small. Generally, t has been concluded that the OFDM scheme s an effcent and robust method for transmttng data at very hgh rates. However, some crtcal hardware ssues, as for nstance the lnearty of amplfers and the phase nose of local oscllators, have to be solved.

9 Table of Contents Summary... Table of Contents... Chapter General Introducton.... Towards Fourth Generaton Moble Systems.... Wdeband Ar-nterface Desgn usng OFDM Framework and Goal of ths Ph.D. Project Organzaton of ths Thess Part I: Channel Characterzaton Part II: OFDM System Proposal and Evaluaton Problems Addressed n ths Dssertaton References... Part I: Channel Characterzaton...5 Chapter Modelng of the Frequency-Selectve Rado Channel...7. Introducton Characterzaton of the Moble Rado Channel Components of a Multpath Channel Model Defntons Varaton of Channel Parameters Due to Bandwdth Lmtaton Frequency-Doman Channel Modelng The WSSUS Channel Model Channel Descrpton... 9

10 v OFDM Ar-Interface Desgn for Multmeda Communcatons.3.3 Relaton to (Physcal) Channel Parameters Frequency-Doman Channel Smulaton Model Descrpton Implementaton of the Smulaton Scheme FD-Smulaton Results Dfferences to Tme-Doman Smulaton Schemes Applcaton to mm-wave Rado Channels Dscusson of Measurement Results Dscusson of Channel Parameters Overvew of Channel Models Applcablty of the FD-model Conclusons References... 5 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate Introducton Frequency-Doman Level Crossng Rate Dervaton of the LCR f from the Contnuous FD-Channel Model LCR f for a Determnstc Two-Ray Channel Dervaton of the LCR f for the Sampled Case Dscusson and Summary Applcaton to Channel Measurements Channel Measurement Procedure Valdaton of the Method usng Measurement Results Valdaton by Tme-doman Channel Smulatons Dscusson of the Measurement Method Analyss of the Influence of Nose Mathematcal Modelng Dervaton of LCR f from the Contnuous FD-Channel Model Dscrete-Frequency Analyss for Raylegh Channels Evaluaton and Applcaton of the Analytcal Results A Robust Measurement Procedure Extended Measurement Procedure Conclusons and Recommendatons References... 97

11 Table of Contents v Part II: OFDM System Proposal and Evaluaton... Chapter 4 OFDM Introducton and System Modelng Introducton OFDM Introducton and System Model OFDM Introducton and Block Dagram Desgn of the OFDM Sgnal OFDM System Model Synchronzaton Errors Performance of an Uncoded OFDM System Mathematcal Modelng Analytcal Evaluaton of the BER Performance Results Conclusons and Recommendatons References...33 Chapter 5 OFDM System Proposal and Emulaton System Introducton OFDM Based System Proposal Ar Interface Physcal Layer Up- and Down-lnk Multple Access Scheme Archtecture of the Transcevers Forward Error Correcton Codng Lnk Budget The Emulaton System Descrpton of the Emulaton System Hardware Characterstcs Implementaton of the Channel Smulator Summary and Conclusons References...65 Chapter 6 DSP Algorthm Development for the Down-Lnk Introducton Overvew of Synchronzaton Steps Classfcaton of Synchronzaton Technques Desgn of the Tranng Symbol Frame Tmng Synchronzaton Fractonal Frequency-Offset Synchronzaton...75

12 v OFDM Ar-Interface Desgn for Multmeda Communcatons 6..5 Applcaton of the FFT Integer Frequency-Synchronzaton Remanng Tmng-Offset Synchronzaton Samplng Frequency-Offsets Carrer Phase-Offset Summary and Conclusons Impact of DC-Offsets and Carrer Feed-Through on Fractonal Frequency- Synchronzaton Mathematcal Modelng and Defntons Analyss of the Synchronzaton Algorthm Extenson of the Algorthm Analytcal and Smulaton Results Conclusons and Recommendatons Channel Estmaton Wener Flterng for Nose Reducton Computatonal Results Concludng Remarks Expermental Results Performance Results for the Full-Rate Recever Performance Results for the Quarter-Rate Recever Dscusson of the Channel s Tme-Varablty Conclusons and Recommendatons References...3 Chapter 7 DSP Algorthm Development for the Up-Lnk Introducton Pre-Equalzaton n OFDM OFDM System Model Impact of Synchronzaton Errors Channel Recprocty and Pre-Equalzaton Is the Channel Recprocal? Power Lmtng Strateges for Pre-equalzaton Phase Pre-Equalzaton for Phase-Modulaton Schemes Phase and Magntude Pre-Equalzaton wth Power Lmtng Performance Results Applcaton of Phase Pre-Equalzaton for QPSK Applcaton of Pre-Equalzaton wth Power Lmtng Synchronzaton Parameter Estmaton on the Up-lnk...37

13 Table of Contents v 7.5. Magntude of the Constellaton Values Estmaton of the Up-lnk Tmng-Offset Expermental Results Performance over Dfferent Rado Channels Impact of the I/Q-Modulator and -Demodulator Conclusons References...48 Chapter 8 Performance Evaluaton and Enhancement of COFDM Introducton Performance of a Coded OFDM System Revew of the Concept of Effectve E b /N Assessment of the Concept of Effectve E b /N PDF of the Effectve E b /N Performance Results and Dscusson Summary Performance Enhancement usng Antenna Dversty Antenna Dversty for OFDM Usng Cyclc Delays Even/odd Sub-carrer Transmtter Dversty Performance Dscusson of the Dversty Schemes Conclusons and Recommendatons References...83 Chapter 9 Conclusons and Recommendatons Part I: Channel Characterzaton Modelng of the Frequency-Selectve Rado Channel Channel Measurement Technque usng the FD-Level Crossng Rate Part II: OFDM System Proposal and Evaluaton OFDM System Modelng OFDM Ar-Interface and Multple Access Scheme Proposal Issues n utlzng the 6 GHz Frequency-Band Synchronzaton and Channel Estmaton on the Down-Lnk Pre-Equalzaton for the Up-Lnk Emulaton System and OFDM Implementaton Performance Evaluaton and Enhancement of COFDM...93 Appendx A Correlaton Coeffcent for the Dscrete Impulse Response...95

14 v OFDM Ar-Interface Desgn for Multmeda Communcatons A- Defntons...95 A- Calculaton of the Correlaton Coeffcent...96 A-3 References...97 Appendx B FD-Level Crossng Rate n the Presence of Nose...99 B- Dervaton of the FD-Level Crossng Rate...99 B- Approxmaton...3 B-3 Approxmaton...3 B-4 References...3 Appendx C Analyss of Fne Tmng-Offset Estmaton...33 C- Revew of Estmaton Technque and System Model...33 C- Estmaton Bas over Dspersve Channels...35 C-3 Estmaton Varance on the AWGN Channel...36 C-4 Estmaton Varance on Raylegh Fadng Channels...38 C-5 References...3 Appendx D PDF of Wde-band Average Receved Power...3 D- PDF of Average Receved Power for Raylegh Fadng Channels...3 D-. Approxmatons...33 D-. Analytcal and Smulaton Results...35 D- PDF of Average Power for Rcean Fadng Channels...38 D-. Approxmatons...39 D-. Analytcal and smulaton results...3 D-3 References...34 Lst of Acronyms...35 Publcatons by the Author...39 Journal Papers...39 Conference Papers...39 Reports...33 Relaton to ths Thess...33 Samenvattng Acknowledgements Currculum Vtae...337

15 Chapter General Introducton. Towards Fourth Generaton Moble Systems The expected convergence of the nternet and moble telephony fuels major research and development efforts n the telecommuncatons ndustres. Thrd generaton (3G) cellular systems, called IMT- (Internatonal Moble Telecommuncatons n the year ) or UMTS (Unversal Moble Telecommuncatons System), are currently deployed to meet ths demand, supportng data rates up to Mbt/s for local coverage and at least 44 kbt/s for wde-area coverage [] [3]. But wll those systems become as successful as ther ancestors, partcularly the (dgtal) second-generaton systems lke GSM (Global System for Moble Communcatons), whch for many years largely exceeded the expected growth rates, reachng penetraton factors of well above 5 % n most western European countres? Are the new servces offered suffcent motvaton to buy new, n the begnnng certanly rather expensve, moble phones? Wll the enormous cost of rollng-out such systems ncludng lcense fees ever be amortzed? In my opnon, moble telephones are the prerequste to acheve large penetraton rates wth nternet servces. Many dsadvantages of current nternet access methods are elmnated: there s no need to buy or possess a computer, to cable a modem, to subscrbe wth an nternet servce provder, to go through lengthy start-up and log-n procedures, etc. Moreover, nche-tme can be used to browse the Web; for nstance the tme spent on publc transport, commutng to ones work. Advanced servces can make effectve use of the moblty aspect: Locaton-based servces can provde the user wth nformaton related to hs whereabouts (restaurant gude, cultural program, etc.), whch s most useful n an unknown cty but can be nterestng n ones home-town as well. For the mass-market, man ngredents for a successful deployment of 3G systems are: cheap, easy-to-use termnals,

16 Chapter General Introducton large color dsplays, and attractve bllng schemes (flat rates). The huge success of the Japanese -mode system, whch mplements the above-mentoned features (however, provdng low data rates compared to UMTS), proves the nterest of the consumer n moble nternet servces [4]. On the other hand, voce telephony (possbly augmented by stll mages and vdeo) wll reman an mportant applcaton n future systems, where enhanced capacty and spectral effcency need to be acheved. Whle the roll-out of 3G systems s under progress, research actvtes on the fourth generaton (4G) have already started [5] [9]. At the tme beng, however, there s no clear vson whch ngredents wll defne ths future system generaton. Certanly, transmsson rates wll be further ncreased bt rates n the order of Mbt/s are consdered, but many doubt that t wll ever be feasble (affordable) to provde such data rates wth naton-wde coverage. For local coverage, on the other hand, current wreless local area networks (W-LAN) standards can already provde data rates up to 54 Mbt/s. (Those W-LAN standards are: IEEE 8.a n the USA, HIPERLAN/ n Europe, and MMAC n Japan [], []). Therefore, a popular vson suggests to combne W-LAN systems for hgh peak data rates wth cellular systems (GSM, UMTS) for wde area-coverage, and to allow ntersystem handovers []. Techncal aspects of ar-nterface standards for mult-standard termnals supportng W-LAN and cellular technologes are dscussed n [3]. However, the more mportant factor for the user may be the smple fact that a W-LAN can be nstalled and operated by the user, free of cost for subscrpton and call-charges. That s, the user may own a part of the system nfrastructure, and eventually provded the requred bllng mechansms are n place even charge foregn termnals for accessng the system at hs premses. Ths factor may become a key-ngredent of 4G systems. Other challenges to be solved n order to realze mult-standard systems nclude hardware ssues for termnals supportng multple ar-nterface standards, the above mentoned nter-system handovers, bllng aspects, and securty/prvacy. But s such an ntegraton of systems enough reason to speak of a new system generaton, partcularly f only current ar-nterface standards are consdered? The scenaros weakly supported by current technology pont out some lmtatons. Adhoc networkng for nstance, where a number of termnals form a small wreless network passng on nformaton from node-to-node wthout the ad of an access pont or a base staton, s a concept that wll become ncreasngly mportant [4]. Bluetooth, ntended as a cable-replacement [5], supports ths dea at somewhat lmted bt-rates up to about 8 kbt/s and at very lmted ranges of a few meters. At hgher rates, the IEEE 8. W-LAN standard s consdered by many as an enablng technology for ad-hoc networks [6]. Serous problems are encountered, however, when ts current multple access control (MAC) protocol s appled n such systems [6].

17 . Wdeband Ar-nterface Desgn usng OFDM 3 A wreless dgtal recordng or televson studo requres the support of multple constant-rate data streams at specfed bt-error-rates and low delay a scenaro that s very dfferent to the prevous one. A centralzed, scheduled MAC could be most effcent for such applcatons, whch may also be supported by 4G systems. Last but not least, a real 4G ar-nterface to be developed may support data rates n the order of Mbt/s at full moblty,.e., at veloctes up to 3 km/h [5] [9], []. The term Moble Broadband Systems (MBS) refers to ths type of technology, n a number of references [5] [7]. In ths thess, rado ar-nterface technology for future wde-band communcatons systems s studed, startng wth the mathematcal modelng of the fadng rado channel. Ths work has been motvated on the one hand by the huge potental market of wdeband communcatons systems, partcularly of wreless LANs, and on the other hand and more mportantly, by the technologcal challenge of developng ar-nterfaces for transmttng such large data rates over the hostle moble rado channels. The followng secton elaborates on the technology aspect.. Wdeband Ar-nterface Desgn usng OFDM Multpath propagaton s the prmary ssue n the ar-nterface desgn for wdeband (hgh data-rate) communcatons systems: multple replcas of the transmtted sgnal arrve at the recever wth varous propagaton delays, due to reflectons on all knds of objects and obstacles n the envronment. Therefore, f a hgh-rate data stream s transmtted on such a channel, multple data symbols nterfere wth each other, makng the data recovery dffcult. At 55 Mbt/s, for nstance, the symbol perod s about 3 ns usng QPSK (quadrature phase shft keyng) and neglectng error correcton codng. Magntude Magntude (a) Delay tme (b) Frequency Fgure -: (a): Impulse response of a multpath rado channel. (b): Frequency-selectve channel transfer functon. The Fourer transform relates the mpulse response and the transfer functon.

18 4 Chapter General Introducton Channel mpulse response Sgnal bandwdth Symbol perod Channel transfer functon tme (a) Symbol perod Sub-carrer bandwdth frequency frequency tme (b) Fgure -: Symbol perod and sgnal bandwdth n comparson wth the channel mpulse response and channel transfer functon. (a): Sngle carrer system (seral transmsson); (b): Mult-carrer system (OFDM) wth parallel sub-channels. Ths value can be compared wth the (relatve) delay of a reflected path wth, say, 3 m path length dfference, beng ns, whch demonstrates that the combnaton of multple data symbols s observed at the recever at any gven tme nstant. Ths phenomenon s called nter-symbol-nterference (ISI). Recevers have to elmnate the ISI. Mathematcally, the nfluence of the channel can be descrbed as a convoluton of the transmtted sgnal by the channel mpulse response depcted n Fgure -a. Fgure -a llustrates the relaton of the symbol perod and the tme-extent of the channel mpulse response for a seral wdeband transmsson system. Another characterstc property of a multpath rado channel s the frequency-selectvty of ts transfer functon (TF), as shown n Fgure -a. (The TF s the response of the channel to a narrow-band sgnal as a functon of the frequency.) It s noted that the TF s the Fourer transform of the channel mpulse response. The comparson of the sgnal bandwdth of the seral data stream and the channel transfer functon demonstrates that a wde-band sgnal gets dstorted when t s transmtted over such a channel (see Fgure -a).

19 . Wdeband Ar-nterface Desgn usng OFDM 5 Magntude Frequency sub-carrer frequency spacng Fgure -3: The overlappng spectra (snc-functons) of four adjacent OFDM sub-carrers. At one sub-carrers center frequency, all other spectra are zero, demonstratng the sub-carrer orthogonalty. Equalzaton s the standard method to combat nter-symbol-nterference n a snglecarrer system [7]. Equalzers consst of lnear flters whose purpose s to combne the sgnal components arrvng at varous delay tmes. The man challenge s to adapt the flter coeffcents to the tme-varant channel condtons. The methods for achevng ths adaptaton are computatonally extremely demandng, partcularly f long flters are requred as n our case, where the channel mpulse response typcally spans many data symbols. Orthogonal frequency dvson multplexng (OFDM) can drastcally smplfy the equalzaton problem [], [8] [3]. In OFDM, the hgh-rate seral data stream s splt up nto a number (several dozens up to a few thousand) of parallel data streams at a much lower (common) symbol rate, whch are modulated on a set of sub-carrers (frequency dvson multplexng). Fgure -b llustrates the parallel transmsson prncple. Hgh spectral effcency s acheved by selectng a specfc (orthogonal) set of sub-carrer frequences. Inter-carrer-nterference s avoded due to the orthogonalty, although the spectra of the sub-carrers actually overlap (see Fgure -3). The dea s to make the symbol perod long wth respect to the channel mpulse response n order to reduce ISI. Ths mples that the bandwdth of the sub-carrers gets small (wth respect to the channel s coherence bandwdth [7]), thus the mpact of the channel s reduced to an attenuaton and phase dstorton of the sub-carrer symbols ( flat fadng ), whch can be compensated by effcent one-tap equalzaton. Dgtal sgnal processng s used to generate a complex-valued baseband sgnal conta-

20 6 Chapter General Introducton nng all OFDM sub-carrer sgnals. (The block dagram of an OFDM transmsson chan s shown n Chapter 4.) Next to the correct estmaton of the channel transfer functon, whch s requred for equalzaton, the followng problems requre partcular attenton n the mplementaton of OFDM modems: Lnear power amplfers are needed at the transmtter (and pre-amplfers at the recever) to avod any dstorton of the OFDM sgnal. Dstorton would lead to ntercarrer-nterference (ICI), mplyng performance degradaton. At the recever, synchronzaton ssues are of prme mportance. The start of the OFDM symbols and the exact locaton of the sub-carrer frequences have to be found to be able to recover the data symbols (tme- and frequency-synchronzaton). Phase nose of any mxer oscllators also yelds ICI and thus has to be avoded/mnmzed..3 Framework and Goal of ths Ph.D. Project The man topc of ths dssertaton s the desgn of the ar-nterface of an OFDMbased, wde-band moble communcatons system for ndoor and low-range, low-moblty outdoor scenaros. Wreless computer networks (W-LAN) are the ntended applcaton of such systems, enablng wreless multmeda communcatons. Ths work was conducted under the framework of a cooperatve research program between Delft Unversty of Technology (Delft, The Netherlands) and Korea Telecom (Seoul, South Korea). Fundng was provded by Korea Telecom. The emphass of ths study lay on the physcal rado lnk. Wreless transmsson of ATM (asynchronous transfer mode) cells should be supported at peak data rates of 55 Mbt/s, accordng to the target specfcatons of the ar-nterface multple access scheme under development. The 6 GHz mm-wave frequency band was consdered, manly because the requred bandwdth n the order of several hundreds of MHz s only avalable at these frequences [4]. The mathematcal modelng of the rado channel was the frst goal of ths project. Another mportant aspect was the mplementaton and valdaton of the proposed system on a hardware platform to be developed. A number of students have contrbuted to the project and to ths Ph.D. thess, workng on ther graduaton projects or on nternshps [5] [35]..4 Organzaton of ths Thess Ths Ph.D. thess s dvded n two parts. In Part I, the wde-band rado channel s modeled and nvestgated, whle the OFDM system desgn s presented n Part II.

21 .4 Organzaton of ths Thess 7.4. Part I: Channel Characterzaton The rado channel model s probably the most mportant tool for the desgn of a communcatons system. It has to approprately descrbe the relevant propertes of the physcal channel, and t should be sutable for computer smulatons and analytcal studes of the system under development. As n OFDM nformaton s transmtted over a set of parallel sub-carrers, the man aspect of nterest s the frequency-selectvty of the channel transfer functon caused by multpath propagaton. The frequency-doman channel model proposed and studed n Chapter of ths dssertaton drectly descrbes ths property by characterzng the varatons of the transfer functon va second-order stochastc propertes. The model s behavor s compared to physcal propagaton mechansms and ts parameters are related to parameters of the rado channel. Throughout ths thess, the model s appled for the desgn and evaluaton of the OFDM system. In Chapter 3, the frequency-doman level crossng rate (LCR f ) of the channel transfer functon s analyzed. The LCR f specfes the number of up-gong level crossngs over a gven threshold per unt of bandwdth. Orgnally, the motvaton for ths study was to derve parameters equvalent to the (tme-doman) level crossng rate and average fade duraton [36], whch are consdered to be useful n the development and evaluaton of moble communcatons systems [37]. The most relevant applcaton, however, was found n a slghtly dfferent feld. It was dscovered n ths Ph.D. research that the LCR f can be used for estmatng the RMS delay spread of the channel, whch s the most sgnfcant sngle parameter for characterzng the channel s tme-dsperson (and frequency-selectvty). Ths relatonshp enables channel measurements usng a rather smple measurement setup, because t s suffcent to scan the power transfer functon of the channel versus frequency to determne the LCR f. The novel measurement technque s extensvely studed n Chapter Part II: OFDM System Proposal and Evaluaton Chapter 4 gves a bref ntroducton to the OFDM transmsson technque. System models are derved for the analyss of varous aspects of OFDM. In Chapter 4, for nstance, they are used to evaluate the bt-error-rate (BER) performance of an uncoded OFDM system, consderng varous modulaton- and detecton schemes, and dfferent channel condtons. The results wll serve as benchmarks for the evaluaton of the OFDM recevers nvestgated n ths thess. The ar-nterface and multple access scheme of a novel OFDM-based wde-band communcatons system are descrbed n Chapter 5. The system supports the transmsson of sngle asynchronous transfer mode (ATM) cells at bt-rates up to 55 Mbt/s. To effcently transmt such short data packets (one ATM cells conssts of just 53 bytes) at

22 8 Chapter General Introducton defned qualty of servce requrements, a fxed (but potentally asymmetrc) frame structure s employed wth tme-dvson duplexng (TDD). Tranng symbols perodcally transmtted on the down-lnk are used by the moble for synchronzaton and channel estmaton, whle pre-equalzaton s consdered for the up-lnk to enable coherent detecton at the base staton wthout ntroducng addtonal tranng symbols. Chapter 5 also descrbes a dgtal sgnal processor (DSP) based expermental platform, the so-called emulaton system, whch has been developed for demonstratng the OFDM ar-nterface. All parameters have been largely downscaled to decrease the requred processng speed (and to thereby smplfy the software and hardware development), enablng the mplementaton of the transmtter and the recever on sngle (but separate) DSP chps. A thrd DSP s used to smulate the multpath rado channel. Analog hardware performs n-phase/quadrature (I/Q) -modulaton (to an ntermedate frequency) and -demodulaton, ntroducng frequency-offsets. Thus, real-tme frequencysynchronzaton algorthms can be demonstrated. All system components are nterconnected by analog, complex-valued baseband sgnals (I/Q-sgnals). In Chapter 6, the sgnal processng steps for the down-lnk are nvestgated and evaluated. The estmaton of synchronzaton parameters and of the channel transfer functon are thoroughly descrbed, utlzng the perodcally transmtted tranng symbol. Novel contrbutons n ths chapter concern the analyss of a hghly accurate tmngsynchronzaton scheme, and the nvestgaton of the mpact of DC-offsets and carrer feed-through on a popular class of frequency-synchronzaton technques. The latter study leads to an extenson of the technque wth mproved robustness aganst these mparments. To save transmsson power, to enhance the spectral effcency, and to smplfy the symbol detecton, pre-equalzaton has been proposed for the up-lnk of the OFDM system. That s, the up-lnk symbols are pre-dstorted usng channel knowledge from the down-lnk, n order to compensate for the phase rotatons and attenuatons of the data symbols, ntroduced by the multpath rado channel. Channel recprocty and slow tme-varablty are assumed. In Chapter 7, a number of basc ssues of ths prncple are nvestgated, as for nstance synchronzaton steps and technques for lmtng the transmtted power on the up-lnk. Moreover, t s dscussed whether the channel recprocty can be exploted for pre-equalzaton as proposed. Forward error correcton codng s a crucal component of most OFDM systems. Errors caused by the frequency-selectve channel on severely attenuated sub-carrers can be corrected usng the relable data of strong(er) sub-carrers. That s, the frequencydversty of the wde-band rado channel s exploted. In Chapter 8, the performance of coded OFDM systems s evaluated usng the concept of effectve E b /N [38]. In ths method, the fadng pattern of the rado channel s converted to a scalar value, the effectve E b /N, whch quantfes the sgnal-to-nose

23 .5 Problems Addressed n ths Dssertaton 9 rato on an AWGN channel resultng n equvalent error rates. Channel smulatons have to be performed to generate realstc fadng patterns that can then be transformed to error rate results n ths way. A novel extenson to ths concept s presented n ths thess. The probablty densty functon of the effectve E b /N s related to channel parameters, allowng for the analytcal computaton of average error rates and outage probabltes. Novel antenna dversty schemes are proposed n the second part of Chapter 8 to enhance the performance n cases where the frequency-dversty of the channel s small ( flat fadng channels). General conclusons and recommendatons are summarzed n Chapter 9..5 Problems Addressed n ths Dssertaton The followng problems are analyzed n ths Ph.D. thess: Modelng of the frequency-selectve rado channel Characterzaton of frequency-selectve, Rcean fadng rado channels Modelng of the frequency-selectve channel usng second order statstcs of complex Gaussan random processes Smulaton of the frequency-selectve channel transfer functon n the frequency-doman Applcaton of the channel model to mm-wave rado channels Selecton of typcal parameters for 6 GHz ndoor and outdoor channels Measurement of channel parameters based on the frequency-doman level crossng rate (LCR f ) of the channel transfer functon Dervaton of the LCR f of a frequency-selectve Rcean channel from ts second order stochastc model Impact of channel parameters on the LCR f Impact of the frequency-doman samplng nterval (for Raylegh channels) Estmaton of the RMS delay spread (a measure for the length of the channel mpulse response) from the LCR f Independence of the LCR f from the channel mpulse response for Raylegh channels wth gven RMS delay spread Analyss of the nfluence of nose on the RMS delay spread estmaton technque OFDM bascs Consderaton of hardware aspects n the desgn of the OFDM system

24 Chapter General Introducton Modelng of an dealzed OFDM system and the mpact of (small) synchronzaton errors Bt-error-rate performance evaluaton of an uncoded OFDM system over Rcean channels usng several modulaton schemes and coherent/dfferental detecton Proposal of an OFDM-based ar-nterface and multple access scheme for the transmsson of ATM cells at data rates up to 55 Mbt/s Dscusson of the lnk budget of the system at 6 GHz Development of a DSP-based emulaton system for the demonstraton of the arnterface Analyss of mportant hardware characterstcs Development of a channel smulator Development and analyss of synchronzaton algorthms for OFDM recevers Desgn of a tranng symbol Development and analyss of synchronzaton steps for tme, carrer-frequency, samplng-frequency, and carrer-phase synchronzaton Implementaton of the synchronzaton algorthms on the emulaton system Performance analyss of a tmng-offset estmaton scheme n Rcean channels Analyss of the mpact of DC-offsets and carrer feed-through on a frequency synchronzaton scheme Proposal of an enhanced frequency-synchronzaton scheme that s robust aganst DC-offsets and carrer feed-through Development and analyss of a computatonally effcent channel estmaton scheme usng the tranng symbol Reducton of the computatonal complexty of a Wener flter used for mnmzng the estmaton error Optmzaton of a fxed flter for varous channel condtons Performance evaluaton n tme-varant channels usng the emulaton system Smulaton of a channel predcton scheme for performance enhancement n tme-varant channels Proposal and analyss of a pre-equalzaton technque for the up-lnk of a tme-dvson-duplex OFDM system Proposal and evaluaton of transmt power lmtaton strateges requred at the moble Development and evaluaton of synchronzaton algorthms for the up-lnk Implementaton of the pre-equalzaton scheme and the synchronzaton algo-

25 .6 References rthms on the emulaton system Performance evaluaton of convolutonally coded OFDM systems (wth bt-level nterleavng) usng the concept of effectve E b /N [38] Assessment of the concept of effectve E b /N Applcaton to OFDM systems Modelng the probablty densty functon of the effectve E b /N for gven channel- and OFDM system parameters Proposal and evaluaton of antenna dversty technques for the OFDM transmtter and/or recever.6 References [] IEEE Personal Communcatons, Specal Issue on IMT-: Standards Efforts of the ITU, vol. 4, no. 4, Aug [] T. Ojanperä and R. Prasad, An Overvew of Ar Interface Multple Access for IMT-/UMTS, IEEE Communcatons Magazne, vol. 36, no. 9, pp. 8 95, Sept [3] M. W. Olphant, The Moble Phone Meets the Internet, IEEE Spectrum, vol. 36, no. 8, pp. 8, Aug [4] K. Enok, -mode: the moble Internet servce of the st century, n Proc. ISSCC (Sold-State Crcuts Conference),, pp. 5. [5] L. M. Correa and R. Prasad, An Overvew of Wreless Broadband Communcatons, IEEE Communcatons Magazne, vol. 35, no., pp. 8 33, Jan [6] M. Dns and J. Fernandes, Provson of Suffcent Transmsson Capacty for Broadband Moble Multmeda: A Step Toward 4G, IEEE Communcatons Magazne, vol. 39, no. 8, pp , Aug.. [7] M. Prögler, C. Evc, and M. Umehra, Ar Interface Access Schemes for Broadband Moble Systems, IEEE Communcatons Magazne, vol. 37, no. 9, pp. 6 5, Sept [8] H. Rohlng, R. Grünhed, and D. Galda, OFDM Ar Interface for the 4 th Generaton of Moble Communcaton Systems, n Proc. 6 th nternatonal OFDM- Workshop (InOWo ), Hamburg, Sept., pp [9] NTT DoCoMo, The Path to 4G Moble, IEEE Communcatons Magazne, vol. 39, no. 3, pp. 38 4, March (Advertsement). [] R. van Nee, G. Awater, M. Morkura, H. Takesh, M. Webster, and K. W. Halford, New Hgh-Rate Wreless LAN Standards, IEEE Communcatons Magazne, vol. 37, no., pp. 8 88, Dec. 999.

26 Chapter General Introducton [] R. van Nee and R. Prasad, OFDM for Wreless Multmeda Communcatons. Boston: Artech House,. [] L. M. Perera, Fourth Generaton: Now, t s personal!, n Proc. PIMRC ( th Internatonal Symposum on Personal Indoor Moble Rado Communcatons), London, Sept., pp [3] J. Kallokulju, P. Meche, M. J. Rnne, J. Vallström, P. Varshney, and S.-G. Häggman, Rado Access Selecton for Multstandard Termnals, IEEE Communcatons Magazne, vol. 39, no., pp. 6 4, Oct.. [4] S. Gordano and W. W. Lu, Challenges n Moble Ad Hoc Networkng, IEEE Communcatons Magazne, vol. 39, no. 6, p. 9, June (Guest Edtoral). [5] R. Schnederman, Bluetooth s Slow Dawn, IEEE Spectrum, vol. 37, no., pp. 6 65, Nov.. [6] S. Xu and T. Saadaw, Does the IEEE 8. MAC Protocol Work Well n Multhop Wreless Ad Hoc Networks? IEEE Communcatons Magazne, vol. 39, no. 6, pp. 3 37, June. [7] J. G. Proaks, Dgtal Communcatons, 3 rd ed. New York: McGraw Hll, 995. [8] R. Prasad, Unversal Personal Communcatons. Boston: Artech house, 998, ch.. [9] O. Edfors, M. Sandell, J. J. van de Beek, D. Landström, F. Sjöberg, An Introducton to Orthogonal Frequency-Dvson Multplexng, Research Report TULEA 996:6, Dvson of Sgnal Processng, Luleå Unversty of Technology, csee/sp/publcatons.html. [] M. Speth, S. A. Fechtel, G. Fock, and H. Meyr, Optmum Recever Desgn for Wreless Broad-Band Systems Usng OFDM Part I, IEEE Trans. Commun., vol. 47, no., pp , Nov [] S. B. Wensten and P. M. Ebert, Data Transmsson by Frequency-Dvson Multplexng Usng the Dscrete Fourer Transform, IEEE Trans. Commun. Techn., vol. COM-9, no. 5, pp , Oct. 97. [] J. A. C. Bngham, Multcarrer Modulaton for Data Transmsson: An Idea Whose Tme has Come, IEEE Communcatons Magazne, pp. 5 4, May 99. [3] L. J. Cmn, Analyss and Smulaton of a Dgtal Moble Channel usng Orthogonal Frequency Dvson Multplexng, IEEE Trans. Commun., vol. COM-33, no. 7, pp , July 985. [4] P. F. M. Smulders, Broadband Wreless LANs: A Feasblty Study. PhD Thess, Endhoven Unversty of Technology, Endhoven, The Netherlands, 995.

27 .6 References 3 [5] V. Tutucu, Channel Estmaton for OFDM System n Multpath Fadng Envronments for Wreless Broadband Communcatons, M.Sc. Thess, IRCTR S-8-98, Delft Unversty of Technology, Sept [6] J. Purwaha, Wde-band Channel Measurements at 6 GHz n Indoor Envronments, M.Sc. Thess, Delft Unversty of Technology (IRCTR ), Aug [7] R. el Hattach, Measurements and Modelng of the 8 GHz Rado Channel, M.Sc. Thess, IRCTR S-9-98, Delft Unversty of Technology, Aug [8] P. Teneva, Pseudo Real-tme Smulaton of an OFDM System for Wreless Broadband Communcatons: OFDM Transmtter, Research Report, IRCTR, Delft Unversty of Technology, Jan [9] K. Büke, DSP Manual, Research Report, IRCTR S-5-99, Delft Unversty of Technology, July, 999. [3] K. Büke, Assessment of OFDM Based Ar-nterface Technques Usng an Emulaton Platform: Investgaton and Implementaton of OFDM Synchronzaton Algorthms, M.Sc. Thess, IRCTR S--, Delft Unversty of Technology, Jan.. [3] I. Gultekn, DSP Software Implementaton for a Broadband Ar-nterface Emulaton Platform: Onderzoek naar de serële nterace tussen de PC an de DSP board en het maken van een GUI voor de DSP applcates, Graduaton Thess, Haagse Hogeschool, June (n Dutch). [3] K. S. Ldshem, A survey of peak-to-average power reducton methods for the OFDM transmsson schemes, Research Report KWATT, IRCTR S-4-, Delft Unversty of Technology, Sept.. [33] A. Snjders, Emulator: De testopstellng voor OFDM, Graduaton Thess, IRCTR S-3-, Technsche Hogeschool Rjswjk, Nov. (n Dutch). [34] D. Murarg, Channel Estmaton Enhancement n OFDM Systems for Wreless Multmeda Communcatons, M.Sc. Thess, IRCTR S-8-98, Delft Unversty of Technology and Techncal Unversty of Lsbon, July. [35] G. Landman, Frequency Doman Study of the Wde-Band Moble Propagaton Channel, M.Sc. Thess, Delft Unversty of Technology (IRCTR), Aug.. [36] W. C. Jakes Jr., Mcrowave Moble Communcatons. New York: Wley-Interscence, 974. [37] J. D. Parsons, The moble rado propagaton channel. New York: Wley-Interscence,. [38] S. Nanda and K. M. Rege, Frame error rates for convolutonal codes on fadng channels and the concept of effectve E b /N, IEEE Trans. Veh. Technol., vol. 47, no. 4, pp. 45 5, Nov. 998.

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29 Part I: Channel Characterzaton 5

30

31 Chapter Modelng of the Frequency- Selectve Rado Channel. Introducton The channel model s the bread and butter for the telecommuncatons engneer ths s how Ramjee Prasad, former Professor for Moble Communcatons at Delft Unversty of Technology, used to emphasze n hs lectures the mportance of the channel model for desgnng rado nterfaces for wreless communcatons systems. And ths was not just a phrase to keep the students attenton. The channel models really are the foundaton, moble communcatons systems are bult on. As the man topc of ths thess s the desgn of OFDM ar-nterfaces, the goal of ths chapter s the descrpton and dscusson of an approprate channel model for such systems. Ths model must allow for analytcal treatment of OFDM related problems and for effcent computer smulaton schemes, to address two general requrements. Accordng to the system s key specfcatons, t should ft to physcal rado channels n the mm-wave frequency band, for ndoor (nroom) and short-range outdoor envronments. Rado propagaton n a moble rado channel s determned manly by ts multpath nature. Multple reflectons, and sometmes a lne-of-sght (LOS) component of the transmtted sgnal arrve at the recever va dfferent propagaton paths and therefore wth dfferent ampltudes and delay tmes. As an effect of ths, the narrowbandreceved power fluctuates dramatcally when observed as a functon of locaton (or tme) and frequency. In the early days of moble systems, the communcatons 7

32 8 Chapter Modelng of the Frequency-Selectve Rado Channel engneer was manly nterested n the tme-varablty of narrowband channels, whch were thus studed extensvely (see e.g. []). By that tme, transmsson bandwdths were small, thus flat-fadng was a reasonable assumpton. As the systems evolved, demand for hgher transmsson rates has been ncreasng, makng the channel s tme dsperson (whch s equvalent to ts frequency-selectvty) a major ssue. In OFDM, the channel s varablty n the frequency-doman (FD) has a smlar role as the tme-varance n a (flat-fadng) narrowband system. Usually, the channel can be assumed to be statc durng the transmsson of at least one OFDM symbols. In ndoor wreless local area networks (WLAN), the channel s even consdered quas statonary durng up to a whole data packet or frame perod. The followng secton revews the propagaton mechansms that have to be characterzed by the channel model. The man propertes of nterest for the OFDM system desgn are emphaszed and mportant channel parameters are defned. The so-called frequency-doman channel model (FD-model) s proposed and analyzed n Secton.3. The model descrbes the frequency-selectve fadng by the delay power spectrum (DPS) of the channel, the Fourer transform of the spaced-frequency correlaton functon []. Ths approach s dual to defnng the tme-varablty by the Doppler power spectrum [3], whch s often referred to as Jakes fadng model [], [4]. Expressons are gven, relatng the DPS (beng specfed by just two to four parameters) to the most mportant physcal channel parameters. Raylegh and Rcean fadng channels are consdered. A drect mplementaton of the FD-channel model n a computer smulaton scheme s proposed n Secton.4. The outputs of ths smulator are (complex-valued) frequency-selectve channel transfer functons. The dfferences are emphaszed between ths approach and (conventonal) tme-doman smulators, whch generate channel mpulse responses. Secton.5 summarzes the basc results of a number of measurement campagns. Some of them were performed at Delft Unversty of Technology, others were found n the lterature. We elaborate on the sutablty of the proposed channel model for descrbng the rado channels nvestgated. Conclusons and recommendatons are gven n Secton.6.. Characterzaton of the Moble Rado Channel Ths secton starts wth a qualtatve descrpton of the man propagaton mechansms resultng from multpath wave nterference. Secton.. revews mathematcal defntons that are useful for the characterzaton of wde-band, frequency-selectve, moble rado channels. Important channel parameters are ntroduced and ther physcal nterpretaton s developed.

33 . Characterzaton of the Moble Rado Channel 9.. Components of a Multpath Channel Model For the mathematcal descrpton of a multpath rado channel, t s convenent to dstngush three mechansms; namely: path loss, shadowng, and multpath nterference. The former two are descrbed by large-scale channel models, whch essentally provde nformaton about the average receved power at a certan locaton. Path loss strctly descrbes the dependency of ths average power on the dstance between transmtter and recever, whle shadowng accounts for the fluctuatons observed at a fxed dstance, due to geometrc features of the propagaton envronment. These fluctuatons occur for nstance because of the blockng of relevant propagaton paths, e.g., the lne-of-sght component, as the moble moves around. Hghly sophstcated large-scale models that typcally employ geographcal nformaton system (GIS) databases n order to account for topographcal features are ncorporated n the cell-plannng tools used by moble system operators. In ndoor envronments, ray-tracng models are often used to predct the receved sgnal strength at a gven locaton. Such models are not relevant, however, for the desgn of new transmsson technques. For ths applcaton, the descrpton of the effects of multpath nterference s requred, snce the ar-nterface has to cope wth them. These effects are often referred to as small-scale fadng. Small-scale models are vald wthn (small) local areas, where the sgnal fluctuatons due to shadowng and path loss can be neglected. The dmenson of such a local area s therefore lmted to approxmately 5 4λ, where λ s the wavelength of the rado frequency (RF) carrer. (Due to the small wavelengths below one centmeter, ths range may be even larger n the mm-wave band.) The channel model nvestgated n ths chapter s lmted to the descrpton of smallscale effects. A set of average parameters specfes the channel s behavor wthn a local area. These parameters are the normalzed receved power, P, the Rcean K- factor, K, and the RMS delay spread (RDS), τ rms. Note, however, that each realzaton obtaned from the model has varyng nstantaneous parameters denoted { Pˆ, ˆ K, τ ˆ rms }, snce the model s a stochastc one. (To be specfc, t s a Gaussan wde-sense statonary uncorrelated scatterng (WSSUS) model, as shown n Secton.3, and [5], [6]). The amount of varaton of these parameters from the local-area parameters depends n The (dmensonless) normalzed receved power s defned as the rato of the receved power P rx and the transmtted power P tx. Equvalently, the absolute receved power P rx [W] could be used for channel descrpton.

34 Chapter Modelng of the Frequency-Selectve Rado Channel partcular on the observed bandwdth. When the bandwdth s much greater than the coherence bandwdth, then the multpath s completely resolved and the channel parameters vary lttle, snce the ndvdual multpath ampltudes do not change rapdly wthn a local area. However, f the system s narrowband, then multpath s not resolved, and the path ampltudes at each resolvable (delay) tme-bn (beng spaced by the recprocal of the bandwdth) vary due to multpath nterference. Ths leads to the fluctuaton of the nstantaneous channel parameters wthn the local area (cf. [6], [7]). The mathematcal defntons of the channel parameters are gven n the followng secton. Thereby, the behavor ndcated above wll be revsted based on the equatons presented. The selecton of these parameters s an attempt to specfy the man characterstcs of the frequency-selectve channel wth a mnmum number of varables. A very strong ndcaton for the sgnfcance and sutablty of the parameters chosen wll follow from the analyss of the FD-level crossng rate n Chapter 3... Defntons... Channel Impulse Response It s most llustratve to start wth the defnton of the channel mpulse response (IR), whch s the straghtforward formulaton of the sum of dscrete multpath components mpngng at the recever. In complex lowpass equvalent notaton, the IR s wrtten as jθ h ( τ ) β e δ ( τ τ ), (-) where {β }, {θ }, and {τ } are the propagaton paths ampltudes, phases, and delays, respectvely, and τ s the delay-tme varable. Normally, the delay of the frst (shortest) ray s defned as τ, because the absolute delay-tmes are not mportant, only the tme-dsperson s. Therefore τ s called the excess delay-tme, and t follows that τ > for >,.e., the channel mpulse response s causal. Note that n a real envronment, the parameters {β }, {θ }, and {τ } are tme-varant. For the sake of smplcty, ths tme dependency was omtted n (-). Wthn a local area,.e., for dsplacements n the order of a few wavelengths λ, the ray ampltudes {β } and the delays {τ } can be consdered relatvely statc correspondng to the assumpton of a neglgble change of the shadowng. The ray phases {θ }, however, change unpredctably wthn the nterval [, π), because they are related to the absolute path-lengths. It s an open ssue whether the assumpton of dscrete paths s vable. Generally, each reflecton wll show some tme-dsperson, and therefore a frequency-dependent magntude. However, for a gven observaton bandwdth, such physcal paths can normally be approxmated by (a number of) dscrete Drac-mpulses.

35 . Characterzaton of the Moble Rado Channel... Channel Parameters All channel parameters ntroduced here are defned from the (statc) power delay profle (PDP), whch s a functon derved from the channel IR (-). The PDP specfes the ray-power versus delay-tme structure of the IR, beng p ( τ ) β δ ( τ τ ). (-) As the ray phases are dropped n ths equaton, the channel parameters must be (largely) constant wthn the local area, provded that the propagaton paths are fully resolvable. The frst parameter s the (normalzed) receved power, beng the sum of the ray powers P β. (-3) The Rcean K-factor s the rato of the domnant path s power to the power n the scattered paths, defned as K β, where β, max max{ β}. (-4) P,max β,max It wll be seen that the K-factor specfes the depth of the fades wthn a local area, as the Rcean probablty densty functon (PDF) wll be used to characterze the ampltude dstrbuton of the channel response. Larger K-factors relate to shallower fades. Note that n the presence of a lne-of-sght, the frst ray s the domnant one, mplyng that β,max β at τ. Fnally, the RMS delay spread s ntroduced, whch s the second central moment of the (power normalzed) PDP, wrtten as τ rms τ τ, where m τ τ β, m {, }. (-5) τ rms s consdered to be the most mportant sngle parameter for specfyng the tmeextent of the dspersve channel. It also characterzes the frequency-selectvty, snce τ rms s related to the average number of fades per bandwdth, and to the average bandwdth of the fades (see Secton 3.). m P Smulders states, based on channel measurements over bandwdths of GHz n the 6 GHz band, that mm-waves have suffcently small wavelengths to be modeled as rays followng dscrete paths (see [8], p. 43 f.).

36 Chapter Modelng of the Frequency-Selectve Rado Channel...3 Channel Transfer Functon An equvalent descrpton of the tme-dspersve channel s obtaned by applyng the Fourer transform to the IR, yeldng the channel transfer functon (TF). Ths step wll demonstrate that a tme-dspersve channel s also frequency-selectve. Frstly, the tme varablty s re-ntroduced to the IR (-), leadng to the tme-varant TF, H ( f, t) jθ ( t ) h( τ, t) β ( t) e δ ( τ τ ( t)), (-6) h( [ π fτ ( t ) + θ ( t )] j fτ j τ, t) e dτ β ( t) e. (-7) The magntude of ths functon shows rapd varatons wth respect to both, the tmeand frequency varables. H(f,t) can be seen as the vector sum of the ray ampltudes {β (t)}, wth vector-angles [ π fτ ( t) + θ ( t)]. As the ray phases {θ (t)} change rapdly for small dsplacements, the vector sum changes, causng the locaton and tmevarablty. The frequency-dependency s due to the dfferent delay tmes {τ (t)}, whch, at dfferent frequences, also lead to drastc changes n the vector sum. The phases at two specfc frequences dffer more wth larger excess delay tmes {τ (t)}. Ths suggests a dependency of the tme-extent of the mpulse response (whch s characterzed by the RMS delay spread), and the number of fades per unt of bandwdth. In Chapter 3, Secton 3., ths relaton s extensvely studed....4 Magntude Dstrbuton Due to the quas-random phases of the terms of (-7), H(f,t) can be seen as the sum of a (large) number of random varables (RV) wth ampltudes {β (t)}, and unformly dstrbuted phases over [, π). Assumng that a consderable number of rays has smlar magntudes (except for possbly one domnant ray), the central lmt theorem leads to the concluson that H(f,t) has a complex Gaussan dstrbuton. Wthout the domnant ray t s zero-mean, otherwse t s non-zero mean. The magntude R H(f,t) of the complex Gaussan process s descrbed by the Rcean PDF ( r + ρ ) r ψ rρ p ( ) R r e I, (-8) ψ ψ where ψ s the common varance of the real and magnary components of the complex Gaussan process, ρ s the ampltude of the mean of H(f,t), ρ E{H(f,t)}, and I ( ) s the zero-th order modfed Bessel functon of the frst knd. For the zeromean case (ρ ), the Rcean PDF reduces to the Raylegh PDF 3. 3 If the domnant component τ,max occurs at a delay tme dfferent to τ (or at a non-zero

37 . Characterzaton of the Moble Rado Channel 3 The parameters of (-8) are related to the channel parameters P and K as K ρ β,max P and ψ P β,max P. (-9) K + K + Note that ρ s the power of the domnant component, whle ψ s the power of the scattered components. If the central lmt theorem (plus domnant path) s not perfectly vald, then the parameters gven n eq. (-9) may stll express a best ft of the Rcean dstrbuton to the gven channel. However, n ths case, the magntude of the domnant path β,max may be rather seen as an equvalent domnant path gan, whch does not strctly relate to one physcal propagaton path....5 Band-Lmtng the Transfer Functon and Samplng the Impulse Response For computer smulaton schemes, a sampled verson of the channel IR s requred, whch mples the band-lmtaton of the respectve TF. Let us frst ntroduce the latter. BW A samplng nterval T s n the tme-doman lmts the bandwdth to ± ± T. s Multplcaton of the TF (-7) by a rectangular wndow W BW (f) apples such bandlmtaton, BW f f H BW ( f, t) H ( f, t) WBW ( f ), where W BW ( f ). (-) BW f f > Ths step s equvalent to a convoluton of the IR by a snc-functon, jθ t t ( ) τ τ ( ) hbw ( τ, t) h( τ, t) snc( τ / Ts ) β ( t) e snc, (-) T sn πx f x where snc x πx. Clearly, rays stop beng resolvable, f the delay-tme f x separaton between adjacent rays s n the range of T s or below. Samplng n the tme-doman can be seen as a multplcaton by a tran of Dracmpulses wth perod T s. It therefore has the effect of convolutng the frequencydoman representaton by a pulse tran wth perod /T s BW []. The pror bandlmtaton keeps the thereby duplcated spectra from overlappng (.e., alasng s avoded), whch essentally means that no nformaton s lost through the samplng. The sampled IR becomes jθ t n Ts t ( ) τ τ ( ) hbw, n ( t) β ( t) e snc, (-) τ T s s Doppler frequency), then the mean wll become zero as well, as a (determnstc) complex harmonc component results. However, the ampltude dstrbuton s stll approprately descrbed by the Rcean dstrbuton. (Ths case s descrbed by Rce as the Dstrbuton of Nose plus Sne Wave [9], []).

38 4 Chapter Modelng of the Frequency-Selectve Rado Channel wth n τ {,,,,, } beng the dscrete delay tme ndex. From ths equaton, one can observe that the IR has contrbutons of all propagaton paths at any tme-bn n τ. (Except f a ray has an excess delay of τ kt s, where k s an nteger to be exact). Even at negatve delay tmes, some leakage of the (causal) IR s evdent. From (-) t also becomes clear that, for lmted tme-resoluton or bandwdth, the sampled IR (at any tme-bn n τ ) s rapdly tme-varant, due to the tme-dependency of the supermposed rays phases {θ (t)}. Calculatng channel parameters from ths sampled IR results n nstantaneous parameters { Pˆ, ˆ K, τ ˆ rms }, whch are tme-varant, even wthn a local area, as dscussed n Secton... The varablty of these parameters s shown n Secton..3, based on smulaton results. The applcaton of the central lmt theorem agan leads to the concluson that complex Gaussan processes approprately model the coeffcents { hbw, n τ ( t)} (cf. [6], []). Ther varances follow the so-called average power delay profle, whch usually decays wth ncreased delay-tme. In varous channel models, the IR s descrbed n ths way (see e.g., [4] [6]). The complex Gaussan dstrbuton also apples to the ray gans of IRs derved from the FD-channel model, whch s proposed n Secton.3. The above analyss s an attempt to descrbe theoretcally the behavor of the tmevarant, frequency-selectve rado channel. It focuses on the aspects that are mportant for a deeper understandng of the FD-channel model. Therefore, partcularly the frequency-selectvty of a band-lmted, quas-statc channel has been dscussed...3 Varaton of Channel Parameters Due to Bandwdth Lmtaton Smulaton results are presented n ths secton, of the varablty of nstantaneous channel parameters wthn a local area. Channel realzatons were generated wth a tme-doman (TD) smulaton scheme, whch produces channel mpulse responses. The smulaton model assumes a lne-ofsght ray at τ, a Posson process of ray-arrvals (of approx. 6 rays), an exponentally decayng average power delay profle, and complex Gaussan ray ampltudes (compare [6] for one cluster; see Secton.5.3). In a second step, the mpulse responses were normalzed to get the requred K-factor K, τ rms and P [5], allowng for smple evaluaton of the estmaton error. Applyng the Fourer transform to the generated IRs, (complex-valued, dscrete-frequency) TFs were obtaned, wth arbtrary bandwdth. The varablty of τˆ rms and ˆP wthn a local area s depcted n Fgure -a and Fgure -b, respectvely. For analyzng τˆ rms, the smulated TFs were transformed back to the delay tme-doman usng the nverse dscrete Fourer transform (DFT) wthout wndowng. Consecutvely, τˆ rms was determned from the postve-τ part of the obtaned, sampled channel IR, usng eq. (-5). ˆP s smply the average power of the band-

39 . Characterzaton of the Moble Rado Channel 5 relatve estmaton error of τ rms [%] RMS delay spread τ rms estmated from the mpulse response; OS standard devaton mean error K K K 4 K relatve estmaton error of P [%] observaton bandwdth n /τ rms (a) normalzed receved power P ; OS K K K 4 K 5 observaton bandwdth n /τ rms (b) Fgure -: (a): Bas and standard devaton of the nstantaneous RMS delay spread τˆ rms wthn a local area due to band-lmtaton. (The bas s caused by leakage effects). (b): Standard devaton of the nstantaneous normalzed receved power ˆP wthn a local area. lmted TFs.

40 6 Chapter Modelng of the Frequency-Selectve Rado Channel The standard devatons of these parameters decrease wth ncreasng bandwdth, because ndvdual propagaton paths become gradually more resolvable. The estmaton bas n τˆ rms (see Fgure -a) s due to leakage effects. Reduced varance and bas for hgher K-factor are ntutvely explaned by the fact that the (determnstc) domnant path largely determnes Rcean channels. Note that K has most nfluence on the nstantaneous values of the average power P. Ths behavor can be antcpated, snce K drectly relates to the depth of the fades. I.e., a channel wth a hgh K-factor (whch has shallow fades) shows less varaton n ths parameter, than for nstance a Raylegh fadng channel (whch has qute deep fades)..3 Frequency-Doman Channel Modelng The channel model proposed n ths secton descrbes the correlaton propertes of the channel transfer functon n the frequency-doman. Startng from the defnton of the channel correlaton functons (and power spectra), ths so-called frequency-doman channel model s derved. Mathematcal expressons are gven, relatng the model s parameters to (physcal) channel parameters..3. The WSSUS Channel Model The channel correlaton functons and power spectra are a set of functons defnng the small-scale characterstcs of multpath fadng channels n more detal than the channel parameters gven above. Introducng some assumptons wll lead to the channel model used throughout ths work. In partcular, we concentrate n ths work on the correlaton propertes of the tme-varant transfer functon H(f,t) (see (-7)), because ths functon determnes the channel s mpact on an OFDM system modeled as a set of parallel Gaussan channels (see Secton 4., [7]). Consderng the moble rado channel as a lnear tme-varant system, t s seen that the TF H(f,t) s only one possble channel representaton (from the famly of Bello s system functons [5], [6]). Another one s, for nstance, the tme-varant mpulse response gven by (-6). Let us frst defne the channel correlaton functons assumng that those functons are wde-sense statonary. Ths means that the autocorrelaton functon * { H ( f, t ) H ( f, )} φ H ( f, f, t, t) E t (-3) depends only on the frequency-separaton f f f and on the tme-separaton t t t, but not on the absolute observaton frequences {f, f } and tmes {t, t }. In other words, the tme-varant transfer functon H(f,t) s wde-sense statonary (WSS) wth respect to both varables f and t. The channel s thus characterzed for all tmes and all frequences by the so-called spaced-frequency, spaced-tme correlaton functon

41 .3 Frequency-Doman Channel Modelng 7 * { H ( f, t) H ( f + f, t + t) } φ ( f, t) E. (-4) H It can be shown that ths assumpton s equvalent to the ntroducton of the wde-sense statonary and uncorrelated scatterng (WSSUS) channel (see e.g., [5], [6], []). In the WSSUS channel, the WSS-property apples to the tme varablty of the IR h(τ,t). The uncorrelated scatterng (US) property s based on the assumpton that the attenuaton and phase of a propagaton path at delay tme τ s uncorrelated to the attenuaton and phase at delay tme τ k, for k. In order to apply the concept of the WSSUS channel to real rado channels, the quas- WSSUS channel (QWSSUS) was ntroduced by Bello [5]. A QWSSUS channel has the propertes of a WSSUS channel wthn a local area, and for a lmted bandwdth and tme. Furthermore, t should be noted that for Gaussan processes, the WSS property mples statonarty n the strct sense. If the dstrbuton of the TF H(f,t) s complex Gaussan, wth zero- or non-zero mean, then the ampltude dstrbuton s Raylegh or Rcean, respectvely. As ths agrees to the channel propertes derved n Secton.., and as Gaussan processes generally smplfy any stochastc mathematcal analyss, the complex Gaussan case wll be assumed. In Fgure -, an overvew s gven of the most commonly used correlaton functons and power spectra defnng the stochastc propertes of the tme-varant channel IR, and TF. These system functons are found n the center of the fgure, surrounded by ther second order moments, whch are nterrelated by Fourer transforms. As mentoned above, our focus les on the spaced-frequency, spaced-tme correlaton functon depcted just above the center of ths fgure..3.. Specal Cases Most of the analyss presented n ths thess concentrates on the case of the tmenvarant frequency-selectve channel. The channel s then descrbed by the TF H(f), whch s a WSS complex Gaussan stochastc process n f, accordng to the above assumptons. The second order statstcal functons characterzng H(f) are the spacedfrequency correlaton functon φ H ( f ) φ H ( f,) and ts Fourer transform (FT), the delay power spectrum (DPS) φ h (τ) (see Fgure -). A mathematcal descrpton of the DPS wll be the bass of the so-called frequency-doman (FD) channel model. More famlar s the dual approach of modelng the tme varablty of a narrowband channel as a WSS complex Gaussan stochastc process H(t). An example for ths method s wdely known n the lterature as Jakes fadng model []. Compared to the FD model, the frequency varable s exchanged wth the tme varable, and the second order statstcs are the spaced-tme correlaton functon φ H ( t) φ H (, t) and the Doppler power spectrum S H (ν) for Doppler frequency ν, whch are a Fourer par as well (see Fgure -).

42 8 Chapter Modelng of the Frequency-Selectve Rado Channel φ h (τ) multpath ntensty profle delay power spectrum τ max max. delay spread FT (τ f) φ H ( f) spaced-frequency correlaton functon ( f) c coherence bandwdth t t wde-band characterzaton (tme-nvarant channel) characterzaton of tme varatons (narrow-band) φ h (τ; t) delay cross-power spectral densty FT (τ f) φ H ( f; t) spaced-frequency, spacedtme correlaton functon f φ H ( t) spaced-tme correlaton functon ( t) c coherence tme ACF (WSSUS) ACF (WSSWSS) h(τ;t) equvalent lowpass tme-varant FT (τ f) H(f;t) tme-varant transfer functon mpulse response FT ( t ν) FT ( t ν) FT ( t ν) S(τ;ν) Scatterng functon FT (τ f) S H ( f;ν) Doppler cross-power spectral densty f S H (ν) Doppler power spectrum f m max. Doppler freq.; Doppler spread Fgure -: Overvew of the two tme-varant system functons descrbed the channel mpulse response and the channel transfer functon and a set of correlaton functons (second order moments) descrbng ther stochastc propertes..3.. Addtonal Channel Parameters Fgure - also ntroduces some addtonal channel parameters, whch are derved from the correlaton functons and power spectra. Coherence-tme and -bandwdth ndcate the ranges (n tme and frequency) over whch the TF H(f,t) shows sgnfcant correlaton. They are defned as the tme- or frequency-separatons t and f, where the spaced-tme or -frequency correlaton functons, respectvely, drop below.9. (Sometmes.5 s used for ths threshold.) Related to the power spectra, the maxmum delay spread and the Doppler spread are defned, correspondng to the maxmum delay-tme and frequency-components n these spectra. Often, mathematcal relatons are gven n-between these parameters,.e., between the coherence-bandwdth and the (recprocal of the) maxmum delay spread or the RMS delay spread, and between the coherence-tme and the (recprocal of the) Doppler spread. However, these relatons loose sgnfcance n the Rcean case, snce the domnant component (leadng to the non-zero mean of the Gaussan dstrbuton)

43 .3 Frequency-Doman Channel Modelng 9 causes a constant addtve term n the channel correlaton functons [5]. Therefore, these relatonshps should be used wth care..3. Channel Descrpton The delay power spectrum (DPS) characterzes the frequency-selectvty n the FDchannel model. In agreement wth measurements reported n [4], the shape of the DPS s defned as shown n Fgure -3. It s specfed by four parameters: ρ the normalzed power of the drect ray; Π [/s] the normalzed power densty of the constant-level part; τ [s] the duraton of the constant level part; and γ [/s] the decay exponent of the exponentally decayng part. Mathematcally, the DPS can be wrtten as τ < ρ δ ( τ ) τ φh ( τ ). (-5) Π < τ τ γ ( τ τ) Πe τ > τ In many cases, the number of (free) parameters can be further decreased. The exponentally decayng DPS s a good approxmaton for most practcal channels, whch s mplemented by lettng τ. The exstence of a lne-of-sght (LOS) ray at τ mples that the channel TF has non-zero mean, thus the fadng envelope dstrbuton s Rcean. Raylegh fadng channels have ρ. For the analyss t s approprate to defne u τ γ, beng a sngle parameter to account for the shape of the DPS. u can take values u [, ], where the two extreme cases u and u descrbe an exponentally decayng and a rectangular DPS, respectvely. Note that n the latter case (rectangular DPS), the maxmum excess delay wll be much smaller than for u, thus u can be used to adjust ths parameter (see below). Relatons between the model parameters defned above and the channel parameters are presented n Secton.3.3. φ h (τ) [db] ρ Π γ τ Excess delay τ [s] Fgure -3: Model of the delay power spectrum (DPS).

44 3 Chapter Modelng of the Frequency-Selectve Rado Channel.3.3 Relaton to (Physcal) Channel Parameters For the applcaton of the FD-channel model, t s most mportant to relate ts parameters {ρ,π,γ,τ } to the channel parameters defned n Secton..: the normalzed receved power P, the Rcean K-factor K, and the RMS delay spread τ rms. The channel parameters derved from the channel model are the local-area means, as dscussed n Secton.. Fnte bandwdth realzatons or measurements wthn a local area have nstantaneous channel parameters Pˆ, Kˆ, τ ˆ } spread around those means. { rms Table - gves an overvew of expressons relatng the model parameters {ρ,π,γ,τ } to the channel parameters {P,K,τ rms } and vce versa. The dervaton of these equatons s outlned below. For notatonal convenence we ntroduce u u +, u u + u +, 3 and u 3 u 3 + u + u +, wth u τ γ. An mportant specal case s gven by u, the exponentally decayng DPS, whch s an approprate descrpton for many practcal channels. Table - also lsts the smplfed expressons for ths case Dervaton of Channel Parameters From the contnuous DPS φ h (τ) defned by (-5), the analytcal expressons gven n Table -: Relaton between model and channel parameters. (The symbols are defned n the text). model Æ channel u τ γ [, ] u Π γ P ρ + u ρ γ K Πu τ rms γ u K + u 3 ( K + ) u u P Π ρ + γ ρ γ K Π channel Æ model u τ γ (must be known) u ρ P γ τ K K + u ) 3 rms K + u ( K + P γ K + u u u τ ρ rms γ γ P τ rms K + K + K K + Π Π γ P K + K + K +

45 .3 Frequency-Doman Channel Modelng 3 Table - can be derved for the expected values of normalzed receved power P, Rcean K-factor K, and RMS delay spread τ rms. P relates to the DPS as P φh ( τ ) dτ ρ + Π τ +. (-6) γ The K-factor s used to characterze the ampltude dstrbuton of Rcean channels, relatng the power of the drect path to the power of the scattered paths. ρ ρ K (-7) P ρ Π ( τ + γ ) The RMS delay spread τ rms s the sngle most mportant parameter characterzng the frequency-selectvty. It can be nterpreted as the centralzed second moment of the normalzed DPS where () τ τ rms τ, (-8) τ τ τ τ φ ( τ ) τ τ h dτ Π + + P γ γ, and (-9) 3 φ ( τ ) τ τ τ h dτ Π P 3 γ γ γ. (-).3.3. Spaced-Frequency Correlaton Functon The spaced-frequency correlaton functon s used repeatedly throughout ths thess to mplement the channel-behavor n the mathematcal analyss of the rado channel and n the analyss of OFDM system aspects. It s derved from the DPS (-5) va the Fourer transform: * φ ( f ) E{ H ( f ) H ( f + f )} F H ρ + Π τ snc( τ f ) e { φ ( τ) } h + Π e γ + jπ f jπτ f j πτ f (-) For τ,.e., for the specal case of an exponentally decayng DPS, the spacedfrequency correlaton functon can be wrtten as where, K ( K + ) K. + φ P H ( f ) K + K + + jπ fτ rmsk, (-)

46 3 Chapter Modelng of the Frequency-Selectve Rado Channel Maxmum Excess Delay The shape factor u ntroduces another degree of freedom n the channel model, whch allows the varaton of the maxmum excess delay τ max by a certan factor, for a gven RMS delay spread τ rms. Strctly speakng, the maxmum delay spread s nfnte due to the exponentally decayng part of the DPS, whch never becomes zero. In practce, however, multpath components can be neglected that are attenuated very sgnfcantly. We therefore defne the maxmum excess delay as the delay tme, where the exponentally decayng part has decreased by about 43 db. Such attenuaton s reached, f the duraton of the exponentally decayng part s exactly τ exp /γ, leadng to the maxmum delay spread τ max τ + τ exp τ + / γ. Expressed n terms of channel parameters ths s whch smplfes for u (.e., τ ) to u ( K + ) τ max τ rms ( u + ), (-3) uu3 ( K + ) u K + τ max τ rms τ rms K. (-4) K + It s seen that τ max and τ rms are related by a factor, whch s a functon of K and u. Fgure -4 llustrates ths factor. Accordng to ths defnton, τ max s exactly ten tmes larger than τ rms at K, and u. Larger K-factors generally ncrease ths factor, normalzed maxmum delay spread τ max /τ rms relaton between the maxmum delay spread and the RMS delay spread u (exponental DPS) u u u (rectangular DPS) Rcean K factor Fgure -4: Factor between the maxmum delay spread τ max and the RMS delay spread τ rms, as a functon of the Rcean factor K and wth the shape factor u as a parameter.

47 .4 Frequency-Doman Channel Smulaton 33 larger parameters u decrease t. For nstance, τ max s only about three tmes τ rms for the rectangular DPS, at low K-factors. As the maxmum delay spread τ max defnes the maxmum frequency component of the DPS, t s ths parameter whch defnes the Nyqust frequency when a sampled verson of the channel transfer functon s needed n measurements or computer smulatons. That s, the samplng nterval n the frequency-doman must be smaller than /(τ max )..4 Frequency-Doman Channel Smulaton The dscusson of smulaton schemes n ths secton s restrcted to the case of statc (tme-nvarant) frequency-selectve channels. Such smulatons are for nstance approprate for the study of OFDM systems, wth a system model that reduces the channel ncludng the IFFT at the OFDM transmtter and the FFT at the recever to a set of parallel Gaussan (sub-) channels (see Chapter 4, [7]). These sub-channels have complex attenuaton factors gven by the channel s TF H(f) at the frequency nstants of the OFDM sub-carrers f nf, where F [Hz] s the samplng nterval n the frequencydoman and n {,,, N }. The smulaton scheme presented n ths secton drectly generates H(f) for well defned channel parameters. In some cases, for nstance for evaluatng channel estmaton schemes, the tmevarablty of the TF s also of great mportance. The extenson of the statc smulaton scheme to a tme-varant one s dscussed. A dscusson of the channel-varablty n an OFDM-based wreless LAN system s gven n Secton 5... The nduced performance degradaton s studed n Secton Model Descrpton The smulaton system for tme-nvarant channels s shown n Fgure -5. Real-valued whte (or wde-band) Gaussan random processes W(f) n the frequency-doman are generated by a nose source. The approprate spaced-frequency correlaton s obtaned by FD-flterng of W(f) wth a (low-pass) flter g(f). The output of ths flter s the realvalued, colored nose process r H'(f) W(f) g(f), where denotes convoluton. The nverse FT of r H'(f) (n delay-tme-doman representaton) s complex-valued and hermtan,.e., symmetrc wth respect to the τ axs. It s not causal, n contrast to the mpulse response (IR) of a real channel. The requred causalty n the tme-doman s obtaned by applyng the Hlbert transform to r H'(f) and addng the result H'(f) as H'(f) r H'(f) j H'(f). Dong ths, the negatve part of the IR s canceled. The ampltude of the TF H'(f) s Raylegh dstrbuted snce H'(f) s a complex Gaussan nose process. A Rcean fadng channel may be smulated by addng a jθ ρ complex constant ρ e to H'(f), representng the LOS path at τ.

48 34 Chapter Modelng of the Frequency-Selectve Rado Channel (real-valued) Nose source W(f) (real) Nose shapng flter G(τ), g(f) rh'(f) (real) H'(f) (cmplx.) H(f) Hlbert transform H'(f) (real) PSDs: S W (τ) (flat) S r H'(τ) (colored) S H' (τ) (causal) φ h '(τ) j jθ ρ ρ e (cmplx.) φ h (τ) (+ LOS) τ τ τ τ Fgure -5: Frequency-doman smulaton of the frequency-selectve rado channel..4. Implementaton of the Smulaton Scheme To obtan a computer smulaton program producng TFs wth the desred DPS, two elements of the above smulaton scheme must be approprately desgned; the noseshapng flter g(f) and the varance of the nose source. The smulator produces a sampled verson of the TF, H(nF), where F [Hz] s the samplng nterval n the frequency-doman and n {,,,, N }. F must be selected accordng to the samplng theorem,.e., F < /(τ max ). The power spectral densty (PSD) of the output of the smulaton scheme (whch s n τ-doman) has to match the contnuous DPS defned by (-5). Ths s acheved by desgnng the flter g(nf) to have a TF G(τ) proportonal to the DPS (for τ > ;.e. skppng the LOS component). Any classc flter desgn method can be used n ths process []. By defnton we let G(τ) durng the constant-level part (or at τ + f there s no constant-level part), whch leads to the varance σ W Π (4F), as derved below..4.. Dervaton of the Varance of the Nose Source The nose source produces ndependent, real-valued nose samples wth varance The sequence W(nF) thus has a (perodc) spectrum wth constant PSD σ W σ W. S ( τ ) σ W F. (-5) Applyng these samples to the nose shapng flter wth ampltude TF W τ τ G ( τ ) γ ( τ τ), (-6) e τ > τ leads to the PSD of Re{H'(nF)} wrtten as

49 .4 Frequency-Doman Channel Smulaton 35 S ( τ ) σ W F G( τ ). (-7) r H ' The next step n the smulaton scheme s the addton of the Hlbert transformed (HT) sequence, whch ncreases the PSD for τ > by a factor of four. (The HT cancels the negatve-τ part of the Fourer spectrum, whle doublng the postve-τ part, resultng n four-fold power for τ > ). Ths yelds the PSD to be compared wth the model (the DPS) as whch yelds σ Π /(4F). W S ( τ ) 4σ F G( τ ) φ ( τ ), for τ, (-8) H ' W h >.4.. Extenson to a Tme-Varant Channel Smulator In order to extend ths statc smulaton scheme to a tme-varant one, the TF H(f,t) must have the requred Doppler spectrum when the tme-varatons are nvestgated at any gven frequency f f. Ths may be acheved by generatng a number of ndependent TFs H(f,t k T s ), k {,, 3, } and flterng them n tme-drecton at each frequency sample, accordng to a specfc Doppler spectrum. (Separablty of the jont tme-frequency correlaton functon φ H ( f, t) s thereby assumed 4 ). A set of N flters s requred for applyng tme-varablty to the transfer functons n ths way. It should be noted that ths smulaton scheme gets rather complex. It mght thus be preferable to use a conventonal fadng smulator one that generates a (tme-varant) IR and transform the IR to the frequency-doman, f requred. Usually, the IR s defned by much less than N coeffcents, therefore the complexty s reduced..4.3 FD-Smulaton Results In Fgure -6, a smulated TF s shown (Fgure -6a) and compared to a measured one (Fgure -6b). The two channels IRs are gven n Fgure -7a and b, both derved from the respectve TFs usng the nverse dscrete FT (IDFT) wthout wndowng. The measurement was performed wth a network analyzer, observng a bandwdth of GHz around a center frequency of.5 GHz 5. The channel parameters P 6. db, K.9 db, and τ rms 9. ns were extracted from the measured TF (Fgure -6b), and (wth τ ) used to generate the smulated TF (see Fgure -6a). (The method proposed n Secton 3.3 of ths thess was employed to estmate the channel parame- 4 Separablty of the two-dmensonal spaced-frequency, spaced-tme correlaton functon φ H ( f, t) means that t can be wrtten as a product φ H ( f, t) φ H ( f) φ H ( t). Ths assumpton s vald f τ max f m << [8], whch s gven for practcal propagaton channels (τ max denotes the maxmum excess delay; f m s the Doppler spread). 5 The author would lke to thank Dr. G. J. M. Janssen for provdng measurement results for the valdaton of the proposed methods [4]. The measurements were conducted at the TNO Physcs and Electroncs Laboratory n The Hague, The Netherlands, n the perod of August December 99.

50 36 Chapter Modelng of the Frequency-Selectve Rado Channel ampltude H(f) [db] frequency [MHz] phase arg(h(f)) [rad] frequency [MHz] (a) ampltude H(f) [db] phase arg(h(f)) [rad] frequency [MHz] frequency [MHz] (b) Fgure -6: (a): Smulated transfer functon (TF); (b): TF measured wth a network analyzer (corrected for lnear phase shft); ters.) Both TFs have a length of 8 samples. A 5-tap FIR flter was used for the nose shapng flter g(nf) n the smulaton scheme. The TF s obtaned from a stochastc smulaton model. Therefore we do not expect t to be dentcal to the measured TF. However, t s clearly seen that the characterstc of the fadng s well reproduced. Orgnally, a lnearly ncreasng phase shft was evdent n the measured TF correspondng to the propagaton delay of the shortest path. In the

51 .4 Frequency-Doman Channel Smulaton ampltude [db] excess delay tme [ns] (a) ampltude [db] excess delay tme [ns] (b) Fgure -7: (a) Impulse response (IR) derved by IDFT from the smulated TF shown n Fgure -6a. (b): Impulse responses derved from the measured TF (see Fgure -6b). llustraton ths was compensated, to have the frst component arrve at (excess) delay τ, n agreement wth the smulaton model. The probablty densty functon (PDF) and the cumulatve dstrbuton functon (CDF) of the smulated ampltude TF are shown n Fgure -8 and compared to the Raylegh dstrbuton. Because of the low K-factor (K.9 db), good agreement s evdent.

52 38 Chapter Modelng of the Frequency-Selectve Rado Channel PDF p( H(f) ) pdf of data Raylegh ampltude H(f) Fgure -8: Pr( H(f) < abscssa) 3 cdf of data Raylegh ampltude [db] PDF and CDF of the ampltude of the smulated transfer functon. Second order statstcal propertes estmated from smulated TFs are shown n Fgure -9. The power spectrum obtaned by averagng over perodograms of smulated TFs agrees well wth the used DPS model (upper plot). The lower plot shows (spacedfrequency) correlaton propertes and compares them to the theoretcal functon gven by (-). Coherence bandwdths are determned by solvng numercally for the fre- ampltude [db] 3 4 smulaton model excess delay tme [ns] correlaton coeff correlogram correl. fct. analytcal 5 5 frequency seperaton [MHz] Fgure -9: Delay power spectrum (DPS) and spaced-frequency correlaton functon for the FD-smulaton model. Upper plot: DPS and estmated power spectrum. Lower plot: Correlogram; estmated and analytcal correlaton functons; markers { : Coherence bandwdths.5 and.9.

53 .5 Applcaton to mm-wave Rado Channels 39 quency-separatons, where the correlaton functon s magntude drops to.9 (or.5 accordng to the defnton)..4.4 Dfferences to Tme-Doman Smulaton Schemes The equally spaced tap-gans of the sampled (and band-lmted) mpulse response are not uncorrelated, accordng to the analyss shown n Secton.. (see eq. (-)). That s, there exsts a certan autocorrelaton between dfferent delay-bns of the IR. Ths correlaton results from the band-lmtaton needed for the tme-quantzaton, whch mples a convoluton of the dscrete, non-sampled mpulse response wth a snc-functon. Another effect of ths convoluton s vsble n spectral components at negatve delay-values, due to leakage effects. The FD-smulaton scheme shows these propertes (see Fgure -7a and Fgure -9). Many tme-doman smulators, however, mplement the channel mpulse response by smply generatng ndependent, complex-valued path gans at the (sample-spaced) delay bns. Leakage effects,.e., components at negatve delays, are not consdered ether (see e.g. [6], Fgure.; [9]). (One sampled smulaton model, whch does consder those effects s descrbed n [8].) In partcular, these smplfcatons are used, when the channel models are appled for the desgn of dgtal rado nterfaces. Normally, the resultng dfferences are neglgble, but there are cases, where the mpact gets mportant. An example s dscrete Fourer transform (DFT) based channel estmaton schemes for OFDM. Such channel estmators determne frstly a coarse estmate of the channel TF, for nstance from a tranng sequence. In order to reduce the mean-square-error (MSE) of the estmate, the next step s a transform of the transfer functon to the delay tme doman, yeldng a nosy channel mpulse response. In ths form, lkely nose components at negatve or very large delay values can be dentfed and set to zero, followed by a back transformaton to the frequency-doman. The result s an estmate of the channel TF wth enhanced sgnal-to-nose rato (SNR) and hopefully reduced MSE. The smulaton of such a scheme suggests excellent performance, f a so-called samplespaced channel smulator s used, because then the channel IR s ndeed zero at the sample-bns set to zero. On a real channel, however, mportant nformaton s lost, as channel taps are set to zero whch correspond to leakage-components. Ths leads to rreducble error floors n terms of bt-error-rate and MSE [] []. In ths respect, the proposed FD-smulaton model has an nherent advantage over conventonal, sampled TD-models, because the correlaton among channel taps and leakage effects are consdered, n closer agreement to realty..5 Applcaton to mm-wave Rado Channels Ths secton has two man purposes. Frstly, the sutablty of the proposed FD-channel model and smulaton scheme s verfed, and secondly, parameters are found for the

54 4 Chapter Modelng of the Frequency-Selectve Rado Channel model. These goals are approached through a dscusson of measurement campagns reported n the lterature. In partcular, our focus les on mm-wave rado channels, whch s the consdered frequency-band for the communcatons system descrbed n Part II of ths thess. Wthn the mm-wave frequences, the 6 GHz band has receved most attenton n the lterature, for the followng man reasons: Large amounts of bandwdth are unallocated n ths band; bandwdths that are requred for communcatons systems at the ntended data rates of Mbt/s and above. Another advantage of 6 GHz s due to a physcal property of the propagaton channel at ths specfc frequency. Oxygen absorpton leads to attenuaton above db/km, between 57 and 63 GHz. Ths attenuaton (addtonal to the path loss) s beleved to enable shorter reuse dstances n cellular systems because t counteracts co-channel nterference. Over short dstances, the addtonal attenuaton can be neglected. It s a general property of mm-wave propagaton that the behavor of propagaton rays s well characterzed by geometrc optcs. That s, waves do not penetrate through walls or other obstacles, and wave reflecton s the man mechansm leadng to multpath. Scatterng, dffracton, and wave gudng are consdered far less mportant [3]. Ths secton starts wth a dscusson of measurement results (Secton.5.). In Secton.5., typcal channel parameter values are gven. The nfluence of features of the propagaton envronment on those parameters s dscussed. Channel models suggested n the lterature are treated separately, n Secton.5.3. Secton.5.4 deals wth the applcablty of the newly proposed FD-channel model to (mm-wave) rado channels the valdaton of the FD-model..5. Dscusson of Measurement Results A major actvty n the feld of mm-wave propagaton has been conducted n the framework of the European RACE (Research nto Advanced Communcatons systems n Europe) project 67, Moble Broadband Systems (MBS) [3], [4]. The measurement campagns descrbed nclude materal characterzaton, and ndoor and outdoor propagaton studes. Ray-tracng models have been developed for predctng propagaton parameters and for nvestgatng the mpact of envronment features, antenna characterstcs, etc.. An extensve lst of lterature on mm-wave propagaton s found n the Fnal report on propagaton aspects of the RACE-MBS project [3]. Partly related s the actvty carred out wthn the COST 3 (European Co-Operaton n the feld of Scentfc and Techncal research) program [8]. Ths study also covers ndoor and outdoor channels. A major contrbuton on ndoor propagaton orgnates from the research of Smulders, conducted at Endhoven Unversty of Technology [4]. Other work on ndoor channel s found n [], [4], [5], and [5] [35], outdoor studes are presented n [36] [38]. Note that most of the work has been done on ndoor

55 .5 Applcaton to mm-wave Rado Channels 4 channels and ther modelng, probably also because of the range lmtaton of mmwave propagaton. The man parameters of nterest for applyng the FD-model to mm-wave channels are the normalzed receved power (NRP), P, the Rcean K-factor, K, and the RMS delay spread, τ rms. For the ar nterface desgn, the latter two parameters, {K, τ rms } are generally suffcent. The NRP s requred for lnk budget consderatons (see Chapter 5). Whle most studes present results of τ rms and the NRP, the K-factor s unfortunately commonly not nvestgated. Generally, t s dffcult to compare measurements conducted by varous research groups, because of dfferences n the measurement equpment and method used, dfferent antenna characterstcs and confguratons, dfferent parameters measured and presented, and dfferent envronments nvestgated. We try to organze ths comparson and overvew by dscussng the parameters of nterest and elaboratng on the mpact of some of the above lsted factors. Only wdeband measurements are consdered, because of the mportance of characterzng the tme-dspersve and frequency-selectve nature of the channel. The modelng of these channel propertes s essental for the ar-nterface desgn, the ntended applcaton of the channel model under development..5.. Measurement Set-Ups and Technques Most ndoor measurement campagns use vector network analyzers to scan the channel transfer functon (phase and magntude) versus frequency (see e.g., [8], [] [5], [3], and [33] [35]). The condtons to use such equpment are short dstances, because a phase reference must be provded between the transmttng and the recevng sdes, and a (quas) statc channel, because of the tme t takes to acqure the frequency transfer functon. These condtons are feasble n ndoor scenaros. The man advantages of ths approach are the hgh tme-resoluton acheved by scannng over a large bandwdth, and the good SNR, because a narrowband (contnuous wave) sgnal s transmtted n whch the whole transmt power s concentrated. The delay-tme resoluton nvestgated s normally around ns, correspondng to a scannng bandwdth of GHz. In [38], a network analyzer was used for outdoor measurements. Correlaton type channel sounders were developed for the extensve measurement campagns performed n the RACE-MBS project [3], [4]. For outdoor channels, a wde-band test sgnal (chrp) was generated by rapdly sweepng a carrer over a bandwdth of up to MHz [36], [39]. A separate ndoor channel sounder s based on

56 4 Chapter Modelng of the Frequency-Selectve Rado Channel the transmsson of a pseudo random bnary sequence and a sldng-correlator on the recever s sde (see [4]). Smlar equpment was employed n [3] for ndoor measurements, and n [37] for outdoor measurements. Wthn ths Ph.D. research, a novel, non-coherent channel measurement technque was developed that can estmate the NRP, K-factor, and of τ rms from swept-frequency power measurements. No phase measurement s requred, whch smplfes the equpment needed. The measurement technque s descrbed n detal n Chapter 3 of ths thess. Measurement campagns conducted wth ths method at TU-Delft are descrbed n [5] [8]. Indoor and outdoor channels were studed, at 7 and 6 GHz..5. Dscusson of Channel Parameters The RMS delay spread (RDS) τ rms and the Rcean K-factor are the two most mportant parameters for specfyng the channel s frequency-selectve nature, n the context of ar-nterface desgn. It wll be seen from the study of the frequency-doman level crossng rate that the RDS determnes the number of fades per bandwdth, whle the K- factor specfes the depth of the fades (see Chapter 3). The normalzed receved power (NRP) just determnes the average sgnal-to-nose rato (SNR). Snce the SNR s usually consdered as a varable n any knd of system studes, absolute values of NRP are not of major mportance for the ar-nterface desgn..5.. RMS Delay Spread The followng man features of the propagaton envronment nfluence the RDS. Note that the mentoned propertes are applcable for ndoor channels only. Smlar features, however, wll also have an mpact on the RDS n outdoor scenaros. Room sze Generally, the RDS ncreases wth the room sze. Such behavor was for nstance reported n the work by Smulders [4], who measured typcal values of RDS between 5 and 45 ns n small rooms wth dmensons m 3, and values between 3 and 7 ns n larger rooms. These values are rather large, compared to the results from many other ndoor measurement campagns found n the lterature. Man reason for the large values s next to the large rooms nvestgated, the antenna desgn mplemented. The bconcal horn antennas, havng an omndrectonal radaton pattern n the azmuth plane, a 3- db beam-wdth of 9 n the elevaton plane, and a drectvty of 9 db, were desgned such that the NRP hardly depends on the poston wthn a room. Therefore, they radate qute a large fracton of the transmtted power towards the walls, leadng to strong frst reflectons and long delay spreads. Although the delay spreads are qute large, ths desgn mght be of advantage, because self-shadowng effects become less harmful. That s, sgnal loss due to the obstructon of the LOS-path by the user (see

57 .5 Applcaton to mm-wave Rado Channels 43 [4]) s assumed to be less sgnfcant for such antenna set-ups. Antenna drectvty Drectve antennas attenuate parts of the mpngng reflected waves. Therefore, the RDS usually decreases, as more drectve antennas (n the azmuth plane) are employed. Such behavor s clearly seen from measurements and ray-tracng smulatons performed by T. Manabe et al. [3]. In a room wth dmensons of m, they measured typcal RDS-values of 8, 4, 5, and ns, for, respectvely, an omndrectonal antenna (λ/-dpol), and antennas wth 3 db beam-wdths of ~6, ~, and ~5. A smlar study based on a ray-tracng tool s presented n the fnal report of the RACE-MBS project [3]. In the nvestgated room of approxmate dmensons 7 3 m 3, dfferent antenna confguratons were evaluated, leadng to RDS-values of 5 ns for the less drectonal antennas, and values (sgnfcantly) lower than 5 ns for the most drectonal ones. In order to nvestgate ths antcpated dependency between the RDS and the antenna characterstcs, Smulders has conducted some addtonal measurements usng a 5 db crcular-horn antenna (n stead of the 9 db omndrectonal bconcal horn antenna) on one sde of the measured lnk [4]. Hs results confrm the expected behavor f medan values of RDS are consdered (RDS decreases from ~4 ns to ~5 ns). However, the max. RDS values observed were even larger than for the standard antenna confguraton (ncrease from ~48 ns to ~6ns). A smlar behavor was reported by Bulttude et al. [33], who performed a measurement campagn at 4 GHz, n a large open offce envronment. It s a possble explanaton that the more drectve antenna, whch also has the hgher gan, may emphasze some reflected paths wth a rather large delay tme. Such paths contrbute strongly to the RDS. Buldng materal The reflectvty of buldng materal s expected to be another mportant factor nfluencng the RDS. Ths behavor was e.g. reported by Smulders [4], who measured hgher RDS values n a small room wth metal walls (room dmensons ~ 9 3 m 3 ; τ rms 45 ns), than n a much larger audtorum room wth walls covered by wood and acoustcally soft materal (room dmensons ~3 6 m 3 ; τ rms 35 ns). In a small room (~3 9 4 m 3 ) wth wood-covered walls, RDS-values of ~ ns were measured. Outdoor measurements Measurements n seven dfferent streets downtown Oslo were reported n [3], [4], [36] (MBS-RACE project). The RDS s typcally lower than ns, except for one measurement where a major reflecton source (tourst bus) was located on the street. In the latter case the RDS was < 5 ns. The maxmum delay spread (the sldng delay wndow,.e., the shortest perod of the IR contanng 9 % of the receved energy) s

58 44 Chapter Modelng of the Frequency-Selectve Rado Channel less than 45 ns for 9 % of the measurement ponts. However, maxmum values up to 7 ns were observed. Results from measurements at cty squares show hgher values of RDS and maxmum delay spread. Outdoor measurement results reported n [5], [6] (for 7 GHz), [38] (for 6 GHz), [37] (for 4, 6 GHz) also show RMS delay spread values startng below ns and occasonally gong up to about ns and above [38]. Lttle work has been done on outdoor propagaton n mm-wave bands..5.. Rcean K-factor Parameter pars of RMS delay spread, τ rms and the Rcean K-factor are requred for modelng multpath rado channels usng the FD-channel model ntroduced n Secton.3. Whle statstcs of the RDS are found n most propagaton studes, the Rcean K- factor s often not (explctly) nvestgated. Many studes assume Raylegh fadng ampltude dstrbutons,.e., K-factors of zero. In stuatons where the lne-of-sght (LOS) between transmtter and recever s obstructed, ths assumpton may be reasonable. However, as a LOS path s often requred for relable transmsson at mmwave frequences [4], the K-factor becomes an mportant channel parameter. Typcal values of K are gven below. The nfluence of a LOS path and the nfluence of the antenna characterstcs are nvestgated. Influence of a lne-of-sght path Two measurement campagns that consder the K-factor were conducted by Janssen [4], [5] and by Bohdanowcz [5], [6]. Although those measurements were performed at lower frequency-bands (at.4, 4.75, and GHz, and at 7 GHz, respectvely), the results are nterestng for modelng the 6 GHz channel. One mportant reason s that most of the measurement stuatons were smlar to the expected scenaros for 6 GHz systems, where both, the transmtter and the recever are typcally located wthn the same room. Moreover, results for all these frequencybands are qute smlar, suggestng that a shft to the 6 GHz band would not have a large mpact, ether. The comparatve study of a.7 GHz and a 6 GHz channel presented n [3] confrms the latter. Characterstc channel parameters reported by Janssen ([4], [5]) are τ rms ns, K.5 db n LOS stuatons, and τ rms 5 ns, K 3 db wthout LOS. All measurements were performed n relatvely small rooms. The 7 GHz channel study by Bohdanowcz ([5], [6]) gves typcal K-factors between.3 and.5 db for LOS ndoor scenaros (τ rms 5 7 ns), and values around db for ndoor non-los stuatons (τ rms 9 ns). Larger K-factors of 3 5 db were determned from outdoor LOS measurements, where τ rms 3 ns. Clearly, ncreased K-factors are observed n the presence of a (domnant) LOS path, correspondng to ampltude dstrbutons wth shallower fades. Whle K-factors below 3 db can be well represented by the Raylegh dstrbuton, hgher values should be

59 .5 Applcaton to mm-wave Rado Channels 45 modeled by the Rcean dstrbuton. In partcular f K db,.e., the domnant path carres greater or equal power than all the reflected paths, the Rcean model must be used. Antenna drectvty It s expected that more drectve antennas yeld hgher K-factors, because f the antennas are ponted towards one another, the domnant path s amplfed whle the reflected ones are attenuated. Inspecton of the mpulse responses shown by Manabe et al. n [3] confrm such behavor. Unfortunately, no values of K-factors are gven there. The channel model parameters gven by Smulders [4] and by Kunsch et al. [] can be used to estmate the Rcean K-factor and nvestgate the mpact of the antennas drectvty. Those model parameters were obtaned from 6 GHz channel measurements. Smulders model parameters [4] mply that even for the 5 db drectve antenna, and n the presence of a LOS path, the K-factor would be less or equal to 6 db, and therefore well descrbed by the Raylegh model. Note that n ths study the drectve (receve) antenna was not ponted towards the transmtter. Ths may be a partal explanaton for ths unexpected result. Kunsch s model parameters [] correspond to Rcean K-factors between 7.3 db and 5 db (and τ rms between 5.7 and ns, respectvely). Kunsch s measurement set-up used an 8 db antenna at the transmtter and two recever antennas ponted towards the transmtter, wth respectve gans of and db. It appears that such an antenna confguraton can effectvely reduce the multpath fadng. Adaptve antennas (beamformng) can avod the need of pontng the antenna manually. Larger K-factors reduce τ rms, when the decay exponents of the average power delay profle reman constant. Ths s also seen from the equatons gven n Table -, where γ should be consdered constant. The model parameters gven by Kunsch [] confrm that such a dependency may exst, at least wthn one room..5.3 Overvew of Channel Models Most of the (stochastc) channel models proposed n the lterature for mm-wave channels are based on the ndoor propagaton model presented by Saleh and Valenzuela [6]. Ths secton frst revews ther model. Secondly, a number of modfcatons are dscussed for ts applcaton to mm-wave channels. The sutablty of the FD-channel model for ths frequency band s studed n Secton Revew of the Saleh and Valenzuela Model The Saleh and Valenzuela model s a method to generate tme-dscrete channel mpulse responses as defned by eq. (-). Stochastc processes are specfed to model the

60 46 Chapter Modelng of the Frequency-Selectve Rado Channel ray arrval tmes {τ }, the ray ampltudes {β }, and the ray phases {θ }. The ray phases are consdered to be ndependent random varables that are unformly dstrbuted over [,π), because the phases vary over that range when the path-lengths change by just one wavelength. Two Posson processes mplement the ray-arrval process. Reflectons are assumed to arrve n clusters, where the frst Posson process models the arrval tmes of the clusters wth some fxed rate Λ [/s] 6. Subsequent ray-arrvals wthn the clusters are realzed by the second Posson process wth rate λ τ >> Λ. Per defnton, the frst ray and the frst cluster arrve at τ. A Posson process of (ray) arrvals mples exponentally dstrbuted nter-arrval tmes, wrtten as [ λ ( )] p ( τ) λ exp τ, (-9) τ where τ s the delay tme dfference between consecutve paths of the same cluster. The probablty dstrbuton of the path gans {β } s a Raylegh dstrbuton. (Therefore, the path gans ncludng the unformly dstrbuted path phases { β e jθ } follow a complex Gaussan dstrbuton.) Introducng the varables l and k for ndexng the cluster and ray-wthn-cluster, respectvely, the mean square values of the magntudes { β kl} are wrtten τ β kl SV e T l / Γ τ / γ kl β e, (-3) where {T l } and {τ kl } are the cluster and ray-wthn-cluster arrval tmes, respectvely, and Γ and γ SV are the correspondng power decay tme-constants. Ths functon s called the average power delay profle (PDP), because t characterzes the average ray power of the mpulse response as a functon of the excess delay-tme. It s composed of a set of exponentally decayng parts, one for each cluster of rays. For more detals on the Saleh and Valenzuela model, the reader s referred to [6] Modfcatons to the Model Several authors have appled a number of modfcatons to the above-descrbed model n order to match t to mm-wave channels. Most of the mplementatons found n the lterature reduce the number of clusters to one (see e.g. [] [5]). Ths smplfcaton s made, snce n a typcal ndoor mmwave channel, the reflectons orgnate all from wthn one room, leadng to a sngle, 6 Accordng to [6], the formaton of clusters s related to the buldng superstructure,.e., clusters of rays typcally orgnate from (steel-renforced) exteror or nteror walls or large metal doors or objects. The rays wthn the clusters are due to reflectons n the vcnty of the transmtter or recever. Clusterng of rays s therefore a property of ndoor channels at longer ranges and at lower carrer frequences, where propagaton through walls s possble. Clusterng of rays also occurs n outdoor channels [4] [44].

61 .5 Applcaton to mm-wave Rado Channels 47 dense cluster of ray arrvals. Remember that mm-wave frequences hardly penetrate through buldng materal. An excepton s the work of Park [35], who gves a set of parameters for the orgnal, mult-cluster verson of Saleh and Valenzuela s model. Park nvestgated ndoor channels at 6 GHz. In several cases, the model has been augmented by a separately specfed path at τ ([] [5]) n order to extend the model to Rcean channels by ntroducng a (domnant) LOS path. Smulders [4] proposes a composte average PDP, where the exponentally decayng part of the sngle cluster s preceded by a constant-level part. The reason for ntroducng ths part s to better descrbe frst-order reflectons arrvng at smlar strength due to the antenna desgn chosen. Such a constant-level part s also mplemented n the frequency-doman channel model proposed n ths Thess (see Secton.3.). Janssen shows n [5] how to adjust the generated dscrete-tme mpulse responses n order to exactly realze a gven set of channel parameters {P,K,τ rms }. (Note that those are local-area mean parameters; see Secton..). He also suggests a method to ncorporate small-scale fadng effects resultng from movements wthn a local area. That mechansm s based upon ray-arrval drectons relatve to the assumed transcever movement..5.4 Applcablty of the FD-model The proposed frequency-doman (FD) channel model characterzes the moble rado channel by ts delay power spectrum (DPS), the Fourer transform of the spacedfrequency correlaton functon. Ths model agrees well wth the modfed (snglecluster) versons of the Saleh and Valenzuela model ntroduced above, because the DPS of the FD-model s descrbed n an almost equvalent way to the average power delay profle of the (sngle-cluster) Saleh and Valenzuela model. In the FD-model, Rcean channels may be mplemented usng the dscrete, drect path at τ. Moreover, a constant-level part s ncorporated as n [3], whch allows for a better match to certan channel mpulse responses, and whch also enables varyng the maxmum excess delay n some range, as nvestgated n Secton.3.3. Accordng to the overvew of channel models presented above, a sngle cluster of rays s an approprate descrpton of mm-wave ndoor channels, where the transmtter and recever are typcally located wthn the same room. The sutablty of the proposed channel model for such scenaros was also confrmed by the comparson of measurement results to computer smulatons (see Secton.4.3). Clusterng of rays can be mplemented n the proposed model by modfyng the DPS accordngly,.e., by defnng a DPS consstng of multple exponentally decayng parts. Smlarly, arbtrary outdoor channels could be realzed. However, usng the model for the desgn of OFDM systems, I am confdent that the smple model

62 48 Chapter Modelng of the Frequency-Selectve Rado Channel ntroduced n Secton.3. s applcable to a much wder range of actual envronments. For such systems, the most mportant channel propertes are the correlaton among (adjacent) sub-carrers and the dstrbuton of ther ampltudes (or powers). These propertes are well preserved by the model as long as the channel parameters are matched to the envronment under nvestgaton. And these parameters can be freely (and easly) chosen n the proposed model. It can be even proven that, for Raylegh fadng channels and for small frequency-separatons, the correlaton coeffcent n frequency-doman s ndependent of the channel model (see Appendx A). (The correlaton coeffcent s the normalzed auto-correlaton functon of the squared magntudes of the TF.) Ths fndng strongly supports the clam that such a smple stochastc model s suffcent for many ar-nterface desgn problems..6 Conclusons The man noveltes dscussed n ths Chapter concern the so-called frequency-doman (FD) channel model and ts mplementaton on a computer smulaton scheme. The FD-model s the frequency-doman dual of Jakes Doppler-spectrum model [], [3], [4]. Just as n Jakes model the (narrowband) channel s tme-varablty s descrbed by the spaced-tme correlaton functon and by the Doppler spectrum, n the FD-model the (tme-nvarant) channel s frequency-selectvty s descrbed by the spaced-frequency correlaton functon and by the delay power spectrum. (The power spectra and correlaton functons are nter-related by Fourer transforms.) The smulaton scheme ntroduced drectly generates realzatons of channel transfer functons wth well-defned channel parameters. Note that a frequency selectve channel s equvalent to a tme-dspersve (multpath) channel. The major advantages of the proposed models are: Good agreement wth physcal propagaton channels, n partcular n mm-wave frequency bands and n ndoor envronments (see Secton.5). Avalablty of analytcal expressons relatng model parameters to physcal channel parameters and vce versa, allowng to straghtforwardly match the model to any gven envronment (see Secton.3.3). Sutablty for OFDM system desgn, the goal of ths research (see Part II). The smplcty of the model allows for the mathematcal analyss of many aspects of transmsson schemes, lke the performance evaluaton and optmzaton of bterror-rates, synchronzaton, and channel estmaton schemes (see Part II). Avalablty of an effcent smulaton model (see Secton.4). However, the extenson of the smulaton model from the statc verson presented, to a tme-varant verson s rather complex. Ths may be a dsadvantage of the FD-model. The (physcal) channel parameters specfyng the FD-model are elaborately dscussed.

63 .6 Conclusons 49 The channel at a local area of dmensons of a few wavelengths (approx. 5 4 λ) s defned by a set of fxed parameters: the normalzed (or average) receved power P, the Rcean K-factor K, and the RMS delay spread τ rms. At a lmted observaton bandwdth, however, these parameters appear to be tme- (or locaton) varant wthn a local area, because ndvdual propagaton paths are not resolvable and multpath nterference between them leads to rapd (small-scale) varatons of the resultng channel mpulse response. Reduced-bandwdth smulatons performed wth the FD-model also show a varablty of these nstantaneous parameters among realzatons. It was suggested that the RMS delay spread τ rms and the Rcean K-factor are equally mportant for the characterzaton of frequency selectve multpath rado channels. In the next chapter, t wll be shown that τ rms effectvely specfes the number of fades per bandwdth and ther average bandwdth, whle the K-factor descrbes the depth of fades. Most expermental studes, however, nvestgate τ rms only. The K-factor s analyzed n rather few cases, although lne-of-sght condtons and drectonal antennas are commonly consdered, two factors that are antcpated to ncrease the K-factor. Raylegh fadng channels have a K-factor of zero. Channel parameters depend on a number of features of the propagaton envronment and of the antenna set-up. Larger rooms and more reflectve buldng materals gener- Table -: Typcal channel parameters of frequency-selectve, mm-wave rado channels. Ttle Small / medum room, LOS Small / medum rooms, non-los Comments and Reference measurem. at.4, 4.75, and GHz [4], [5] Outdoor 7 GHz [5], [6] Medum room, drectonal ant. Computer room (~ 9 3 m 3 ) Large Hall (~ m 3 ) Corrdor (~ m 3 ) Hgh-gan antenna ponted at BS; 6 GHz [] 6 GHz [3] Lecture room (~3 9 4 m 3 ) BS: Base Staton; PS: Portable staton Antenna confguraton ~.5 db bconcal antennas (~ beamwdth) BS: 8 db PS: ~ db 9 db b-concal antennas (~9 beam-wdth) RMS delay spread ns.5 db Rcean K-factor 5 ns 3 db (Raylegh) 3 ns 3 db 5 ns db 45 ns (Raylegh) 6 ns (Raylegh) 75 ns (Raylegh) ns (Raylegh)

64 5 Chapter Modelng of the Frequency-Selectve Rado Channel ally ncrease the RMS delay spread τ rms. Hgher antenna drectvty decreases τ rms and ncreases the K-factor. The presence of a lne-of-sght between the transmt- and receve-antennas leads to larger K and sometmes to lower τ rms. Wthn the same envronments and wth smlar antenna set-ups, the frequency band has surprsngly lttle nfluence on those parameters. A lst of typcal parameter-values wth short descrptons of the man features of the correspondng envronments s gven n Table -. Mm-wave channels (e.g. 6 GHz) are consdered for the multmeda communcatons system studed n Part II of ths thess. Most nvestgatons of these channels conclude that a lne-of-sght between the transmtter and the recever s requred for relable communcatons. However, the results from [3], where a specal antenna desgn was used, suggest that the reflectons can be suffcent as well. Snce the channel parameters are nfluenced by many factors and n ways that are hard to predct, a method s desrable to measure them n a cheap and smple way. The next chapter presents a method that can be used to accurately estmate these parameters {P, K, τ rms } from scans of the channel s power response versus frequency. Standard laboratory equpment can be used to apply that scheme..7 References [] W. C. Jakes Jr., Mcrowave Moble Communcatons. New York: Wley-Interscence, 974. [] J. G. Proaks, Dgtal Communcatons, 3 rd edton. New York: McGraw Hll, 995. [3] M. J. Gans, A Power-Spectral Theory of Propagaton n the Moble-Rado Envronment, IEEE Trans. Veh. Technol., vol. VT-, no., pp. 7 38, Feb. 97 [4] R. H. Clarke, A Statstcal Theory of Moble-Rado Recepton, Bell Syst. Tech. J., vol. 47, pp. 957, July Aug [5] P. A. Bello, Characterzaton of randomly tme-varant lnear channels, IEEE Trans. on Commun. Systems, vol. CS-, pp , Dec [6] R. Steele, Moble Rado Communcatons. New York: John Wley and Sons, 99. [7] T. S. Rappaport, Wreless Communcatons: Prncples and Practce, Upper Saddle Rver: Prentce-Hall, 996. [8] European Commsson, Cost Acton 3, Dgtal moble rado towards future generaton systems, Fnal Report, EUR 8957, Luxembourg, ISBN , 999.

65 .7 References 5 [9] S. O. Rce, Mathematcal Analyss of Random Nose, Bell Syst. Tech. J., vol. 3, pp. 8 33, July 944; vol. 4, pp , Jan [] S. O. Rce, Statstcal Propertes of a Sne Wave Plus Random Nose, Bell Syst. Tech. J., vol. 7, pp. 9 57, 948. [] A. V. Oppenhem and R. W. Schafer, Dscrete-tme Sgnal Processng, nd edton. New Jersey: Prentce-Hall, 999. [] J. Kunsch, E. Zollnger, J. Pamp, and A. Wnkelmann, MEDIAN 6 GHz Wdeband Indoor Rado Channel Measurements and Model, n Proc. IEEE Vehc. Techn. Conf. (VTC 99-fall), Amsterdam, The Netherlands, Sept. 999, pp [3] P. F. M. Smulders, Broadband Wreless LANs: A Feasblty Study. PhD Thess, Endhoven Unversty of Technology, Endhoven, The Netherlands, 995. [4] G. J. M. Janssen, P. A. Stgter, and R. Prasad, Wdeband ndoor channel measurements and BER analyss of frequency selectve multpath channels at.4, 4.75 and.5 GHz, IEEE Trans. on Commun., vol. 44, no., pp. 7-88, Oct [5] G. J. M. Janssen, Robust recever technques for nterference-lmted rado channels, Ph.D. Thess, Delft Unv. of Techn., Delft, The Netherlands, June 998. [6] A. A. M. Saleh and R. A. Valenzuela, A statstcal model for ndoor multpath propagaton, IEEE J. Select. Areas Commun., vol. 5, no., pp. 8 37, Feb [7] O. Edfors, M. Sandell, J. J. van de Beek, D. Landström, and F. Sjöberg, An ntroducton to orthogonal frequency-dvson multplexng, Dvson of Sgnal Processng, Luleå Unversty of Technology, Research Report TULEA 996:6 ( [8] Wemn Zhang, Smulaton and modellng of multpath moble channels, n Proc. VTC 94 (IEEE Vehcular Technology Conference), Stockholm, Sweden, 994, pp [9] K. Pahlavan and A. H. Levesque, Wreless Informaton Networks. New York: John Wley and Sons, 995. [] A. Chn, M. S. Tanany, and S. A. Mahmoud, Transmsson of hgh rate ATM packets over ndoor rado channels, IEEE J. Select. Areas Commun., vol. 4, no. 3, pp , Apr [] O. Edfors, Low-complexty algorthms n dgtal recevers. PhD Thess, Luleå Unversty of Technology, Luleå, Sweden, Sept. 996.

66 5 Chapter Modelng of the Frequency-Selectve Rado Channel [] J.-J. van de Beek, O. Edfors, M. Sandell, S. K. Wlson, and P. O. Börjesson, On channel estmaton n OFDM systems, n Proc. IEEE Vehc. Technol. Conf., Chcago, IL, July 995, pp [3] L. M. Correa, et al., Fnal Report on Propagaton Aspects, RACE 67, Delverable R67/IST/..5/DS/P/7.b, RACE Central Offce, European Commsson, Brussels, Dec [4] S. A. Mohamed, G. Løvnes, E. Antonsen, R. Rækken, B. Ngeon and J. J. Res: Report on Propagaton Measurements, RACE 67, Delverable R67/BTL/../DS/P/ 35.b, RACE Central Offce, European Comsson, Brussels, Dec [5] A. Bohdanowcz, G. J. M. Janssen, S. Petrzyk, Wdeband ndoor and outdoor multpath channel measurements at 7 GHz, n Proc. VTC 99-fall (IEEE Vehcular Technology Conference), Amsterdam, The Netherlands, Sept. 999, pp [6] A. Bohdanowcz, Wdeband ndoor and outdoor rado channel measurements at 7 GHz, Delft Unv. of Technol., UbCom-Techncal Report//, Jan. ( [7] R. El Hattach, J. M. M. de Njs, K. Wtrsal, and R. Prasad, Characterzaton and smulaton of the 8 GHz rado channel, n Proc. IEEE Benelux 6 th Symposum on Vehcular Technology and Communcatons, Brussels, Belgum, Oct [8] J. Purwaha, A. Mank, D. Matc, K. Wtrsal, and R. Prasad, Wde-band channel measurements at 6 GHz n ndoor envronments, n Proc. IEEE Benelux 6 th Symposum on Vehcular Technology and Communcatons, Brussels, Belgum, Oct [9] J. J. G. Fernandes, J. C. Neves, and P. F. M. Smulders, MM-Wave Indoor Rado Channel Modellng vs. Measurements, Wreless Personal Comm., vol., no. 3, pp. 9, Kluwer, 995. [3] A. Kato, T. Manabe, et al., Measurements of Mllmeter Wave Indoor Propagaton and Hgh-Speed Dgtal Transmsson Characterstcs at 6 GHz, n Proc. PIMRC 97 (IEEE 8 th Intern. Symp. on Personal Indoor Moble Rado Commun.), pp , Helsnk, Sept [3] T. Manabe, Y. Mura, and T. Ihara, Effects of Antenna Drectvty on Indoor Multpath Propagaton Characterstcs at 6 GHz, n Proc. PIMRC 95 (IEEE 6 th Intern. Symp. on Personal Indoor Moble Rado Commun.), pp , Sept. 995.

67 .7 References 53 [3] R. Daves, M. Bensebt, M. A. Beach, and J. P. McGeehan, Wreless Propagaton Measurements n Indoor Multpath Envronments at.7ghz and 6Ghz for Small Cell Systems, n Proc. 4 st IEEE Veh. Techn. Conf., pp , St. Lous, USA, May 99. [33] R. J. C. Bulttude, R. F. Hahn, and R. J. Daves, Propagaton Consderatons for the Desgn of an Indoor Broad-Band Communcatons System at EHF, IEEE Trans. Veh. Technol., vol. 47, no., pp , Feb [34] J. Hübner, S. Zesberg, K. Koora, and A. Fnger, Smple channel model for 6 GHz ndoor wreless LAN desgn based on complex wdeband measurements, n Proc. IEEE Vehc. Techn. Conf. (VTC 97), 997, pp [35] J.-H. Park, Y. Km, Y.-S. Hur, K. Lm, and K.-H. Km, Analyss of 6 GHz Band Indoor Wreless Channels wth Channel Confguratons, n Proc. PIMRC 98 (IEEE 9 th Intern. Symp. on Personal Indoor Moble Rado Commun.), Tawan, Sept. 998, pp [36] G. Løvnes, J. J. Res, and R. H. Rækken, Channel Soundng Measurements at 59 GHz n Cty Streets, n Proc. PIMRC 94 (IEEE 5 th Internatonal Symposum on Personal Indoor Moble Rado Communcatons), The Hague, The Netherlands, Sept. 994, pp [37] S. W. Wales and D. C. Rckard, Wdeband propagaton measurements of short range mllmetrc rado channels, Electroncs and Commun. Eng. Journal, pp , Aug [38] N. Danele, D. Chagnot, and C. Fort, Outdoor mllmetre-wave propagaton measurements wth lne of sght obstructed by natural elements, IEE Electroncs Letters, vol. 3, no. 8, pp , Sept [39] G. Løvnes, S. E. Paulsen, and R.H. Rækken, A versatle channel sounder for mllmetre wave measurements, n Proc. PIMRC 93 (IEEE 4 th Internatonal Symposum on Personal Indoor Moble Rado Communcatons), Yokohama, Japan, Sept [4] D. C. Cox, Delay Doppler Characterstcs of Multpath Propagaton at 9 MHz n a Suburban Moble Rado Envronment, IEEE Trans. Ant. and Prop., vol., no. 5, pp , Sept. 97. [4] M. Flament, On 6 GHz Wreless Communcaton Systems. PhD Thess, Chalmers Unv. of Techn., Göteborg, Sweden,. [4] G. L. Turn, F. D. Clapp, T. L. Johnston, S. B. Fne, and D. Lavry, A statstcal model of urban multpath propagaton, IEEE Trans. Veh. Technol., vol. VT-, pp. 9, Feb. 97. [43] H. Suzuk, A statstcal model for urban rado propagaton, IEEE Trans. Commun., vol. COM-5, pp , July 977.

68 54 Chapter Modelng of the Frequency-Selectve Rado Channel [44] H. Hashem, Smulaton of the urban rado propagaton channel, IEEE Trans. Veh. Technol., vol. VT-8, pp. 3 4, Aug. 979.

69 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate 3. Introducton Channel measurements are requred to obtan parameters for the channel model proposed n the prevous chapter. A novel technque for conductng such measurements s ntroduced here, whch s based on the frequency-doman level crossng rate (LCR f ) of the fadng rado channel. Usually, the level crossng rate (LCR) s defned and nvestgated for tme-dependent stochastc processes, where t specfes the number of up-gong level crossngs through a gven threshold. In ths chapter, the LCR f of the transfer functon (TF) of a frequency-selectve channel s studed, specfyng the average number of fades per bandwdth. From the analyss of the LCR f, whch s one of the man topcs of ths chapter, t was recognzed that the LCR f s proportonal to the RMS delay spread (RDS) τ rms of the multpath-fadng channel. That s, the average number of fades per bandwdth (and also the average bandwdth of the fades) s related to τ rms by a gven factor. Ths factor was studed on the bass of the frequency-doman (FD) channel model ntroduced n the prevous chapter. It has been notced that the factor does depend on the K-factor of the Rcean fadng channel, but the actual form of the channel model has lttle or no mpact. Ths property can be used for estmatng the RDS from the LCR f, whch can be determned from non-coherent channel measurements (power-vs.-frequency sweeps of the channel TF). Snce the normalzed receved power P and the Rcean K-factor can be derved from such data as well [], full sets of channel parameters {P, K, τ rms } can be 55

70 56 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate obtaned from pure power measurements. Hence, standard laboratory equpment may be used to conduct channel measurements, as e.g. a swept-frequency contnuous-wave (CW) sgnal generator and a power meter or spectrum analyzer. Its smplcty makes the method partcularly useful at extremely hgh frequences (> 3 GHz; mllmeter wave band), where for nstance network analyzers become very cumbersome and expensve. Moreover, large dstances can be allowed between the transmtter and the recever, because no reference connecton s requred. Snce the proposed measurement method s based on a statstcal model, a suffcently large bandwdth must be observed to obtan hgh accuracy, just lke a large frequencyband must be scanned wth a network-analyzer n order to obtan a certan tme-resoluton. An advantage of our method s that because of ergodcty the observaton bandwdth can be ncreased by analyzng the combned data of a number of narrowband measurements performed n a local area. The sze of ths local area must be selected suffcently small for the channel parameters not to vary due to shadowng. Well de-correlated spectra can be obtaned when the recever s locaton s changed n the order of one or a few wavelengths λ. Especally at the mllmeter wave band wth wavelengths below cm, many spectrum samples can thus be taken wthn small areas. Note that due to the lack of phase nformaton, the Fourer transform cannot be used for transformng a magntude TF to the delay tme-doman, whch would allow determnng delay spread parameters as the RDS drectly. However, the causalty of the mpulse response mples that the Hlbert transform descrbes the relatonshp between the real and magnary components of the complex valued TF. Donaldson et al. have appled ths property for analyzng magntude TFs [], yeldng estmates of the channels mpulse responses. Ther method can be an alternatve way of determnng delay spread parameters usng ths type of measurements. Ths chapter begns wth the analyss of the LCR f based on the FD-channel model ntroduced n the prevous chapter (see Secton 3.). For the Raylegh fadng case t s proven that the channel mpulse response has no nfluence on the factor relatng τ rms and the LCR f. Some mpact of the FD samplng nterval wll be seen, because level crossngs may be overlooked f t s selected too large. A measurement procedure derved from the relaton of τ rms and the LCR f s descrbed n Secton 3.3, and ts performance s nvestgated. We fnd that an observaton bandwdth of /τ rms leads to estmaton errors wth standard devatons n the order of 5 %. The method s senstvty to addtve nose s of major concern for ts practcal applcaton, snce addtonal level crossngs caused by the nose lead to a systematc overestmaton of the RDS. Such nose may be due to measurement naccuraces, when scan-

71 3. Frequency-Doman Level Crossng Rate 57 nng the channel TF. Ths problem s extensvely studed n Secton 3.4. The Chapter s concluded n Secton 3.5, where also recommendatons for further work are gven. 3. Frequency-Doman Level Crossng Rate The level crossng rate (LCR) s usually defned for tme-doman fadng (or other tme-dependent stochastc processes) as the average number of crossngs per second at whch the envelope of a sgnal ξ(t) crosses a specfed level r n an up-gong drecton. Its dmenson s [s ]. Consderng the TF n the frequency-doman, the LCR f gves the average number of crossngs per Hertz bandwdth at whch the ampltude R(f) H(f) of the TF crosses a level r n an up-gong drecton. Ths LCR f wll be denoted by N R (r), ts dmenson beng [s]. The dervaton of the LCR f s frstly conducted on the bass of the FD-channel model, whch descrbes the frequency-selectvty as a contnuous stochastc process (see Chapter, Secton.3). A soluton s found for Rcean and Raylegh fadng channels. We apply ths result for analyzng the mpact of channel parameters (τ rms and Rcean K-factor) and model parameters (the shape of the delay power spectrum (DPS)) on the LCR f. A proportonal relatonshp between the LCR f and τ rms s found. In Secton 3.., the sgnfcance of ths relaton s assessed by analyzng a determnstc two-ray channel. As mentoned above, the LCR f can be used to estmate the RDS of tme-dspersve rado channels. In order to employ ths relatonshp for channel nvestgatons, the power response of the channel has to be scanned versus frequency, whch s usually done at dscrete frequency ponts. Selectng thereby the samplng nterval n the frequencydoman too large, some level crossngs may be overlooked, leadng to a bas n the estmated τ rms. In order to analyze the mpact of samplng, the LCR f s also derved for the sampled case (see Secton 3..3). Ths study s lmted to Raylegh channels, however, because for the Rcean case, the mathematcal expressons nvolved requre numercal solutons. Moreover, t wll be shown that for Raylegh channels the proportonalty relatonshp between τ rms and LCR f s ndependent of the channel mpulse response. 3.. Dervaton of the LCR f from the Contnuous FD-Channel Model The followng dervaton s based on the FD-channel model ntroduced n Chapter, Secton.3, whch characterzes the frequency-selectvty (tme-dspersve nature) of the multpath rado channel based on ts delay power spectrum (DPS):

72 58 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate τ < ρ δ ( τ ) τ φh ( τ ). (3-) Π < τ τ γ ( τ τ) Πe τ > τ For notatonal convenence we ntroduce u τ γ, expressng the shape of the DPS, 3 and u u, u u + u, and u u 3 + u + u Proof of the Proportonalty of the LCR f and the RMS Delay Spread An analytcal expresson for the LCR of Rcean processes wth cross-correlated realand magnary parts of the underlyng complex Gaussan process '( f ) H '( f ) + j H '( f ) s gven as (cf. [3], and [4], [5]) r + ρ π ψ + 3 H r ( αρ snθ ) { e παρ sn( θ ) erf( αρ sn θ )} dθ / r β rρ N R ( r) e cosh cosθ / π ψ ψ, (3-) where ψ φ H '( ) Πu / γ s the varance of the real or magnary component of φ φ H'(f) (.e. half of the power of the scattered rays), and α and β ψ ψ β ψ account for the second order statstcs of H'(f). ( φ and ψ are gven n (3-4).) H'(f) s defned by the DPS (3-) after subtracton of the LOS-component ρ δ(τ), or equvalently by ts auto-correlaton functon (ACF): jπτ f j πτ f φ H '( f ) F{ φh' ( τ )} Π τ snc( τ f ) e + e (3-3) γ + jπ f Note that the real and magnary parts of ths ACF denote respectvely the ACF of the real or magnary component of H'(f), and the cross-correlaton functon (CCF) between ts real- and magnary components, wrtten as φ f ) [ φ ( f ) + H '( r H ' jφ r H ' H '( f )]. To calculate α and β, the curvature of the ACF φ H ' ( f ) and the gradent r of the CCF φ ( f ) have to be evaluated at f, yeldng r H ' H ' d Π ψ and (3-4a) φ H '( f ) π u r 3 3 d f γ f d Π φ φ H ' H '( f ) u d f r π. (3-4b) γ f Next, t wll be shown that the LCR f for the FD-model can be expressed n the form

73 3. Frequency-Doman Level Crossng Rate 59 N R ( r' ) τ f ( K, u, r'), (3-5) rms where f(k,u,r') s the proportonalty factor between τ rms and the LCR f. Note that ths factor s constant at a gven K-factor, normalzed threshold level r', and DPS shape defned by u. It wll be seen below that the mpact of the channel model (wrtten by u) s usually neglgble. Wth (3-4) we get γ α Π β π u 3u Π 3 u γ 3 u u u u u. and (3-6) The threshold level r s related to the square root of the normalzed receved power P (the RMS ampltude of the TF), to elmnate the nfluence of P from the LCR f : r' Π γ r P r ρ + u. (3-7) Usng (3-6), (3-7), ψ Π u γ, and the expresson for τ rms (K,γ,u) from Table - (Secton.3.3, page 3) yelds wth (3-) where N R ( r') τ rms a e π / b ( d snθ ) { e + π d snθ erf( d snθ )} dθ cosh( c cosθ ), (3-8) 4 a r'( K + ) π 3 3/ b r' ( K + ) + K c r' K( K + ) d K u u u u 3 u u u 3 u u ( K + ) u. (3-9) It s observed from (3-9) that {a, b, c, d} are expressed as functons of {K, u, r'},.e., they are ndependent of τ rms, whch proves (3-5). Ths result can be used for estmatng τ rms from the LCR f, whch can be obtaned from non-coherent wde-band measurements (.e. from wde-band power measurements) [6]. It enables the wde-band characterzaton of the rado channel usng a very smple measurement prncple, as explaned n the ntroducton. Secton 3.3 dscusses ths method n detal.

74 6 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate 3... Average Bandwdth of Fades The average bandwdth of fades (ABF), B R (r), s the mean value for the bandwdth over whch the ampltude R(f) of the TF s below a specfed level r. Equvalently to the respectve tme-doman parameter (the average duraton of fades [7]), the ABF s wrtten as FR ( r) BR ( r), (3-) N ( r) where F R (r) denotes the (Rcean) CDF of the sgnal envelope,.e., the probablty that R(f) s below the level r. r xρ FR r ( ) Pr ψ ψ R ρ x ψ ψ { R( f ) r} e xe I dx (3-) In ths equaton, I ( ) desgnates the zeroth-order modfed Bessel functon of the frst knd. Computatonal results of the normalzed level crossng rate and the average bandwdth of fades are shown n Fgure 3-a and b, respectvely. They are compared to computer smulatons generated wth the FD-smulaton scheme ntroduced n Chapter, Secton.4. The comparson clearly demonstrates that the analytcal expressons descrbe the statstcal propertes of the smulated channel approprately Influence of Channel and Model Parameters Usng the analytcal expressons, the nfluence of the channel parameters {P, K, τ rms } and the nfluence of the shape of the DPS (expressed by u τ γ) on the LCR f and on the ABF s studed. One of the man results s that the LCR f s proportonal to τ rms, as seen from the mathematcal analyss above. For ths reason t s approprate to show LCR f and ABF normalzed to τ rms. Furthermore, the result s ndependent of the NRP P, f the threshold varable r s normalzed to P. Therefore, the shape of the LCR f s characterstc for partcular K-factors (and parameters u) as seen from the factor f(k,u,r') n (3-5). Normalzed LCR f and ABF are depcted n Fgure 3-a and b, respectvely, as a functon of r' and for varous K-factors and parameters u. It s observed from these fgures that even n the extreme cases u (exponentally decayng DPS) and u (rectangular DPS), the LCR f and ABF reman smlar, provded τ rms and K are kept constant. The dependency on u dsappears completely for K,.e., for Raylegh fadng channels. For any K, the LCR f at r' ( r P ) shows lttle varaton, whch s also evdent from Fgure 3-3a, llustratng the factor f(k,u,r' ) as a functon of K wth parameter u. Fgure 3-3b depcts the systematc

75 3. Frequency-Doman Level Crossng Rate 6 normalzed level crossng rate N R (r )/τ rms theory smulaton sms threshold level r [db], normalzed to RMS ampltude (a) average bandwdth of fades B R (r ) [MHz] 3 theory smulaton sms. 4 3 threshold level r [db], normalzed to RMS ampltude (b) Fgure 3-: (a): Normalzed level crossng rate for Rcean K-factor K 7.5 db. Analytcal results compared wth results from one sngle smulaton and averaged results from smulatons (smulated bandwdth.8 GHz; τ rms 5.3 ns); (b): Average bandwdth of fades for the same smulatons. estmaton error that would yeld from usng (3-5) wth u for estmatng τ rms of channels wth u {, }. It s seen that the dfference of f(k,u,r' ) for a rectangular DPS and an exponentally decayng one s less than 4% at any gven K-factor. The other curves n Fgure 3-3 are descrbed n Secton 3...

76 6 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate normalzed level crossng rate N R (r )/τ rms u u u K 6 db K 6 db K 9 db K 5 db threshold level r [db], normalzed to RMS ampltude (a) normalzed average bandwdth of fades B R (r ) τ rms u u u K 6 db K 6 db K 9 db K 5 db threshold level r [db], normalzed to RMS ampltude (b) Fgure 3-: (a): LCR f for varous K-factors and parameters u; (b): ABF for the same parameters. Both fgures are normalzed to τ rms and P. The small nfluence of the shape of the delay power spectrum (expressed by the parameter u) s observed. From the behavor of the LCR f -curves, conclusons can be drawn on the sgnfcance of the channel parameters {P, K, τ rms } used n ths study. Each of them has a very dstnct mpact on the LCR f, thus one mght expect them to have dfferent mpact on performance results as well.

77 3. Frequency-Doman Level Crossng Rate 63 proportonalty factor N R (r )/τ rms at the RMS ampltude u (exponental DPS) u u (rectangular DPS) two ray model ray; K statstcally eval Rcean K factor (a) close up systematc estmaton error 3 max (. db,36 %) max ( db,3 %) max (.4 db,3. %) max (.96 db,.7 %) DPS has u DPS has u two ray channel two ray ch.; K estmated Rcean K factor [db] (b) Fgure 3-3: (a): The factor f(k,u,r' ) N R (r' )/τ rms as a functon of the Rcean K-factor for varous channel models. (b): Estmaton error of τ rms, when f(k,u,r' ) s used, but the channels are characterzed by other models. The Rcean K-factor characterzes the depth of the fades about the mean power gven by P. Therefore, the dstrbuton of the sgnal-to-nose rato s related to P and K, whch generally determnes the bt error rate (BER) achevable, at a gven nose and nterference power level.

78 64 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate The RMS delay spread specfes the number of fades per bandwdth and the average bandwdth of the fades. Consderng mult-carrer transmsson systems (e.g. coded OFDM), one would expect a dependency of the BER on the number of fades wthn the transmsson bandwdth. From the LCR f, ths parameter s seen to be strctly related to τ rms. Performance evaluatons of OFDM systems have confrmed these observatons (see Sectons 4.3 and 8.). For (non-equalzed) sngle-carrer modulaton schemes, the relatonshp between τ rms and the BER s even more obvous, snce the delay spread determnes the amount of nter-symbol-nterference, whch tself mpacts on rreducble error floors. Numerous studes are avalable for varous modulaton and detecton schemes, reportng on qualtatve and quanttatve relatons between τ rms and the BER. Although no general result s known, τ rms s probably the most mportant sngle parameter for characterzng the tme-dsperson or frequency-selectvty of the wde-band rado channel. 3.. LCR f for a Determnstc Two-Ray Channel In ths secton, a bref analyss s presented n order to assess the valdty of the proportonalty factor f(k,u,r') (whch relates the LCR f to τ rms ) for dfferent channel models. A determnstc two-ray model s nvestgated for ths purpose. The IR of such a channel s defned as jθ jθ h ( τ) β e δ ( τ ) + β e δ ( τ τ ), (3-) δ where β β are the ray ampltudes, {θ,θ } are the ray phases, and τ δ > s the relatve delay among the two paths. Applyng the FT leads to the ampltude TF R f ) H ( f ) β + β + β β cos(πτ δ f + θ ). (3-3) ( θ From (3-3), the LCR f s seen to be constant: τ + δ β β r β β N R ( r) (3-4) otherwse τ rms must be calculated for ths model to obtan the normalzed LCR f, whch s the proportonalty factor requred. Analyzng the IR yelds β β κ τ rms τ δ τ δ, (3-5) β + β κ + where κ β / β s the power rato of the two rays. Takng κ as K-parameter, (3-4) and (3-5) can be used to derve the proportonalty factor as a functon of K (see Fgure 3-3a, { { ). In fact, the Rcean dstrbuton s not descrbng the ampltude dstrbuton of (3-3), thus comparng κ to the Rcean K-factor n (3-5) mght be napproprate. One method

79 3. Frequency-Doman Level Crossng Rate 65 of dervng K from a set of ampltude values R s to calculate E{R} and E{R }. The rato E { R} E{ R } can then be related to K as elaborated n []. Usng ths defnton of K, the proportonalty factor s found as ndcated by + + n Fgure 3-3a. The smlarty of all the results shown n ths graph confrms the sgnfcance of the relatonshp found between τ rms and the LCR f. It suggests that the proposed measurement method can be appled qute generally,.e., even f the nvestgated propagaton channel does not match to the model defned by eq. (3-). Ths statement s further evaluated below. In Fgure 3-3b, the error of τ rms s depcted, resultng from strctly usng f(k,u,r' ) when estmatng τ rms for channels descrbed by the two-ray model (and by the FD-model for u {, }). If a two-ray channel s evaluated wth ths method, the maxmum error s 36 % when both rays have equal powers, and t drops below % when κ s above 6 db Dervaton of the LCR f for the Sampled Case The dervaton of the LCR f for the sampled channel TF s the goal of ths secton. Purpose of ths analyss s to evaluate the mpact of the samplng nterval, whch f selected too large may lead to systematc errors n the τ rms estmaton, because level crossngs n-between samplng nstants may be overlooked. Note that the followng dervatons are lmted to Raylegh channels, because for the Rcean case the mathematcal expressons do not yeld analytcal solutons. The probablty of a level crossng between adjacent samples s the probablty that the current sample s magntude R n s larger than a specfed threshold value, R n r, whle the precedng sample R n was smaller, R n < r. The LCR f s thus wrtten as N ( R r, R r) F ( r) Pr, (3-6) R n n < where F [Hz] s the samplng nterval n the frequency-doman, and R n and R n denote correlated random varables. Knowledge of the bvarate cumulatve dstrbuton functon (CDF) of {R n,r n }, F r, r ), s requred to obtan the LCR R f from Pr ( n, R n ( R r, R < r) Pr( R < r) Pr( R < r, R < r) F ( r) F ( r, ) n n n n n R, r n Rn Rn, (3-7) where FR ( r) F (, ), r n Rn R s the CDF of any one sample, e.g. R n n. Usng an expresson of the bvarate Raylegh CDF gven n [8] (eq. (--3)), the probablty (3-7) becomes r ' ( ) ρ c ρ c Pr R n r, Rn < r e Q r ', r' Q r ', r',(3-8) ρ c ρ c ρ c ρ c where Q (a,b) s the Marcum s Q-functon (see [9], (--3)), r' s the normalzed

80 66 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate threshold level r ' r ψ r P, and ρ c s the correlaton coeffcent of the squared magntudes defned as ρ cov( R, R ) var( R ) var( R ), ρ c <. ρ c s related to c n n n n the auto-correlaton of the underlyng complex Gaussan process Z n ( Z n R n ) by * c, where ψ m { } E Z nz n+ m ρ ψ ψ (cf. []) Pr r ' ( Rn r, Rn < r) e. An alternatve expresson for (3-8) s gven as π π π e + ρc snθ r ' ρc ρc dθ. (3-9) + ρ + ρ snθ c c It s seen that the crossng probablty (3-8), (3-9) s solely determned by the correlaton coeffcent ρ c and by r'. Calculatng ρ c based on the stochastc or determnstc model of a Raylegh dstrbuted process (e.g. for the FD-channel model defned by (3-)) thus leads to the level crossng rate. Ths secton contnues wth the dervaton of an approxmaton for (3-8) (and (3-9)) for the case that ρ c, whch s for nstance gven when the samplng nterval approaches zero, F. Note that n ths lmt, the sampled case approaches the contnuous case analyzed above (Secton 3..). Secondly, the correlaton coeffcent s derved from the FD-channel model and n Appendx A from the dscrete mpulse response defned by eq. (-), Secton... It wll become evdent that a common expresson relates ρ c to τ rms n the lmt F. Therefore, there s no nfluence of the channel mpulse response on the proportonalty factor between τ rms and the LCR f for the contnuous case and for Raylegh fadng channels. Based on the analytcal results, the mpact of samplng on the LCR f s evaluated Approxmaton of the Crossng Probablty for the Sampled Case Both expressons for the sampled verson of the LCR f, eqs. (3-8) and (3-9), are dffcult to evaluate f ρ c s close to one. The goal of ths dervaton s to fnd an approxmaton for ths case. In order to fnd an asymptotc expresson for (3-8) n the lmt ρ c, we use the relaton of the Marcum s Q-functon to the CDF of a Rcean random varable (see [9], (--4)) Q b ( v + a ) / ( a, b) ve I ( av) dv. (3-) When av becomes large, I (av) may be replaced by ts asymptotc expresson, as suggested n [4], eq. (3.-9). Ths yelds the followng approxmaton for the Rcean CDF, beng vald for ab >> and a >> b a (see [4]), whch s fulflled for ρ. c

81 3. Frequency-Doman Level Crossng Rate ) ( 8 ) ( 4 8 ), ( a a b a a b e a a b erf b a Q a b π (3-) Replacng the error functon by the frst terms of ts power seres expanson, the most mportant terms of (3-) can be dentfed, + 6 ) ( 3 a b a b a b erf π. (3-) For the two Q-functons n (3-8), b a and a are ( ) ' ' ' ' ) (,, >> << r r a r r a b c c c II I c c c c II I ρ ρ ρ ρ ρ ρ ρ # #, (3-3) respectvely, where the approxmatons and the nequtes hold for c ρ. Keepng the most sgnfcant terms yelds ' 4 ' 8 ) ( ), (,,, r r a a b b a Q c c II I II I II I π ρ π ρ π π + ± +. (3-4) Substtutng these expressons for the Q-functons n (3-8), the approxmaton c r n n e r r R r R ρ π < ' ), Pr( ', (3-5) s obtaned, whch becomes exact n the lmt c ρ. Ths condton s fulflled strctly for F,.e., for an nfntely small samplng nterval, and approxmately, f the samplng theorem holds. The systematc error s less than ~ % and ~5 %, for ρ c.9 and ρ c.65, respectvely, and for thresholds r' between 6 db and 6 db (see Fgure 3-4). Larger negatve errors are evdent for smaller r', snce the samplng nterval gets more mpact as the fades get deeper and narrower Calculaton of the Correlaton Coeffcent ρ c The correlaton coeffcent s obtaned from ρ ψ ψ c, where { } * m n n m Z Z E + ψ s the auto-correlaton functon of the dscrete complex Gaussan process, whch s underlyng the sampled Raylegh process. Therefore, ψ m has to be determned from the channel model n order to calculate the LCR f for the sampled case. Ths calculaton s gven here for the FD-channel model, and n Appendx A, for a generc dscrete channel mpulse response. The spaced-frequency correlaton functon for the Raylegh case (see eq. (3-3)), leads

82 68 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate 8 error of approxmated level crossng prob. [%] r 6 db r 3 db r db r 3 db r 6 db correlaton coeffcent ρ c Fgure 3-4: Error of the approxmated level crossng probablty for the sampled case. Relatve error [%] as a functon of the correlaton coeffcent ρ c, wth r' as a parameter. to ρ c for the FD-channel model, wth ψ m φ H '( mf). For the two mportant specal cases of an exponentally decayng DPS (u ) and a rectangular DPS (u ), ρ c becomes for u ρ c + (πτ rmsf). (3-6) snc ( 3τ rmsf ) for u Introducng the seres expansons of the functons nvolved n the above expressons, the common approxmaton ρ c (πτ rms F) (3-7) s obtaned, n the lmt F. It s shown n Appendx A that the same approxmaton (3-7) holds for any arbtrary channel IR. Therefore, there s no dependency of the level crossng probablty on any of the channel model parameters, provded the channel s a Raylegh channel. The valdty of the approxmatons ntroduced s dscussed below Approxmated LCR f Inspecton of eqs. (3-6) and (3-7) suggests that the LCR f s proportonal to τ rms, for the followng reasons. Provded that the samplng theorem s not volated (.e., strctly speakng, for F ), the LCR f must be ndependent of the samplng nterval F. Therefore, the probablty (3-8) must be proportonal to F, to yeld a constant LCR f

83 3. Frequency-Doman Level Crossng Rate 69 wth (3-6). Ths mples that (3-8) s also proportonal to τ rms, because t s seen from (3-7) that F and τ rms have the same nfluence on ρ c. Thus the LCR f s proportonal to τ rms. Based on the approxmaton (3-5), ths observaton can be confrmed mathematcally. Wth (3-7) and (3-6), the LCR f for Raylegh fadng channels becomes N R ( r') r ' π r' e τ rms, (3-8) whch clearly shows the proportonalty. Note, moreover, that (3-8) s dentcal to the result of the contnuous-frequency analyss presented n Secton 3.. [cf. eq. (3-), for K (.e., ρ )]. Therefore, the dfference of the approxmaton (3-8) to the exact LCR f for the sampled case (whch can be calculated from (3-6) and (3-8) or (3-9), wth (3-6)) quantfes the mpact of a fnte samplng-nterval. Ths mpact s analyzed below Dscusson of the Impact of Samplng Results of LCR f vs. τ rms are depcted n Fgure 3-5a. Due to samplng effects, there s a devaton between the exact LCR f for the sampled case ( + + for u and for u ) and the lnear relaton obtaned from the contnuous model and the approxmatons ( { { ). An ncreasng number of level crossngs s mssed, when the samplng nterval s selected too large wth respect to the channel s τ rms. Fgure 3-5b llustrates the systematc estmaton error resultng from the applcaton of the lnear relaton (3-5) for estmatng τ rms from the power-frequency-scan of a channel wth a certan samplng nterval F. To analyze ths error, the exact LCR f s calculated from (3-6) and (3-8), wth (3-6) for a specfc τ rms F. (As seen from (3-6), the product τ rms F determnes ρ c, therefore, τ rms can be normalzed n ths way). The proportonal relaton (3-5) (and (3-8)) s appled to calculate the erroneous estmate τˆ rms for ths observed LCR f, leadng to the relatve estmaton error τˆ LCR rms f,sampled case ε τ. (3-9) τ LCR rms f, contnuous case Consderng the Nyqust theorem, the samplng nterval should be F /(τ max ), whch means at K (and u ) that τ rms F /, followng eq. (-4), Secton.3.3. In ths range of τ rms F, the maxmum bas s below 4 %, at r'. The errors ncrease for smaller thresholds r', where the fades get deeper and narrower, and also for larger ones (see Fgure 3-5b; curves and ). Investgatng the channel model wth the rectangular DPS,.e., u, the errors decrease, snce channels havng shorter mpulse responses mply hgher oversamplng (see Fgure 3-5b; curve, for r' ).

84 7 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate normalzed FD level crossng rate N R (r ) F proportonal relaton (contnuous case) samplng nterval F; u (exponental DPS) samplng nterval F; u (rectangular DPS) normalzed RMS delay spread and samplng nterval τ rms F (a) 5 relatve error [%] u ; r db u ; r 3 db u ; r 6 db u ; r db u ; r 3 db u ; r 6 db u ; r db normalzed samplng nterval τ F rms (b) Fgure 3-5: Influence of samplng on the proportonalty of τ rms and the LCR f. Parameters: Raylegh fadng; F Hz. (a): LCR f vs. τ rms at r', u {, }. Contnuous and sampled cases. (b): Relatve error of the proportonal relatonshp (contnuous case). All results for u except for, where u.

85 3. Frequency-Doman Level Crossng Rate Independence from the Channel Impulse Response A number of smulaton results are depcted n Fgure 3-6 n order to support the clamed ndependence of the relaton between the LCR f and τ rms from the channel IR. Sets of 5 mpulse responses were generated for ths purpose, where each IR conssted of L 5 rays wth unt varance, Raylegh dstrbuted magntudes, and arrval tmes beng unformly dstrbuted wthn a unt tme nterval. The IRs were then normalzed wth respect to power and τ rms. Next, the exact LCR f was calculated for each IR (for r' ), usng equatons (3-6) and (3-8) (or (3-9)), wth the correlaton coeffcent obtaned from (A-6) (see Appendx A). Fgure 3-6 llustrates the error compared wth the proportonalty relatonshp as a functon of the (normalzed) samplng nterval τ rms F. The errors mean, mnmum and maxmum values are ndcated as well as ther standard devaton. A systematc error s evdent from ths fgure, whch s zero at F and whch ncreases wth F. Remarkable are also the errors small standard devatons, meanng that ρ c s largely ndependent of the structure of the IR. Mnmum and maxmum values are evdence for an asymmetrc dstrbuton of errors about the mean. Thereby, above average values of ρ c lead to larger negatve errors of the LCR f. A smulaton for a smaller number of rays would show smlar mean errors, but ncreased standard devatons. To obey to the samplng theorem, F < (τ max ) (τ rms ) should be gven. In ths range of F, the mean error s less than ~ %. The mean error as a functon of F s com- relatve error of LCR f [%] mnmum error to maxmum error range mean of errors standard devaton of errors normalzed samplng nterval τ F rms Fgure 3-6: Relatve error of the LCR f compared wth the proportonal relaton (at r' ). These results are for smulated random mpulse responses wth L 5 rays.

86 7 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate parable to the curve shown n Fgure 3-5 for the case of the rectangular DPS. Indeed, the ensemble of smulated IRs agrees wth ths model of a rectangular average power delay profle Dscusson and Summary In Secton 3.., t was shown that a strct proportonal relatonshp exsts between the level crossng rate of a frequency-selectve rado channel n the frequency doman (LCR f, N R (r')), and the channel s RMS delay spread τ rms. Ths relaton s wrtten as N R ( r') τ rms f ( r', K, u) (3-5), where the proportonalty factor f ( r', K, u) s a functon of the threshold level at whch the LCR f s observed (r'), the Rcean K-factor of the channel (K), and channel parameters (expressed by u). It was suggested to use ths relaton for estmatng the channel s τ rms usng smple swept-frequency power measurements, from whch the LCR f can be determned. The measurement prncple s further dscussed n Secton 3.3. The Rcean K-factor can be determned pror to applyng (3-5). However, the mpact of the current channel on f ( r', K, u) (expressed by u) remans an uncertanty, and mght thus be a source of systematc estmaton errors. In Appendx A t s shown for Raylegh fadng channels that the channel model does not nfluence the proportonalty factor between the LCR f and τ rms. Ths fndng strongly supports the clam that the LCR f s a valuable means for estmatng τ rms n a smple way. Analytcal results from eq. (3-5) have shown that the proportonalty factor does depend on the channel model n the general Rcean case. The factor has been compared for wdely varyng channel models, suggestng that the mpact s very small and can thus be neglected n many cases. So s the dfference of f ( r', K, u) for a rectangular delay power profle and an exponentally decayng one less that 4 % at any K-factor, and at r'. A determnstc two-path channel model was analyzed n Secton 3.. to assess the relatonshp between the LCR f and τ rms. Although ths model s very dfferent to the Raylegh and Rcean stochastc models on whch eq. (3-5) was based, smlar proportonalty factors were found. The proportonalty relatonshp (3-5) was derved from the FD-channel model (see Secton.3), whch descrbes the frequency-selectve transfer functon of the multpath channel as a contnuous, WSS stochastc process. In Secton 3..3, the LCR f was derved for the sampled case,.e., for transfer functons gven at dscrete frequency-nstants. When the samplng nterval s selected too large, then some level-crossngs nbetween samplng nstants may be overlooked, and the LCR f devates from the value suggested by (3-5). The systematc errors ntroduced have been analyzed.

87 3.3 Applcaton to Channel Measurements Applcaton to Channel Measurements In ths Secton, we dscuss the applcaton of the relatonshp between the LCR f and the RMS delay spread τ rms for estmatng τ rms. A measurement procedure s ntroduced and valdated usng expermental data. Fnally, the estmaton accuracy s evaluated based on computer smulatons Channel Measurement Procedure A practcal channel measurement procedure based on the power response n the frequency doman s outlned n ths secton. Although the procedure operates only on power measurements, where no nformaton about the phase of the receved sgnal s avalable, all the mportant channel parameters (.e. the average receved power P, Rcean K-factor, RMS delay spread τ rms ) and ther statstcs can be obtan. The measurement setup comprses of a transmtter and a recever. The transmtter s made up of a sne wave generator, an up-converter, an amplfer, and a transmt antenna. The recever consst of an antenna, a preamplfer, a down-converter and a power meter (e.g. a spectrum analyzer) [] [4]. Calbraton measurements are necessary n order to evaluate the amount of nose and naccuracy caused by the system tself. Ths stage gves calbraton data, whch can then compensate for the frequency response of the measurement system. It also quantfes the nose caused by the system, whch s necessary to evaluate the nfluence of nose on the τ rms estmaton (see Secton 3.4). Once the calbraton data has been gathered, the channel measurements can be performed. For each pont wthn the frequency range to be measured (e.g. /τ rms bandwdth) the transmtter sends a sne sgnal, the power of whch s measured by the power meter tuned to the frequency of the transmtted wave. At the end of the procedure a sampled magntude transfer functon n the measured frequency range s composed R n H(nF), n {,,,N}. From the data, the channel parameters are obtaned n the followng steps:. Compensaton for the measurement system s characterstcs s performed by subtractng the calbraton data [db] from the measurement data. N. The average receved power Pˆ N n R n s estmated. 3. The Rcean K-factor s determned, e.g. by the method gven n [], based on the average power ˆP and the average ampltude ˆ N N Rn. R n 4. The RMS delay spread τˆ rms s estmated from the LCR f at threshold level r ˆP (.e., at r' ) 7, usng (3-5) and (3-3). 7 Other threshold levels could be selected as well, but r' s most smple to determne, t s close

88 74 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate The above procedure descrbes the steps to be followed to obtan the channel parameters from one measured TF. Several measurements performed at one partcular locaton can be combned, leadng to mproved estmaton results, as elaborated below Approxmaton of the Proportonalty Factor For measurements, the followng approxmaton of f(k,u,r') at u and r' can be used, whch results n errors below % for all values of K, compared to the exact f(k,u,r' ): 3/ ~ K +.34 K 4 f ( K, u, r' ) K + (3-3) K K > K Increasng the Effectve Measurement Bandwdth The accuracy obtaned depends heavly on the observaton bandwdth, snce the measurement method s based on a statstcal model. By ncreasng the bandwdth, the number of detected level crossngs s ncreased, and thus the accuracy of the estmated RDS s enhanced. A valuable advantage of the proposed method s found n the fact that because of ergodcty the observaton bandwdth can be extended not only by ncreasng the bandwdth of the measurement, but also by combnng data from several measurements that are performed wthn a local area. Ths local area must be suffcently small (maxmum sze 5 4λ) so that we can assume the channel parameters (and thus the statstcal propertes of the channel) to be constant. In other words, the shadowng must be constant (see Secton.). Data collected for such a cluster of measurements s analyzed as follows. The NRP and the K-factor are determned by smply combnng all measured ampltudes and calculatng Rˆ and ˆP for the resultng data set. Level crossng rates must be calculated for each measurement separately, but at a common threshold r'. Consecutvely, they are averaged to obtan the LCR f for the combned data set. The proposed method s evaluated below, usng channel measurements performed wth a network analyzer, and usng tme-doman channel smulatons Valdaton of the Method usng Measurement Results Coherent measurements conducted wth a network analyzer allow the calculaton of the channel s IR, from whch a reference-value of τ rms can be derved. Clusters of sx to the maxmum of the N R (r') curves thus yeldng nearly optmum accuracy, and the dependency of f(k,r',u) on u s very small at ths r' (cf. Fgure 3-a). One could also estmate τ rms at a set of threshold levels and consecutvely combne the estmates to enhance the accuracy. In [5], performance results are depcted for such a scheme, ndcatng some mprovement.

89 3.3 Applcaton to Channel Measurements 75 measurement theory normalzed level crossng rate N R (r )/τ rms threshold level r [db], normalzed to RMS ampltude (a) proportonalty factor N R (r )/τ rms at the RMS ampltude Rcean K factor (b) sngle spectra, GHz clusters combned, GHz theoretcal factor Fgure 3-7: (a): Comparson of measured and theoretcal level crossng rates for matched channel parameters. (b): Indcated ponts: Emprcal proportonalty factor between the estmated LCR f obtaned from the ampltude TF and the reference τ rms obtaned from the IR. Curve ( ): Theoretcal factor f(k,u,r' ). The msmatch ndcates the estmaton error. measurements were nvestgated wthn the local areas (of dameter λ). Each TF scanned had GHz bandwdth around a center frequency of.5 GHz [6] (see footnote 5 on page 35).

90 76 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate Fgure 3-7a shows the emprcal LCR f of one measured TF as a functon of r' and the analytcal curve for the estmated parameters Kˆ and τˆ rms (assumng u ). The good agreement demonstrates the sutablty of the FD-model for characterzng the frequency-selectve channel. To assess the accuracy of the estmated RDS, the proportonalty factor N ˆ R ( r' ) / τ rms s depcted n Fgure 3-7b as a functon of the Rcean K-factor. The estmated LCR f N ˆ ( r' R ) and K-factor Kˆ were derved from the ampltude TF R n H(nF) usng the proposed method to be evaluated and (the reference) τ rms was calculated from the channel IR usng a conventonal method [7], [8]. The RDS was estmated for every sngle measured TF and also for the combned data sets of each cluster of sx measurements. The theoretcal factor N R (r' )/τ rms f(k,,) s shown n the same fgure for comparson. The dstance between ths curve and the data ponts ndcates the estmaton error. It s observed from ths fgure that the estmaton error s decreased sgnfcantly by nvestgatng the combned data of the measurement clusters Valdaton by Tme-doman Channel Smulatons Channels obtaned from a tme-doman (TD) channel smulator were analyzed for evaluatng estmaton errors. Ths approach was taken because τ rms s defned from the channel s IR the output of the TD smulator Computer Smulaton Scheme The TD smulaton model assumes a lne-of-sght ray at τ, a Posson process of ray-arrvals (of approx. 6 rays), an exponentally decayng average power delay profle, Raylegh dstrbuted ray ampltudes, and unformly dstrbuted ray phases (compare [7] for one cluster; and Secton.5.3). In a second step, the generated mpulse responses were normalzed to get the requred K-factor K, τ rms and P [9], allowng for smple evaluaton of the estmaton error. Applyng the Fourer transform to the generated IRs, (complex-valued, dscrete-frequency) TFs were obtaned. The FD-samplng nterval of these TFs, F, s related to the maxmum delay spread τ max of the channel mpulse responses, whch can be wrtten as a functon of the Rcean K- factor and τ rms (see eq. (-4) on page 3). Usng ths expresson of τ max, the oversamplng factor OS s defned as OS τ F F max τ rms + In the smulatons of ths secton, OS was used. K +. (3-3) K

91 3.3 Applcaton to Channel Measurements Accuracy of the Estmaton Technque After generatng TFs for well-defned channel parameters, the RMS delay spreads were estmated usng the proposed procedure, yeldng τˆ rms. The estmaton error s defned as ε τ τ ˆ τ τ rms rms rms. (3-3) Performng smulatons for dfferent values of K and dfferent observaton bandwdths, the mean and standard devaton of the error ε τ are nvestgated. Results are depcted n Fgure 3-8a, as a functon of the normalzed observaton bandwdth. (The PDF of the estmaton error ε τ was observed to be approprately descrbed by a Gaussan dstrbuton.) For the estmaton method descrbed above, a small systematc estmaton error (~ 5 %) and decreasng standard devaton wth ncreased bandwdth can be seen from the results. The systematc error agrees farly wth the bas ntroduced by the samplng of the TF, whch was analyzed n Secton 3..3 for K. (Note that n the smulaton here τ rms F.5 at K.) The results gven n Fgure 3-5b can thus be used for cancelng ths systematc error. However, the bas s also partly caused by a bas n the estmated K-factors, because the K-factor estmaton s performed pror to the τ rms estmaton. An evaluaton of the accuracy of ths estmaton step s a recommended topc for further work. It can result n a compensaton table that ndcates the requred correctons as a functon of the normalzed samplng nterval and K-factor. In Fgure 3-8b, the standard devaton of the error s shown as a functon of the number of level crossngs. Ths dagram clearly reveals that the number of observed level crossngs determnes the estmaton accuracy. Note that the varance appears to be proportonal to the recprocal of the level crossng rate,.e., the standard devaton σ ( r'). ε τ N R The results gven n Fgure 3-8 specfy the estmaton error of τ rms compared to the local area mean parameters,.e., compared to the constant parameters of the WSSUS channel model. Consderng a lmted bandwdth, however, there s a certan varaton of the nstantaneous channel parameters wthn a local area anyway, because the structure of the mpulse response s not resolved completely (see Secton.). Ths varaton of the nstantaneous channel parameters was nvestgated n Secton..3 (see Fgure -). The results gven there should be compared to the accuracy of the novel estmaton technque for τ rms (Fgure 3-8), because the estmaton error of the novel method ncludes the varaton of the channel parameters due to the lmted observaton bandwdth.

92 78 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate relatve estmaton error of τ rms [%] RMS delay spread τ rms estmated from power transfer functon; OS standard devaton mean error K K K 4 K observaton bandwdth n /τ rms (a) standard devaton of the τ rms estmaton [%] RMS delay spread τ rms estmated from power transfer functon; OS K K K 4 K number of level crossngs observed (at r ) (b) Fgure 3-8: Relatve estmaton error of τ rms, derved from sets of hundred TD smulatons. (a): Mean and standard devaton of the estmaton error ε τ as a functon of the normalzed bandwdth. (b): Standard devaton of the estmaton error ε τ as a functon of the number of level crossngs. It s seen that the standard devatons of these parameters are n the same order of magntude as the estmaton errors of the proposed τ rms estmaton technque. The stan-

93 3.4 Analyss of the Influence of Nose 79 dard devaton of τ rms due to bandwdth lmtaton s by a factor of about two below the standard devaton of the estmaton error, at a gven bandwdth. The error between the estmated τ rms and the nstantaneous τ rms was also evaluated n order to analyze the correlaton between the two values. A small decrease of standard devaton compared wth the result shown n Fgure 3-8 (about %) ndcates that the devatons from the local-area-mean parameters are partly correlated. A correlaton coeffcent of about.45 was obtaned from the computer smulatons Dscusson of the Measurement Method It s seen that the RDS can be estmated wth reasonable accuracy when the observaton bandwdth s larger than /τ rms, or when more than ten level crossngs are present. Whle the requred bandwdth mght be hgher than the bandwdth needed for other measurement technques, t can be ncreased easly by combnng multple measurements performed wthn a small local area. Another advantage les n the smplcty of the hardware that can be used. It makes the method partcularly nterestng at extremely hgh frequences (mllmeter wave band), where e.g. network analyzers become very expensve and cumbersome due to the phase reference requred, whch s very dffcult to provde over large dstances. A clear advantage compared to other channel soundng technques s that no specfc equpment must be desgned. A contnuous wave frequency generator and a power meter or spectrum analyzer may be used to collect measurement data. Prelmnary measurement campagns performed at Delft Unversty of Technology ([] [4]) have shown the practcal sutablty of the descrbed methods. But they have also led to the dscovery of an nterestng problem. Even a small measurement nose level may ncrease the number of level crossngs detected. Improved measurement methods have been proposed n these references to reduce ths effect. The followng secton gves the theoretcal analyss of the mpact of measurement nose. These nvestgatons show that the frequency-doman samplng nterval of the measurements should be selected as large as possble to mnmze the nfluence of nose. 3.4 Analyss of the Influence of Nose A major practcal problem of the novel technque for estmatng τ rms s ts senstvty to addtve nose n the measured power TF. Ths nose may ntroduce addtonal level crossngs and thus lead to systematc overestmaton of τ rms, as llustrated n Fgure 3-9. In ths secton, the nfluence of nose on the LCR f s analyzed mathematcally. Introducng the nose to the frequency-doman (FD) channel model, whch s modeled as a contnuous stochastc process, quantfes the mpact of nose for the general case of Rcean fadng channels. However, ths analyss s not suffcent, because a measurement s typcally performed on dscrete-frequency nstants, spaced by the samplng

94 8 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate transfer functon magntude [db] transfer functon wthout nose 64 threshold up crossngs frequency [MHz] (a) transfer functon magntude [db] transfer functon wth nose 64 threshold up crossngs frequency [MHz] (b) Fgure 3-9: Influence of nose on the level crossng rate. (a): Channel transfer functon wthout addtve nose. (b): Channel transfer functon wth addtve nose. nterval F. The result from the analyss of the contnuous-tme model predcts a large mpact of the samplng nterval on the nose s nfluence, but t fals to descrbe that mpact accurately, due to the napproprate mathematcal model. To elaborate on ths effect, we also nvestgate the LCR f for the sampled case. Ths analyss s agan lmted to Raylegh channels, however. The analytcal results presented can be used for evaluatng the systematc estmaton

95 3.4 Analyss of the Influence of Nose 8 error due to a gven nose level. Unfortunately, the result s less sutable for correctng ths systematc error. Computer smulatons have ndcated that applyng the analytcal result can ndeed reduce the systematc estmaton error; the error s varance, however, s boosted at the same tme. More successfully, a method was appled that reduces the nfluence of nose on the counted LCR f by ntroducng a second threshold []. Thereby, level crossngs are gnored, whch are lkely due to nose and not due to fades. For a good performance, the threshold separaton must be adapted to the nose and channel parameters. Ths method s presented n Secton and basc performance results are gven Mathematcal Modelng The measurement nose s ntroduced to the FD-channel model (see eq. (3-), Secton 3.. and Secton.3) as an addtve band-lmted Gaussan nose component. To model the ndependence of the addtve nose samples, band-lmtaton to ±/(F) s assumed, where F [Hz] s the samplng nterval n the frequency-doman. Note that the samplng nterval has been ntroduced although the mathematcal model s a contnuous one. The magntude of the nose process s defned by the power densty Π N [/s], yeldng the nose power P N Π N /F E{ n n }. The {n n } denote ndependent complex Gaussan nose samples that are added to the complex-valued TF H(nF). The FDchannel model and the model for the nose process are depcted n Fgure 3-. measurement nose /(F) Π N drect path (lne-of-sght) Π φ h (τ) [db] ρ τ constant-level part γ exponentally decayng part Excess delay τ [s] /(F) Fgure 3-: Model of the delay power spectrum (DPS) wth addtve measurement nose Defntons The nose power s related to the varance of the (zero-mean) complex Gaussan nose process underlyng the Rcean fadng process. Ths s wrtten N' P N /(ψ ), where ψ φh '() Π u γ. φ H' ( f) s the auto-covarance of the channel transfer functon (see eq. (3-3)). (Note that the lne-of-sght component s excluded from the normalzaton term.) The addtve nose component ncreases the average power of the observed TF and t decreases the K-factor as

96 8 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate ~ N' P P + PN ρ + ψ ( + N') P + K +. (3-33) ~ K K ( + N') Independence of the nose processes s assumed. The tlde ndcates parameters nfluenced by the addtve nose. Snce usually N' <<, ths nfluence s small and can be neglected n the mathematcal dervatons and n channel parameter estmaton. That ~ ~ s, K K P P, and furthermore ~ r ' r'., The above defntons specfy the frst order statstcs,.e., (the change of) the ampltude dstrbuton. Second order statstcs, as the LCR f can be derved from the spacedfrequency correlaton functon, whch for our model s gven by ~ φ ( f ) φ H φ ( f ) H H ( f ) + P N snc( f / F); j πτ f e. (3-34) jπτ f ρ + Π τ snc( τ f ) e + γ + jπ f It wll be seen below that the nfluence of nose depends strongly on the samplng nterval F. Therefore, ths parameter must be approprately defned. Accordng to Nyqust s samplng theorem, F /(τ max ) must be gven, where τ max s the maxmum excess delay of the channel. The oversamplng factor OS, as defned by eq. (3-3) wll be used to specfy F n relaton to τ rms and K. Calculatng the level crossng rate for the contnuous model descrbed above (usng the equatons gven n Secton 3..) yelds a compact expresson quantfyng the mpact of nose for Rcean channels. These dervatons are outlned n Secton 3.4. and n Appendx B. In practce, however, the LCR f s determned from measurements taken at dscrete frequency nstants. The LCR f s qute senstve to ths samplng; therefore we also analyze the LCR f for the sampled case, called the dscrete-frequency LCR f (see Secton 3.4.3). Ths analyss s lmted to the Raylegh fadng case, however. For the Rcean case, a constant correcton factor s ntroduced to the result from the contnuous-frequency analyss, whch can partly correct for samplng effects (Secton 3.4..) Dervaton of LCR f from the Contnuous FD-Channel Model It s shown n Secton 3.. that wthout addtve nose, the LCR f, N R (r'), and the RMS delay spread τ rms are proportonal as N R ( r') τ rms f ( r', K, u) (3-5). The proportonalty factor f(r',k,u) the normalzed LCR f (of a channel havng τ rms ) s a functon of the Rcean K-factor K, the normalzed threshold level r ' r P (normalzed to the average power), and the channel model parameter u. The latter has lttle mpact on f(r',k,u) and can thus be let u n practce (see Fgure 3- and Fgure 3-3). The straght, dashed lnes n Fgure 3- show ths proportonalty relatonshp. In or-

97 3.4 Analyss of the Influence of Nose 83 frequency doman level crossng rate N R (r ) [s] K K 6 db K db prop. w/o nose RMS delay spread τ [s] rms Fgure 3-: Relaton between τ rms and the LCR f wth and wthout nose. The asymptotc behavor s seen. Relatve nose power N'.; samplng nterval F Hz. LCR f for r' and c s. der to apply t for estmatng τ rms, the factor f(r',k,u) must be known. It can be calculated from eq. (3-8) wth (3-9), or from the approxmaton (3-3). Measurement nose may rase the level crossng rate for a gven channel. The dea of ths analyss s to quantfy the mpact of nose on the LCR f, and to use the resultng equaton for correctng for t. Wth the mathematcal model and the defntons ntroduced n Secton 3.4., and wth two approxmatons (see Appendx B), a rather smple relaton (3-35) between the ~ LCR f nfluenced by nose, ( r '), and τ rms s found. N R ( ~ N' N ( r') ) c h ( r', K) τ f ( r', K, u) R s rms (3-35) F Fgure 3- llustrates ts behavor for varous K-factors. It s seen that nose determnes the level crossng rate at low τ rms, where the number of level crossngs due to the multpath channel s low. Just as the factor f(r',k,u) s the normalzed LCR f for the multpath rado channel, so s h(r',k) the LCR f for the addtve, uncorrelated measurement nose, scaled by N' F ( 8 ). Note that ths result was obtaned from the contnuous FD-channel model, consderng nose wth a flat, band-lmted spectrum. The constant c s s used to correct for 8 Ths statement becomes clear when the specal case of a flat fadng channel s consdered (.e., τ rms ), where level crossngs are due to nose only.

98 84 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate.38 factor h(r,k) h(r,k) Rcean K factor [db] Fgure 3-: Evaluaton of h(r',k) at r'. samplng effects that are overlooked by ths approach. A thorough explanaton of ths ssue and the value of c s are gven n Secton Note that the rght-hand-sde of (3-35) s the LCR f for the noseless case (compare eq. (3-5)), therefore, the left-hand-sde quantfes the nfluence of nose on the LCR f. To evaluate the expresson, the factor h(r',k) s needed, whch s shown n Fgure 3- as a functon of K, at r'. It s obtaned from (see Appendx B) ( r' K( K ) ) π r ' ( ) ( ', ) ' ( + ) K + K h r K r K e I +, (3-36) 3 where I s the zero-th order modfed Bessel functon of the frst knd. The components of the LCR f due to the fadng channel and due to measurement nose, and the total LCR f can be seen as the sdes of a rght-angled trangle. Its hypotenuse stands for the LCR f of the nosy measurement, whle the adjacent sdes are the component LCRs, as llustrated n Fgure 3-3. It appears that the two uncorrelated nose processes correspond to LCR-components n orthogonal drectons of a plane, whle ther vector sum s length corresponds to the total LCR. Note that ths observaton was made from (3-35). It was not tred to prove mathematcally f ths s a general property of the LCR of sums of (ndependent) stochastc processes. The nature of the square root n (3-35) ndcates that the estmaton of τ rms becomes ~ more dffcult when the measured LCR f, ( r '), gets n the range of the subtracted N R ~ N R ( r ' ) nose N' csh( r', K ) F LCR f due to measurement nose nfluenced LCR f τ rms f ( r', K, u) LCR f due to frequency-selectvty Fgure 3-3: Interrelaton of level crossng rates n the nose-nfluenced case.

99 3.4 Analyss of the Influence of Nose 85 term ( N' F) cs h( r', K). No meanngful result can be obtaned when t s smaller than ths value. Ths dffculty s also seen from Fgure 3- and Fgure 3-3. It corresponds to the case where the observed LCR f s less than the (expected) LCR f -component due to the (specfed) measurement nose. In Fgure 3-, ths value s seen as the LCR f at τ rms. In Fgure 3-3 t would mean that the hypotenuse becomes shorter than the sde representng the nose component, whch s mpossble. A man concluson drawn from (3-35) s that the samplng nterval F has a major mpact on the nfluence of nose. Doublng the samplng nterval has the same effect as reducng the nose power by a factor of four. Whle the samplng nterval can be easly ncreased as long as the samplng theorem s not volated, t s usually very dffcult to reduce the nose. Thus the samplng nterval should always be selected as large as possble. An over-sampled measurement should be down-sampled approprately pror to the estmaton of τ rms Correctng for Samplng Effects The soluton gven by eq. (3-35) was obtaned through the ntroducton of the measurement nose to the contnuous tme (and -frequency) model shown n Secton The measurement s done on dscrete frequency nstants however, whch leads to a systematc underestmaton of the LCR f compared to the theory, because the contnuous model also consders level crossngs n-between samplng ponts. Such crossngs occur mostly due to the nterpolaton mpled by the flat, band-lmted model for the measurement nose (see also []). Computer smulatons have been performed n order to quantfy ths error and to n factor h(r,k) systematc error n h(r, K) due to samplng effects.4. theoretcal smulaton; N db smulaton; N db smulaton; N 3 db smulaton; N 4 db... Rcean K factor Fgure 3-4: Smulated factor h(r',k) compared to the theoretcal one. A constant offset of approx. % s observed.

100 86 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate vestgate the possblty of ncorporatng t n the constant h(r',k). Results are depcted n Fgure 3-4, where the smulated h(r',k) as a functon of K s compared to the theoretcal one, at r'. The smulaton was performed for dfferent values of N'. Ensembles of flat-fadng channels (τ rms ) wth Rcean ampltude dstrbuton accordng to K were generated. It s observed that the smulated h(r',k) s below the theoretcal one, by approxmately %. Multplcaton of h(r',k) n eq. (3-35) by c s.78 can account for ths modelng error. The sutablty of ths correcton factor wll be seen from numercal evaluatons and computer smulatons presented below Dscrete-Frequency Analyss for Raylegh Channels The correcton factor c s can account for the modelng defcences of the addtve nose process. However, as the samplng nterval s ncreased, also level crossngs may be overlooked, whch are due to fades. For Raylegh channels, all effects related to the samplng of the nosy magntude TF can be extracted from the dscrete-frequency analyss presented n Secton The LCR f for a dscrete Raylegh process has been shown to be a functon of the threshold level r', and the correlaton coeffcent between the squared magntudes of adjacent samples, ρ c. In order to evaluate the mpact of nose, ths correlaton coeffcent has to be determned for the frequency-selectve channel plus addtve nose. ρ c s related to the auto-correlaton coeffcents of the underlyng complex Gaussan * process Z n as ρ c ψ ψ, where ψ E { Z } nz n+. Eq. (3-6) gves the correlaton coeffcent for the noseless case, for an exponentally decayng and a rectangular delay spectrum. In the lmt F, ρ c can be approxmated as gven n eq. (3-7), regardless of the channel model or channel mpulse response. For the LCR f wth nose, we fnd ~ ρc ρ c. (3-37) ( + N') The exact expressons for ~ ρ c (.e., (3-37) wth (3-6)), together wth (3-8) (or (3-9)), s used n Secton to evaluate the nfluence of the samplng nterval on the LCR f. Approxmaton (3-7) s used below to verfy the equaton for the nose nfluenced LCR f obtaned from the contnuous model, (3-35), and to evaluate c s analytcally Valdaton of the Result Obtaned from the Contnuous Model In the lmt ρ c, the level crossng probablty for the sampled case can be approxmated by eq. (3-5) (see Secton 3..3.). Ths condton s fulflled for F (meanng that the contnuous case s approached) and for N' <<. Under these assumptons, and usng (3-37) and approxmaton (3-7), the LCR f for nose nfluenced Raylegh

101 3.4 Analyss of the Influence of Nose 87 fadng channels becomes ~ r ' N' N ( ') ' R r π r e + τ rms. (3-38) F π After some manpulatons t s seen that ths equaton s equvalent to (3-35), for K. Based on ths result we can also verfy the value of c s for Raylegh channels. Lettng τ rms leads to the specal case of the flat channel, where level crossngs are caused by the addtve nose only. Comparng (3-38) and (3-35) then gves c r ' s h( r', K ) / π r' e. (3-39) From ths expresson and (3-36) (for K ) follows c s 6 π. 78. The smulaton results shown n Fgure 3-4 suggest that ths correcton factor s also approprate for any other K-factor Evaluaton and Applcaton of the Analytcal Results Dscusson of the Analytcal Results for Raylegh Channels In ths sub-secton, we study the applcablty and the lmtatons of the analytcal expressons as derved above, for Raylegh channels. The relaton between τ rms and the LCR f s depcted n Fgure 3-5a for the noseless and the nose-corrupted cases. The results from the contnuous analyss (eqs. (3-5) and (3-35)) for the nose-corrupted case wth and wthout the correcton factor c s,.e., for c s {,.78} and the exact results from the dscrete analyss ((3-6) and (3-8), wth (3-37) and (3-6), for u ) are compared. Fgure 3-5b shows the relatve systematc error of the smpler and more general results from the contnuous model compared wth the exact results from the dscrete analyss. For all curves, the RMS ampltude was taken as the threshold level for calculatng LCR f,.e., r'. A fxed samplng nterval F Hz and a fxed, relatve nose strength N'. were selected. A thorough analyss of the noseless case was gven n Secton The relatve estmaton error ε τ s also defned there, n eq. (3-9). The presence of measurement nose causes an ncrease of the LCR f. The relatve ncrease s largest n the regon of low τ rms, where the level crossngs due to nose get domnant. The error of (3-35) (contnuous case) wthout correcton (.e., for c s ) s seen to rase towards % as τ rms (curves n Fgure 3-5a and b). Ths llustrates the samplng effects for the addtve nose that were dscussed n Secton When the correcton factor c s.78 s ntroduced, the curves for the dscrete and the contnuous analyss agree well, f τ rms /(F) (Fgure 3-5a, + + and { { ). For larger τ rms, the nfluence of the samplng s leadng to devatons, as n

102 88 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate frequency doman level crossng rate N R (r ) [s] wth nose contnuous model; no nose dscrete model; no nose contnuous model; wth nose dscrete model; wth nose cont. mod.; corrected; wth nose noseless RMS delay spread τ [s] rms (a) systematc relatve error [%] at r 5 5 no nose wth nose; orgnal relaton (c s ) wth nose; corrected relaton (c s.78) RMS delay spread τ rms [s] (b) Fgure 3-5: Influence of nose and samplng on the relaton of τ rms and the LCR f. Raylegh fadng; nose power N'.; samplng nterval f s Hz; u, r'. (a): LCR f vs. τ rms. (b): Relatve error of the relaton obtaned from the contnuous model vs. τ rms. the noseless case. Thereby, the relatve error s very smlar to the one for the noseless case (compare { { and + + n Fgure 3-5b). Close nspecton reveals a small resdual error < % at τ rms, whch s due to the approxmaton + N', used n (3-35). Ths error reduces for smaller N'.

103 3.4 Analyss of the Influence of Nose Influence of Nose on Estmatng τ rms In ths sub-secton we nvestgate the systematc error resultng from the applcaton of the conventonal, lnear relatonshp for estmatng τ rms from nose-afflcted measurements of the LCR f. That s, (3-5) s used to derve τˆ rms from a nose-nfluenced LCR f, whch s ether obtaned from the equatons presented above (see Fgure 3-6a), or from smulated channel transfer functons (see Fgure 3-6b). The relatve errors shown are derved equvalently to (3-9), but ths tme the errors due to nose were to be evaluated,.e. τˆ LCR rms f, nfluenced ε nose τ. (3-4) τ LCR rms f, noseless All results are shown as a functon of the nose power N', at r'. Parameters are the Rcean K-factor, and the samplng nterval expressed by the oversamplng factor OS (3-3). We frst dscuss the analytcal results depcted n Fgure 3-6a. As expected, the addtve measurement nose ncreases the LCR f f t exceeds a certan value. The mportant role of the samplng nterval F s notced. Doublng F has the same effect as reducng the nose power by a factor of four ( 6 db), accordng to the above equatons. At OS, the systematc error stays below ~ %, f the nose power expressed by N' s below ~ 8 db. Due to the defnton of OS as a functon of F and K (3-3), the Rcean K-factor seems to have lttle nfluence on the results. For the Raylegh fadng case, the nose-nfluenced LCR f was calculated from the equatons for the dscrete analyss and from the equatons for the contnuous model. The dfference among them corresponds to the mpact of the samplng nterval F f t s selected too large. (That s, when level crossngs due to fades are mssed, because the samplng theorem s volated). As seen from Fgure 3-6a, and from Fgure 3-5, the contnuous analyss fals to descrbe these effects. It only descrbes the mpact of addtve nose. An oversamplng factor of.5 leads to systematc underestmaton of τ rms by ~ % (n the absence of nose). Snce nose tends to ncrease the LCR f, those adverse effects partly cancel, therefore, about 5 db more nose can be tolerated for OS.5, compared to OS. The analytcal results have been valdated by computer smulatons, usng the smulaton scheme ntroduced n Secton Complex nose samples were added to the generated transfer functons (TF) to ntroduce the measurement nose. Consecutvely, the measurement procedures were appled to the TFs ampltudes. The mean values and standard devatons of relatve estmaton errors were derved from ensembles of 9 The computer smulatons n ths secton have been performed by Govann Landman. More smulaton results can be found n [].

104 9 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate K ; cont. model corrected K ; cont. model corrected K 4; cont. model corrected K ; cont. model corrected K ; dscrete model estmaton error [%] OS OS OS rato of nose power to scattered power (N ) [db] (a) % error of smulaton compared to theory (ε τ ) K K K 4 K Rato of nose power to scattered power (N ) [db] (b) Fgure 3-6: Bas of the standard estmaton method as a functon of measurement nose power. Parameters are the Rcean K-factor, and the samplng nterval expressed by the oversamplng factor OS. The LCR f s evaluated at r'. (a): Analytcal results; (b): Smulaton results; OS smulated channels. In Fgure 3-6b, smulaton results (mean-errors) are depcted for OS. A good match wth the theoretcal results s evdent. The errors standard devatons are dscussed below.

105 3.4 Analyss of the Influence of Nose Standard Devatons of Estmaton Errors It was seen from the comparson of the analytcal results and computer smulaton results that the analytcal expressons provde a relable predcton of the nose-nduced bas of the τ rms -estmates. In ths secton, smulaton results are used to evaluate the standard devatons of the estmates. The standard estmaton method employng eq. (3-5) s analyzed here. The errors standard devatons depend on the observaton bandwdth. Larger bandwdth mples that more level crossngs can be observed, therefore, the performance of the statstcal method for estmatng τ rms mproves. Smulaton results as a functon of the bandwdth were shown n Secton It s seen that the standard devaton s approx. 5 % for an observed bandwdth of /τ rms. Ths bandwdth was used n all further smulatons. τ rms was estmated from the LCR f at r'. In the presence of nose, a deteroraton s seen as N' s ncreased, because the addtve nose reduces the accuracy of the LCR f determned from the TF (see Fgure 3-7; lnes marked by + ). The smulaton shown s for K and for two-fold oversamplng. The other lnes n ths fgure are dscussed n Sectons and Standard method Analytc method wth correcton Nose reducng method (wth nd threshold) 4 Standard devaton [%] Rato of nose power to scattered power (N ) [db] Fgure 3-7: Standard devatons of the τ rms estmaton errors as a functon of the power of the addtve nose. τ rms s estmated from the LCR f at r', usng dfferent estmaton methods. K, OS Nose Cancellaton by Applyng the Analytcal Results In Fgure 3-8, the performance of the RMS delay spread estmaton method s depcted, ths tme when nose s accounted for by usng (3-35) the analytcal result allowng to separate the nose s component from the LCR f wth c s.78. All results are for an oversamplng factor of two (OS ) and τ rms estmated from the LCR f at r'.

106 9 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate % error of smulaton compared to theory (ε τ ) K K 9 K 4 K Rato of nose power to scattered power (N ) [db] Fgure 3-8: Systematc estmaton error of τ rms usng the analytcal relatonshp for correctng for nose. OS ; c s.78; LCR f determned at r'. Some mprovement can be seen for ths extended method (compare Fgure 3-8 and Fgure 3-6), however, τ rms s underestmated at hgh N'. The underestmaton s due to the applcaton of the non-lnear (hyperbolc) relaton (3-35) for estmatng τ rms from the nose-corrupted LCR f (see Fgure 3-). Consderng that the measured LCR f -values have a certan standard devaton (dependng on the observaton bandwdth), the non-lnear translaton curve ntroduces some bas to the estmates. In partcular, when the measured LCR f s lower than the subtracted nose term, then the square root n (3-35) gets a negatve argument. In these cases, the τ rms value was taken as zero, whch adds to ths bas. Also the estmates varance s ncreased when usng eq. (3-35), because the transformaton functons (see Fgure 3-) get flatter as the nfluence of nose ncreases. Ths s confrmed by the standard devaton results shown n Fgure 3-7b (curve marked by ). Whle the systematc errors suggest that approx. 5 db more nose can be tolerated when nose s corrected for by usng (3-35) wth c s.78, the errors standard devatons show that the estmates are thereby gettng far less accurate. We conclude that the orgnal measurement procedure utlzng eq. (3-5) can be used n the area where the systematc error due to nose s suffcently small. Eq. (3-35) (wth c s.78) can be used to dentfy ths area. Robust measurement methods as the one descrbed below should be appled f nose cannot be neglected A Robust Measurement Procedure A robust measurement procedure s brefly dscussed n ths secton, whch was suggested by Chrs van den Bos and studed by the author n cooperaton wth Adran

107 3.4 Analyss of the Influence of Nose 93 transfer functon magntude [db] transfer functon wth nose 63 man threshold valdaton threshold 64 up crossngs accepted up crossngs frequency [MHz] Fgure 3-9: Illustraton of the robust measurement method usng a valdaton threshold. Bohdanowcz. The dea of ths method s to neglect durng the countng process level crossngs that are lkely due to nose and not due to the fadng Introducton of an Addtonal Threshold The proposed algorthm augments the standard procedure for determnng the FD-level crossng rate by ntroducng an addtonal threshold, whch s then used to valdate the level crossngs through the standard threshold (see Fgure 3-9). The modfed algorthm works as follows. Frstly, the crossngs through the standard threshold are dentfed n the measured data. Then, for each crossng, the data between two crossngs (the one, whch s nvestgated and the next one) s analyzed. If there s a crossng through the addtonal threshold (placed above the standard one) wthn the analyzed nterval, the crossng s accepted. If, however, the data does not exceed the addtonal threshold wthn the nterval, the crossng s rejected. As a result, only the crossngs lkely caused by the channel varablty are counted. The method was used by A. Bohdanowcz n hs measurement campagn as presented n []. Although the promsng potental of reducng the nfluence of nose from the calculaton of the LCR was presented there, no detaled nvestgaton of the method s performance was gven. In the followng secton, we nvestgate ths method wth a relaton to the parameters of the underlyng channel model, based on computer smulatons. No attempt was made to descrbe the performance or the requred parameters C. v. d. Bos and A. Bohdanowcz are wth the Ubqutous Communcatons Program, Delft Unversty of Technology, Department of Electrcal Engneerng.

108 94 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate % error of smulaton compared to theory (ε τ ) K K K4 K Rato of nose power to scattered power (N ) [db] (a).5 K K K4 K threshold separaton [db] Rato of nose power to scattered power (N ) [db] (b) Fgure 3-. (a): Systematc estmaton error of τ rms for the two-threshold method; OS ; LCR f determned at r'. (b): Optmal threshold separatons for OS. analytcally Performance of the Method A large set of channel mpulse responses s generated as descrbed n Secton For each nose level N' and Rcean K-factor, the optmal threshold separaton s then calculated by means of mnmzng the error of the estmated τ rms. The smulaton re-

109 3.4 Analyss of the Influence of Nose 95 % error of smulaton compared to theory (ε τ ) K K K4 K Rato of nose power to scattered power (N ) [db] Fgure 3-. Systematc estmaton error of τ rms wth a global threshold separaton of db. OS ; LCR f determned at r'. sults of the proposed method are depcted n Fgure 3-a, whereas the optmal settngs of the proposed flterng method (the optmal threshold separatons) are shown n Fgure 3-b (for OS ). By comparng the results from Fgure 3-a wth those presented n Fgure 3-6b, one can conclude that, ndeed, the method can be used to reduce the nfluence of nose on the RDS estmaton. The comparson shows that for hgher values of N' the estmaton error s drastcally reduced, whle for low values, effectvely no flterng s requred and the method performs as well as the one based on the standard LCR calculaton. The method can be used to ncrease the accuracy of the τ rms estmaton at the presence of a sgnfcant nose level, but the threshold separaton must be set approprately (see Fgure 3-b). It s seen from Fgure 3-7 that the mpact of nose on the standard devaton of the estmates has also mproved sgnfcantly (curve marked by ), compared to the other methods. The results presented n Fgure 3-b show that the optmal threshold separaton s a functon of two parameters, N' and K. Although we do not provde the explct formula for ths relaton, the curves from Fgure 3-b can be followed n practcal applcatons to set the correct threshold separaton for each measurement. A dfferent oversamplng factor (approxmately) shfts the curves for OS to the left or rght by log(os/) db. The mportance of the threshold separaton s presented n Fgure 3-, where a common value was used for all the measurements. Better performance at hgher values of N' (when compared to Fgure 3-6b) s pad by an ncreased underestmaton of RDS n the range of low N' values.

110 96 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate Extended Measurement Procedure The measurement procedure ntroduced n Secton 3.3. may be extended f measurement nose s an ssue that cannot be neglected. Agan the procedure starts wth the acquston of calbraton data, from whch also the nose power s derved. Consecutvely, sampled magntude transfer functons of the channel R n H(nF), n {,,,N} are measured. From the data, the channel parameters are obtaned n the followng steps, whch nclude testng for the necessty of nose-suppresson:. Compensaton for the measurement system s characterstcs s performed by subtractng the calbraton data [db] from the measured transfer functon. N. The average receved power Pˆ N n R n s estmated. 3. The Rcean K-factor s determned, e.g. by the method gven n [], based on the N average power ˆP and the average ampltude R ˆ N n R n. Note that nose has neglgble nfluence on ths and on the prevous step, f N' ~. (compare (3-33)). 4. Based on the nose power, samplng nterval, and Rcean K-factor, the ncrease of the LCR f due to nose s evaluated, employng eq. (3-35). 5. The RMS delay spread τˆ rms s estmated from the LCR f at threshold level r ˆP (.e., at r' ), usng (3-5) and (3-3). If accordng to the prevous step, nose cannot be neglected, then the LCR f s determned by the robust method descrbed n Secton Conclusons and Recommendatons In ths chapter, an elaborate study of the frequency-doman level crossng rate (LCR f ) of a frequency-selectve rado channel s presented. The LCR f s the average number of up-gong level crossngs of the channel transfer functon (wth respect to a specfed threshold) per unt of bandwdth. It has been derved analytcally from second order statstcal propertes of the FD-channel model, whch was proposed n Chapter, Secton.3. Usng these analytcal results, the nfluence of channel parameters has been nvestgated. It was observed that the RMS delay spread τ rms s proportonal to the absolute value of the LCR f, whle the Rcean K-factor determnes the shape of the LCR f -functon vs. the threshold level. That s, τ rms specfes the number of fades per bandwdth and K ndcates the depth of the fades. By defnng the threshold level relatve to the normalzed receved power P of the channel, any dependency of the LCR f on P s elmnated. Snce these three parameters {τ rms, K, P } have such dstnct and dfferent effects on the LCR f, t was concluded that they comprse a most sgnfcant set of parameters to specfy frequency-selectve rado channels.

111 3.6 References 97 It was observed that other parameters descrbng the channel model have lttle mpact on the LCR f, as for nstance the shape of the delay power spectrum or the actual structure of the channel mpulse response. For Raylegh fadng channels, t has been shown that any dependency on the channel mpulse response dsappears, provded that the samplng nterval s suffcently small. Because of the proportonalty between the LCR f and τ rms, rather smple swept-frequency power measurements can be used to estmate the three most relevant channel parameters {τ rms, K, P }. Standard procedures allow determnng P and K, whle the newly dscovered relaton leads to estmates of τ rms. The estmaton accuracy of ths technque depends on the observaton bandwdth. It can be enhanced by combnng multple measurements performed wthn a small local area. Unfortunately, the method to determne τ rms s qute senstve to measurement nose. The nfluence of nose on the proportonalty relaton has been analyzed, yeldng a compact expresson that allows the separaton of the channel s and the nose s contrbutons to the level-crossng rate. The analytcal result shows that ncreasng the frequency-doman samplng-nterval by a partcular factor has the same effect as reducng the nose power by the square of ths factor, whch s thus a valuable means of nose reducton. Thereby t s mportant not to volate aganst the samplng theorem. Moreover, the analytcal results can be used for partal compensaton of the nfluence of nose. Unfortunately, ths technque ncreases the standard devaton of the estmated τ rms. To enhance the robustness aganst nose, another method s presented, whch uses two thresholds when countng the level-crossng rate. Ths allows for dentfcaton and removal of level crossngs that are lkely caused by nose and not by fades. The drawback of ths technque s that the threshold separaton must be adapted accordng to nose and channel parameters to get the optmum result. Selectng the threshold approprately, both the mean and standard devaton of the estmaton errors reman close to the noseless case. A fxed threshold separaton leads to sub-optmum results. Fndng analytc expressons for the optmum threshold separaton s subject for further work, as well as the approprate estmaton of the nose power. 3.6 References [] F. van der Wjk, A. Kegel, and R. Prasad, Assessment of a pco-cellular system usng propagaton measurements at.9 GHz for ndoor wreless communcatons, IEEE Trans. Veh. Technol., vol. 44, no., pp. 55 6, Feb. 995.

112 98 Chapter 3 Channel Measurement Technque based on the FD-Level Crossng Rate [] B. P. Donaldson, M. Fattouche, and R. W. Donaldson, Characterzaton of nbuldng UHF wreless rado communcaton channels usng spectral energy measurements, IEEE Trans. on Antennas and Prop., vol. 44, no., pp. 8 86, Jan [3] M. Pätzold, U. Kllat, F. Laue and Y. L, On the Statstcal Propertes of Determnstc Smulaton Models for Moble Fadng Channels, IEEE Trans. Veh. Technol., Vol. 47, No., pp , Feb [4] S. O. Rce, Mathematcal Analyss of Random Nose, Bell Syst. Tech. J., vol. 3, pp. 8 33, July 944; vol. 4, pp , Jan [5] S. O. Rce, Statstcal Propertes of a Sne Wave Plus Random Nose, Bell Syst. Tech. J., vol. 7, pp. 9 57, 948. [6] K. Wtrsal, Y.-H. Km, and R. Prasad, RMS delay spread estmaton technque usng non-coherent channel measurements, IEE Electroncs Letters, vol. 34, no., pp , Oct [7] W. C. Jakes Jr., Mcrowave Moble Communcatons. New York: Wley-Interscence, 974. [8] M. Schwartz, W. R. Bennett, and S. Sten, Communcaton Systems and Technques. New York: McGraw-Hll, 966. [9] J. G. Proaks, Dgtal Communcatons, 3 rd Edton. New York: McGraw Hll, 995. [] M. K. Smon and M.-S. Aloun, A Smple Sngle Integral Representaton of the Bvarate Raylegh Dstrbuton, IEEE Commun. Letters, vol., no. 5, pp. 8 3, May 998. [] A. Bohdanowcz, G. J. M. Janssen, S. Petrzyk, Wdeband ndoor and outdoor multpath channel measurements at 7 GHz, n Proc. VTC 99-fall (IEEE Vehcular Technology Conference), Amsterdam, The Netherlands, Sept. 999, pp [] A. Bohdanowcz, Wdeband ndoor and outdoor rado channel measurements at 7 GHz, Delft Unv. of Technol., UbCom-Techncal Report//, Jan. ( [3] R. El Hattach, J. M. M. de Njs, K. Wtrsal, and R. Prasad, Characterzaton and smulaton of the 8 GHz rado channel, n Proc. IEEE Benelux 6 th Symposum on Vehcular Technology and Communcatons, Brussels, Belgum, Oct. 998.

113 3.6 References 99 [4] J. Purwaha, A. Mank, D. Matc, K. Wtrsal, and R. Prasad, Wde-band channel measurements at 6 GHz n ndoor envronments, n Proc. IEEE Benelux 6 th Symposum on Vehcular Technology and Communcatons, Brussels, Belgum, Oct [5] K. Wtrsal, Y.-H. Km, and R. Prasad, A New Method to Measure Parameters of Frequency-Selectve Rado Channels usng Power Measurements, IEEE Trans. on Commun., vol. 49, no., pp , Oct. [6] G. J. M. Janssen, P. A. Stgter, and R. Prasad, Wdeband ndoor channel measurements and BER analyss of frequency selectve multpath channels at.4, 4.75 and.5 GHz, IEEE Trans. on Commun., vol. 44, no., pp. 7 88, Oct [7] A. A. M. Saleh and R. A. Valenzuela, A statstcal model for ndoor multpath propagaton, IEEE J. Select. Areas Commun., vol. 5, no., pp. 8 37, Feb [8] S. J. Howard and K. Pahlavan, Autoregressve modelng of wde-band ndoor rado propagaton, IEEE Trans. Commun., vol. 4, no. 9, pp , Sep. 99. [9] G. J. M. Janssen, Robust recever technques for nterference-lmted rado channels. Ph.D. Thess, Delft Unversty of Technology, Delft, The Netherlands, 998. [] K. Wtrsal and A. Bohdanowcz, Influence of Nose on a Novel RMS Delay Spread Estmaton Method, n Proc. PIMRC ( th Internatonal Symposum on Personal Indoor Moble Rado Communcatons), London, Sept., pp [] G. Landman, Frequency Doman Study of the Wde-Band Moble Propagaton Channel, M.Sc. Thess, Delft Unversty of Technology (IRCTR), Aug..

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115 Part II: OFDM System Proposal and Evaluaton

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117 Chapter 4 OFDM Introducton and System Modelng 4. Introducton The am of ths chapter s to provde some theoretcal background on the OFDM transmsson technque, whch s the general topc of the rest of ths thess. A bref ntroducton to OFDM s gven n Secton 4.. We revew the block dagram of a classc OFDM system, whch employs a guard nterval to mtgate the mparments of the multpath rado channel. We also dscuss several desgn consderatons related to hardware propertes and derve the mathematcal model for an dealzed system, leadng to the concluson that data symbols can be transmtted ndependently of each other (.e., wthout nter-symbol-nterference (ISI) and nter-carrer-nterference (ICI).) Moreover, the effects of synchronzaton mperfectons are analyzed, lke carrer frequency and phase offsets, and tmng errors. Secton 4.3 ntroduces a method of calculatng uncoded BERs for ths dealzed OFDM system model. Ths method s largely based on work presented n []. Dfferental and coherent detecton schemes can be evaluated for Raylegh and Rcean fadng channels. The results obtaned are used n later chapters as a benchmark, n order to evaluate the loss of mplemented algorthms for the OFDM modems. We also show that, for the system proposal under nvestgaton, dfferental detecton n tme-drecton s much preferable to dfferental detecton n frequency drecton. Imperfect synchronzaton and channel estmaton may be assessed by extendng the system model used and by ncorporatng the SNR degradatons due to ICI and ISI. Basc aspects are dscussed n ths chapter. Issues for a further refnement of the methods are addressed. The rest of ths chapter s organzed as follows. The ntroducton to OFDM and the 3

118 4 Chapter 4 OFDM Introducton and System Modelng dervaton of the smplfed system models are presented n Secton 4.. In Secton 4.3, the performance evaluaton of the uncoded OFDM system s outlned, followed by conclusons and recommendatons n Secton OFDM Introducton and System Model Orthogonal frequency dvson multplexng (OFDM) s a parallel transmsson scheme, where a hgh-rate seral data stream s splt up nto a set of low-rate substreams, each of whch s modulated on a separate sub-carrer (SC) (frequency dvson multplexng). Thereby, the bandwdth of the sub-carrers becomes small compared wth the coherence bandwdth of the channel,.e., the ndvdual sub-carrers experence flat fadng, whch allows for smple equalzaton. Ths mples that the symbol perod of the sub-streams s made long compared to the delay spread of the tme-dspersve rado channel. Selectng a specal set of (orthogonal) carrer frequences, hgh spectral effcency s obtaned, because the spectra of the sub-carrers overlap, whle mutual nfluence among the sub-carrers can be avoded (see Fgure -3 n Chapter ). The dervaton of the system model shows that, by ntroducng a cyclc prefx (the so-called guard nterval (GI)), the orthogonalty can be mantaned over a dspersve channel (see Secton 4..3). Ths secton starts wth a bref ntroducton to the OFDM transmsson technque, based on the descrpton of the system s block dagram. We then dscuss some hardware-related desgn consderatons (Secton 4..) that become relevant f an OFDM system s mplemented n hardware. For nstance the DC-subcarrer and sub-carrers near the Nyqust-frequency must be avoded. Next, we derve the system model for a perfectly synchronzed system (Secton 4..3), and we nvestgate the mpact of the most relevant synchronzaton errors (Secton 4..4). For a more elaborate ntroducton to OFDM, the reader may refer to the respectve chapters of [], [3], and to [4] [6]. An excellent overvew over the effects of many non-deal transmsson condtons s gven n [7], wheren numerous further references are found. 4.. OFDM Introducton and Block Dagram Fgure 4- shows the block dagram of a smplex pont-to-pont transmsson system usng OFDM and forward error correcton codng. The three man prncples ncorporated are: The nverse dscrete Fourer transform (IDFT) and the dscrete Fourer transform (DFT) are used for, respectvely, modulatng and demodulatng the data constellatons on the orthogonal sub-carrers [8]. These sgnal processng algorthms replace the banks of I/Q-modulators and -demodulators that would otherwse be requred.

119 4. OFDM Introducton and System Model 5 Data source Data snk Channel codng / nterleavng Symbol mappng (modulaton) symbol demappng (detecton) Channel est. OFDM modulaton (IDFT) N complex data constellatons {x,k } receved data const. {y,k } OFDM demod. (DFT) Multpath rado channel Decodng / denterleavng I/Q Guard I/Q I/Q I/Q-modulaton and up- RF nterval / DAC wndowng converson s RF (t) Guard down-converson and I/Q- r RF (t) nterval ADC removal demodulaton I/Q I/Q I/Q RF Tme sync. transmtted baseband sgnal s(t) receved sgnal r(t) Carrer sync. : dgtal sgnals : analog sgnals Fgure 4-: Smplex, pont-to-pont transmsson usng OFDM. The analyss of Secton 4..3 wll show ths equvalence. Note that at the nput of the IDFT, N data constellaton ponts {x,k } are present, where N s the number of DFT ponts. ( s an ndex on the sub-carrer; k s an ndex on the OFDM symbol). These constellatons can be taken accordng to any phase-shft-keyng (PSK) or quadrature-ampltude-modulaton (QAM) sgnalng set (symbol mappng). The N output samples of the IDFT beng n tme-doman form the base-band sgnal carryng the data symbols on a set of N orthogonal subcarrers. In a real system, however, not all of these N possble sub-carrers can be used for data, as elaborated n Secton Usually, N s taken as an nteger power of two, enablng the applcaton of the hghly effcent (nverse) fast Fourer transform (IFFT; FFT) algorthms for modulaton and demodulaton. The second key prncple s the ntroducton of a cyclc prefx as a guard nterval (GI), whose length should exceed the maxmum excess delay of the multpath propagaton channel [9]. Due to the cyclc prefx, the transmtted sgnal becomes perodc, and the effect of the tme-dspersve multpath channel becomes equvalent to a cyclc convoluton, dscardng the guard nterval at the recever. Due to the propertes of the cyclc convoluton, the effect of the multpath channel s lmted to a pont-wse multplcaton of the transmtted data constellatons by the channel transfer functon, the Fourer transform of the channel mpulse response,.e., the sub-carrers reman orthogonal (see [4] [7]). Ths concluson wll also follow from the dervaton of the system model n Secton The only drawback of ths prncple s a slght loss of effectve transmt power, as the redundant GI must be transmtted. Usually, the GI s selected to have a length of one tenth to a quarter of the symbol perod, leadng to an SNR loss of.5 db. (See also Fgure 4-). The equalzaton (symbol de-mappng) requred for detectng the data constella-

120 6 Chapter 4 OFDM Introducton and System Modelng tons s an element-wse multplcaton of the DFT-output by the nverse of the estmated channel transfer functon (channel estmaton). For phase modulaton schemes, multplcaton by the complex conjugate of the channel estmate can do the equalzaton. Dfferental detecton can be appled as well, where the symbol constellatons of adjacent sub-carrers or subsequent OFDM symbols are compared to recover the data. Forward error correcton (FEC) codng and (frequency-doman) nterleavng are the thrd crucal dea appled. The frequency-selectve rado channel may severely attenuate the data symbols transmtted on one or several sub-carrers, leadng to bt-errors. Spreadng the coded bts over the band-wth of the transmtted system, an effcent codng scheme can correct for the erroneous bts and thereby explot the wde-band channel s frequency-dversty. OFDM systems utlzng error correcton codng are often referred as coded OFDM (COFDM) systems. In Chapter 8, the performance of coded OFDM systems s evaluated. The bt-error-rate (BER) of the uncoded system s analyzed n Secton 4.3. The complex equvalent base-band sgnals generated by dgtal sgnal processng are n-phase/quadrature (I/Q)-modulated and up-converted to be transmtted va an RFcarrer. The reverse steps are performed by the recever. Synchronzaton s a key ssue n the desgn of a robust OFDM recever. Tme- and frequency-synchronzaton are paramount to respectvely dentfy the start of the OFDM symbol and to algn the modulators and the demodulators local oscllator frequences. If any of these synchronzaton tasks s not performed wth suffcent accuracy, then the orthogonalty of the sub-carrers s (partly) lost. That s, nter-symbolnterference (ISI) and nter-carrer-nterference (ICI) are ntroduced. The effect of small synchronzaton errors s analyzed n Secton Synchronzaton algorthms are dscussed n Chapter Desgn of the OFDM Sgnal The proposal of a realstc OFDM-based communcatons system was one of the goals of ths research project. Therefore, we elaborate here on some hardware related desgn consderatons, whch are often neglected n theoretcal studes. Elements of the transmsson chan that have mpact on the desgn of the transmtted OFDM sgnal are: The tme-dspersve nature of the moble channel, whch the transmsson scheme must be able to cope wth. The bandwdth lmtaton of the channel. The sgnal should occupy as lttle bandwdth as possble and ntroduce a mnmum amount of nterference to systems on adjacent channels. The transfer functon of the transmtter/recever hardware. Ths transfer functon reduces the useable bandwdth compared to the theoretcal one gven by the sam-

121 4. OFDM Introducton and System Model 7 Transmtter pulse shape w(t) T wn T guard T FFT T GI Prefx effectve TX-tme k T Channel mpulse response Postfx tme τ max τ excess delay tme Recever flter (mplemented by FFT) T FFT tme Fgure 4-: Cyclc extenson and wndowng of the OFDM symbol. plng theorem. I.e., some oversamplng s requred. Phase-jtter and frequency offsets of the up- and down-converters, and Doppler spreadng of the channel Guard Interval As mentoned above, a guard nterval (GI) s ntroduced to preserve the orthogonalty of the sub-carrers and the ndependence of subsequent OFDM symbols, when the OFDM sgnal s transmtted over a multpath rado channel. The guard nterval, a cyclc prefx, s a copy of the last part of the OFDM symbol, whch s transmtted before the so-called effectve part of the symbol (cf. Fgure 4-). Its duraton T guard s smply selected larger than the maxmum excess delay of the (worst-case) rado channel. Therefore, the effectve part of the receved sgnal can be seen as the cyclc convoluton of the transmtted OFDM symbol by the channel mpulse response Wndowng A rectangular pulse has a very large bandwdth due to the sde-lobes of ts Fourer transform beng a snc-functon. Wndowng s a well-known technque to reduce the level of these sde-lobes and thereby reduce the sgnal power transmtted out of band. In an OFDM system, the appled wndow must not nfluence the sgnal durng ts effectve perod. Therefore, cyclcally extended parts of the symbol are pulse-shaped as depcted n Fgure 4- [3]. Note that ths addtonal cyclc prefx extends the GI to some extent. I.e., the delayspread robustness s slghtly enhanced. On the other hand, the effcency s further reduced, as the wndow part s also dscarded by the recever. The orthogonalty of the

122 8 Chapter 4 OFDM Introducton and System Modelng a (TD) b (TD) c (TD) d (TD) tme doman samples a (FD) b (FD) c (FD) d (FD).5.5 frequency doman (a) (d) 5 frequecy n sub carrers OFDM spectra for N FFT 64, N wn 6, N guard 6 rectangular pulse wndow functon wndowed pulse sgnal strength [db] frequency n sub carrers (e) Fgure 4-3: (a): Shape and spectrum of the OFDM receve flter (realzed by FFT); (b): rectangular pulse of duraton T and ts spectrum; (c): sne-half-wave used for pulseshapng and ts spectrum; (d): transmtter pulse prototype w(t) and ts spectrum. (e): Spectra of (b) (d) n logarthmc scale. sub-carrers of the OFDM sgnal s restored by the rectangular recever flter mplemented by the DFT (Fgure 4-), requrng the correct estmaton of the DFT start tme k T, where T s the OFDM symbol perod.

123 4. OFDM Introducton and System Model 9 The symbol perods n Fgure 4- are gven as tmes. Snce the mplementaton s usually done on dgtal hardware, those perods are also often defned n terms of samples. N, N guard, and N wn then defne the number of samples n the effectve part, guard-, and wndowng-nterval, respectvely. The effectve part s also referred to as the FFTpart, because ths part of the OFDM symbol s appled to the FFT to recover the data at the recever. Spectrum of the transmtter pulse shape Wndowng of the transmtter pulse usng a rased-cosne functon can be seen as a convoluton of the extended rectangular pulse of duraton T wth a sne-half-wave, as shown n Fgure 4-3. In the frequency-doman, ths convoluton means a multplcaton of the snc-spectrum of the rectangular pulse wth the spectrum of the sne-half-wave. It s seen that ths multplcaton reduces the sde-lobes of the transmtter pulse shape. In Fgure 4-3 (a), the zeros of the spectrum occur at postons F /T FFT, {±, ±, },.e., at those postons, where the adjacent sub-carrers are located. The extenson of the rectangular pulse to length T T FFT + T guard + T wn reduces the dstance between zeros to /T (Fgure 4-3 (b)). The wndowng functon (Fgure 4-3 (c)) has zeros at postons ±/T wn {3/, 5/, 7/, } System Transfer Functon (ADCs, DACs, IF-Flters, RF Front-end, etc.) Because of the low-pass flters requred for the analog-to-dgtal and dgtal-to-analog converson (ADC and DAC) of the transmtted and receved (baseband) sgnals, not all N sub-carrers can be used, f an N-pont IFFT s appled for modulaton. The sub-carrers close to the Nyqust frequency f s / wll be attenuated by these flters and thus cannot be used for data transmsson (see Fgure 4-4). (f s /T s s the samplng frequency.) Also the DC-sub-carrer mght be heavly dstorted by DC offsets of the ADCs and DACs, by carrer feed-through, etc., and should thus be avoded for data. Transfer functon of transmtter/recever f s / DC f s / useable sub-carrers useable sub-carrers N/,,,,,, N/ frequency sub-carrer ndex Fgure 4-4: Transfer functon of the transmtter/recever hardware and ts mpact on the desgn of an OFDM system OFDM System Model The above-ntroduced features of the OFDM sgnal are defned mathematcally n ths secton. Ths wll lead to the concluson that, usng the OFDM prncple, data symbols

124 Chapter 4 OFDM Introducton and System Modelng can be transmtted over multpath rado channels wthout nfluencng each other Sgnal Model and Defntons Mathematcally, the OFDM sgnal s expressed as a sum of the prototype pulses shfted n the tme- and frequency drectons and multpled by the data symbols. In contnuous-tme notaton, the k-th OFDM symbol s wrtten s RF, k Re w( t kt) ( t kt ) N / N / x, k e jπ fc + TFFT ( ) t kt kt T wn T guard t kt + T FFT + T wn otherwse. (4-) Most of the mathematcal symbols have been defned n the prevous fgures already. A complete lst of symbols s gven below: T Symbol length; tme between two consecutve OFDM symbols T FFT FFT-tme; effectve part of the OFDM symbol T guard Guard-nterval; duraton of the cyclc prefx T wn Wndow-nterval; duraton of wndowed prefx/postfx for spectral shapng f c Center frequency of the occuped frequency spectrum F /T FFT frequency spacng between adjacent sub-carrers N FFT-length; number of FFT ponts k ndex on transmtted symbol ndex on sub-carrer; { N/, N/+,,,,,, N/ } x,k sgnal constellaton pont; complex {data, plot, null} symbol modulated on the -th subcarrer of the k-th OFDM symbol w(t) denotes the transmtter pulse shape defned as w( t) [ cosπ ( t + T + T ) / T ] wn [ + cosπ ( t T ) / T ] FFT guard wn wn T T T FFT wn guard T guard t T < t T FFT t < T Fnally, a contnuous sequence of transmtted OFDM symbols s expressed as FFT + T wn guard (4-) k s ( t) s, ( t kt) (4-3) RF RF k The smulated spectrum of such an OFDM sgnal s depcted n Fgure 4-5 for dfferent

125 4. OFDM Introducton and System Model power spectrum magntude [db] OFDM spectrum for N FFT 64, N guard 6, oversamplng N wn N wn N wn frequency n sub carrers Fgure 4-5: Spectrum of an OFDM sgnal wth 64 sub-carrers and dfferent wndow lengths. Two-fold oversamplng has been appled n the tme-doman; 48 sub-carrers are used for data. wndow lengths Lowpass Equvalent Transmtted Sgnal From eqs. (4-) (4-3), the complex equvalent lowpass sgnal transmtted can be drectly gven. The complex envelope of the OFDM sgnal s wrtten wth sk k s ( t) ( t kt ), (4-4) w( t kt) sk ( t kt) N / N / x, k e jπ TFFT ( t kt ) kt T wn T guard t kt + T FFT + T wn otherwse Note the smlartes of ths expresson to the equaton of a Fourer seres (4-5) jπnft v( t) c( nf ) e n, (4-6) where the complex-valued Fourer coeffcents c(nf ) represent the complex-valued sgnal constellaton ponts x,k, and the frequences nf correspond to the sub-carrer

126 Chapter 4 OFDM Introducton and System Modelng frequences /T FFT. In a dgtal system, ths modulated waveform can be generated by an nverse dscrete Fourer transform (IDFT) or by ts computatonally effcent mplementaton, the IFFT. The data constellatons x,k are the nput to ths IFFT; the tme-doman OFDM symbol s ts output Tme-Dspersve Channel The nfluence of the tme-varant, multpath fadng rado channel s expressed by ts (lowpass equvalent) mpulse response h(τ,t) plus AWGN n(t): τ max r ( t) h( τ, t) s( t) + n( t) h( τ, t) s( t τ) dτ + n( t) (4-7) The range of ntegraton n ths convolutonal ntegral (* denotes convoluton) has been lmted to [, τ max ], because the channel mpulse response s zero elsewhere. Excess delay τ of the channel s defned as the delay tme at whch the frst wave arrves at the recever. Thus, transmt and receve tme nstants are mathematcally defned equal (compare Fgure 4-). τ max s the maxmum excess delay of the channel. Two assumptons are made to smplfy the dervaton of the receved sgnal. The channel s consdered quas-statc durng the transmsson of the k-th OFDM symbol, thus h(τ,t) smplfes to h k (τ). Furthermore, we defne the maxmum excess delay τ max < T guard. Therefore, there s no nterference of one OFDM symbol on the effectve perod of the consecutve one (cf. Fgure 4-). I.e., nter-symbol-nterference (ISI) s suppressed n case of suffcently accurate tme synchronzaton OFDM Demodulaton The demodulaton of the OFDM sgnal should be performed by a bank of flters, whch are matched to the effectve part [kt, kt + T FFT ] of the OFDM symbol (see Fgure 4-). The reverse operaton to eq. (4-6),.e., the extracton of the Fourer coeffcents c(nf ) ( x,k ) from the tme-doman sgnal v(t) ( r(t)), exactly formulates such a bank of matched flters. It s wrtten c( nf ) T v t ( ) T e jπnft dt, (4-8) where T s the ntegraton perod beng equvalent to T FFT. In a dgtal mplementaton, a DFT or (preferably) a FFT s used to realze these flters. Assumng knowledge of the exact tme-nstants kt at whch the OFDM symbols start, we try to extract the transmtted sgnal constellatons x,k from the receved sgnal r(t). The receved sgnal constellatons are denoted y,k.

127 4. OFDM Introducton and System Model 3 y, k T T FFT FFT kt + TFFT t kt kt + TFFT t kt r( t) e τ max k τ jπ ( t kt ) / TFFT dt h ( τ) s( t τ ) dτ + n( t) e j π( t kt ) / TFFT dt (4-9) Because of the ntegraton ranges n eq. (4-9) and τ max < T guard, there s no nfluence of the adjacent OFDM symbols transmtted, and s(t) can be replaced by s k(t), eq. (4-5). y, k T T FFT FFT kt + T FFT max hk ( τ ) t kt kt + TFFT t kt τ τ n( t) e N / ' N / j π ( t kt )/ TFFT x dt ', k e ' j π TFFT ( t kt τ ) dτ e j π( t kt ) / TFFT dt + (4-) Note that w(t kt) n the range of ntegraton. The wndow s thus omtted n ths equaton. The second ntegral n eq. (4-) leads to ndependent addtve nose samples n,k snce the complex exponental terms represent orthogonal functons. Substtutng u t kt, for the ease of notaton, and changng the order of ntegraton and summaton yelds y, k TFFT τ x τ N / ', k ' N / TFFT u TFFT τ x τ N / ', k ' N / TFFT u max max h ( τ ) e k k h ( τ ) e j π'( u τ ) / TFFT j π ' τ / TFFT dτ e dτ e jπu / TFFT j π ( ') u / TFFT du + n, k du + n, k (4-) The nner ntegral of the second expresson represents the Fourer transform of h k(τ) at the frequency nstants '/T FFT 'F, whch s the sampled channel transfer functon at tme kt. It s expressed by the channel coeffcents τ max j π' τ / TFFT ', k FT{ hk ( τ )} hk ( τ ) e dτ H ( ' F, kt) τ h. (4-) Usng ths notaton, the output of the recever flter bank smplfes to y, k N / TFFT j π ( ') u / TFFT x kh k e ', ', ' N / TFFT u du + n, k (4-3) The ntegral n ths equaton has the value, only f '. For ', and ' beng nteger values, the ntegral s zero. Thus we fnally obtan y k x kh k n,,, +, k. (4-4) From ths form t s seen that a perfectly synchronzed OFDM system can be vewed as a set of parallel Gaussan channels as depcted n Fgure 4-6 [4] [6]. The multpath

128 4 Chapter 4 OFDM Introducton and System Modelng x,k h,k n,k y,k x +,k h +,k n +,k y +,k Fgure 4-6: Idealzed OFDM system model. The sub-channels of the OFDM system can be consdered as parallel Gaussan channels under the assumptons of perfect tme- and carrer synchronzaton and perfect suppresson of multpath by the guard nterval. channel ntroduces an attenuaton/amplfcaton and phase rotaton accordng to the (complex-valued) channel coeffcents {h,k }. Channel estmaton s requred n order to retreve the data contaned n these sgnal constellatons, because the recever must have a phase (and ampltude) reference to correctly detect the transmtted symbol. Dfferental detecton can be used alternatvely, n whch case the decson s made by comparng the phases (and ampltudes) of symbols transmtted over adjacent sub-carrers or subsequent OFDM symbols. Due to the attenuaton/amplfcaton, each sub-carrer typcally has an ndvdual sgnal-to-nose rato (SNR). The SNR per sub-carrer (after the DFT) s defned as ( Ec / N ), k E{ x, k } h, k σ N, (4-5) where σ E{ } s the nose varance. Wth the normalzed receved power beng N n, k wrtten P E{ h, k }, the average SNR becomes Ec / N E{ x, k } P σ N. Usually, the sgnal energy s normalzed to unty,.e., E { } Synchronzaton Errors x, k As an ntroducton to the work on synchronzaton algorthms, the relevant effects of synchronzaton errors are revewed n ths secton. Orgnal work on ths topc s found n numerous publcatons (see e.g. [], []). A comprehensve overvew s gven n [7] FFT Tme Synchronzaton Error The mpact of an FFT-tmng offset at the recever can be analyzed mathematcally by shftng the ntegraton nterval of the matched flter bank, eq. (4-9). For a tmng error of δt, the deal nterval t [kt, kt + T FFT ] becomes t [kt + δt, kt + T FFT + δt] and (4-9) s wrtten

129 4. OFDM Introducton and System Model 5 y kt + TFFT + δt r t, k ( ) TFFT t kt + δt e j π ( t kt δt ) / TFFT dt (4-6) δt s assumed to be suffcently small (typcally δt < T guard ) that no ISI arses due to the tmng error. In other words, the error s small enough for the channel mpulse response to reman wthn the guard nterval. Therefore, the recever wndow stll does not overlap wth the precedng or consecutve OFDM symbol,.e., no energy s collected from these adjacent OFDM symbols, and the demodulated sgnal can be expressed from the transmtted symbol s k (t) agan (compare eq. (4-)). Followng the same steps as n Secton 4..3 (eqs. (4-9) (4-4)), we obtan for the second part of eq. (4-) (wth u t kt δt), N / TFFT τ max y, k x', k h( ' N / T FFT u τ jπ' δt / TFFT Movng the term e out of the ntegral yelds the expresson for the demodulated sgnal constellatons n case of a tmng error, y jπ ' τ / TFFT jπ [( ') u+ ' δt]/ TFFT τ ) e dτ e du + n, k (4-7) j πδt / TFFT jπδt '/ N, k x, kh, ke + n, k x, kh, ke + n, k, (4-8) where δt' s the tmng offset n samples. It s evdent that a tmng offset gves rse to a progressve phase rotaton of the sgnal constellatons. The phase rotaton s zero at the center frequency and t lnearly ncreases towards the edges of the frequency band. It s easly verfed from eq. (4-8) that a tmng-offset of one sample ntroduces a phase shft of ±π to the outermost sub-carrers (havng ±N/), regardless of the FFTlength. In Fgure 4-7, ths effect s vsualzed for a 64-carrer OFDM system wth zero carrers at f c and at the edges of the frequency band. If coherent detecton s utlzed, the nduced progressve phase rotaton s detected mplctly by the channel estmaton algorthm. The subsequent equalzaton (sub-carrerwse multplcaton of the receved symbols by the nverse of the estmated channel coeffcents) wll thus automatcally correct for small tmng-offsets. No performance degradaton s thereby caused. However, f the tmng offset s too large, ISI and ICI are ntroduced because energy s also collected from one of the adjacent OFDM symbols, leadng to a partal loss of orthogonalty [7]. Dfferental detecton s also robust to small tmng-offsets. If the dfferental detecton s appled n the frequency-drecton, the progressve phase rotaton may reduce the dstance between the compared constellaton ponts, however, whch can lead to a performance degradaton. Such performance results are gven n Secton A (small) samplng frequency offset leads to a (slowly) ncreasng tmng offset, and therefore to a progressve phase rotaton at an ncreasng slope. Larger errors yeld ICI, because the SC-spacng at the recever can no longer be assumed equal to the SCspacng at the transmtter. (The SC-spacng s defned as F /(NT s ), where T s s the

130 6 Chapter 4 OFDM Introducton and System Modelng effect of tme offset δt.5 samples.. Q channel..... I channel. sub carrer ndex Fgure 4-7: Vsualzaton of the nfluence of an FFT tmng offset on the demodulated sgnal constellatons. A lnearly ncreasng phase rotaton s observed wth ncreased frequency dstance to the center frequency. + ndcate QPSK constellatons wthout the nfluence of a tmng-offset; œ depct the rotated data symbols. samplng perod.) Carrer Synchronzaton Error Frequency offsets are typcally ntroduced by a (small) frequency msmatch n the local oscllators of the transmtter and the recever. Doppler shfts can be neglected n ndoor envronments. The mpact of a frequency error can be seen as an error n the frequency nstants, where the receved sgnal s sampled durng demodulaton by the FFT. Fgure 4-8 depcts ths two-fold effect. The ampltude of the desred sub-carrer s reduced ( + ) and nter-carrer-nterference ICI arses from the adjacent sub-carrers ( { ). Mathematcally, a carrer offset can be accounted for by a frequency shft δf and a phase offset θ n the lowpass equvalent receved sgnal Wth eq. (4-9) we obtan j(πδ ft+θ ) r '( t) r( t) e. (4-9) y, k T e FFT j πθ kt + TFFT t kt T FFT r( t) e kt + TFFT t kt j(πδft+ θ ) τ max τ e jπ( t kt ) / TFFT dt h( τ ) s( t τ ) dτ + n( t) e j πδft e j π( t kt ) / TFFT dt. (4-)

131 4. OFDM Introducton and System Model 7 ampltude δf frequency offset frequency Fgure 4-8: Inter-carrer-nterference (ICI) arses n case of a carrer synchronzaton error. The fgure llustrates the spectra of three ndvdual sub-carrers. These spectra are supermposed n the OFDM sgnal spectrum. Repeatng the dervaton leadng to eq. (4-3), the receved constellaton ponts become y, k N / TFFT j( θ + πδfkt ) x', kh ', k ' N / TFFT u e e ' j π ( δf ) u TFFT du + n, k. (4-) Due to the frequency error, the ntegral s not equal zero for ', nether t s one for ', as n the dealzed case above. I.e., the orthogonalty between sub-carrers has been partly lost. The evaluaton of ths expresson yelds two terms. The frst term (for ') accounts for equal phase rotaton and attenuaton of all sub-carrers, the second one (for ') descrbes the ICI. y, k e e j( θ + πδfkt ) x, k h, k T TFFT FFT u jπδfu N / TFFT j( θ + πδfkt ) x', kh ', k ' N / T FFT u ' e du + e ' j π ( δf ) u TFFT du + n, k (4-) These expressons are vald for a frequency-offset δf <.5 SC. For larger offsets, the transmtted data symbols x,k would get shfted by one or more postons n the frequency-drecton. I.e., the data symbol of the -th transmtted SC would appear at the ( + δf )-th SC at the recever, where δf round(δf/f) s the nteger part of the frequency-error n sub-carrers. The ICI term can be seen as an addtonal nose term and can thus be represented as a degradaton of SNR. The amount of degradaton has been evaluated by Pollet et al. [] for AWGN channels and by Moose [] for dspersve fadng channels (see also [7]). Frequency-offsets up to % of the sub-carrer spacng F are neglgble, accordng to ther results. Even 5 % can be tolerated n many stuatons.

132 8 Chapter 4 OFDM Introducton and System Modelng dstorton of sgnal constellatons due to frequency offset δf F/6.3 correct states erroneous states cplx. spectrum.. Q channel I channel Fgure 4-9: Phase rotaton due to carrer offset of /6 of the sub-carrer spacng. The receved sgnal constellatons dstorted by ICI are shown. Evaluaton of the phase rotaton and attenuaton due to a frequency error yelds usng T ( f TFFT ) exp{ j[ θ + f ( kt + TFFT / ) ]} n k snc δ πδ +, (4-3) y, k x, kh, k ', TFFT j πδft FFT t e dt jπδft FFT j πδft j ft ft FFT πδ sn πδ FFT FFT jπδftfft [ e ] e e snc δftfft πδft FFT. (4-4) The nose term n',k ncludes the addtonal nose due to ICI. Fgure 4-9 depcts the rotaton and dstorton of the receved sgnal constellaton ponts for a carrer offset of δf F/6, θ, and for QPSK modulaton ( { ). The scatterng of the resultng complex valued sgnal constellatons s caused by ICI. The fgure also shows the projecton of the contnuous Fourer spectrum of one OFDM symbol on the complex plane,.e., the spectrum n-between the sub-carrer frequences. Ths lne results from the superposton of the contnuous snc-spectra of ndvdual sub-carrers of one OFDM symbol. If a frequency-offset s present, the DFT samples ths spectrum at the wrong frequency-nstants leadng to ICI, whch s ndcated n the fgure by {. Wthout frequency-offset, the QPSK constellatons are recovered perfectly, as seen from the ponts marked by Common Carrer and Tmng Offset Evaluatng the above expressons for smultaneous tmng (δt), frequency (δf, δf round(δf/f)) and phase (θ) offsets, the system model for the generalzed case s

133 4.3 Performance of an Uncoded OFDM System 9 obtaned. It s wrtten as y jψ k [( δf ff) TFFT ] e n k, + f k x kh,,, k snc δ + ', δ, (4-5) where the phase dstorton due to the synchronzaton errors s expressed by TFFT Ψ, k θ + πδf kt + + δt + πδt. (4-6) TFFT Note agan that the nose varable n',k n (4-5) ncludes the nose caused by ICI and/or ISI. Often, the tmng offset s expressed n samples,.e., δt' δt/t s, and the frequency-offset s normalzed to the sub-carrer spacng δ f ' δf F. Usng these symbols, the phase dstortons are expressed by N + N guard + N wn t' k f ' k δ Ψ, θ + πδ πδt' N N. (4-7) N 4.3 Performance of an Uncoded OFDM System In ths secton, analytcal expressons are derved for the bt-error probabltes of uncoded OFDM systems over Raylegh and Rcean fadng channels. The analyss s based on the work by Proaks (Appendx B of []). The obtaned expressons are very general, allowng the evaluaton of varous modulaton schemes, demodulaton and channel estmaton technques. The applcaton of the formulas s shown for BPSK, QPSK, 8-PSK, and 6-QAM modulaton, wth coherent detecton (perfect channel estmaton) and dfferental detecton. The dealzed system model derved n Secton 4..3 s employed n ths study. By ncorporatng n the system model the SNR degradaton due to synchronzaton errors, Doppler spread, or phase nose (whch cause ICI and/or ISI), or by ncorporatng the mean-square-error of channel estmaton technques, the effect of these mparments on the BER can be analyzed. The systematc phase rotatons nduced by synchronzaton errors must be consdered as well. Whle we leave the evaluaton of the SNR degradatons for future work, we brefly nvestgate the effects of phase rotatons n presence of (small) synchronzaton offsets. The results presented n ths secton wll serve as benchmarks n the performance evaluaton of varous sgnal-processng aspects of the OFDM ar-nterfaces, whch are treated n Chapter 6 and 7. In OFDM, dfferental detecton can be employed n the tme- and frequency-drectons. From the BER of dfferental detecton t s evdent that the tme-drecton s preferable for the OFDM system parameters under nvestgaton, snce the channel varatons versus frequency are larger. Secton 4.3. revews the OFDM system model and channel model. The dervaton of

134 Chapter 4 OFDM Introducton and System Modelng the average BER s explaned n Secton Performance results are gven n Secton Mathematcal Modelng The OFDM system models derved n Secton 4. are used n ths analyss. For the sake of smplcty we slghtly change the ndexng, however, as we only nvestgate the tme- or frequency drecton at a tme. The system model of eq. (4-4) becomes y x h + n, (4-8) k k where {x k } and {y k } are the transmtted and receved sgnal constellaton ponts (modulated data symbols), respectvely, the {h k } account for the correlated, complexvalued attenuaton factors ntroduced by the tme- and/or frequency-selectve rado channel, and the {n k } denote samples of an AWGN process wth E{ n k } k k σ N. The ndex k can be used as a tme- or as a frequency-ndex, dependng on the system aspect under nvestgaton. The attenuaton factors thereby consttute the tme- or frequencytransfer functon of the channel, respectvely: h k H( f, kt) H( kf, t) at gven at gven t f, (4-9) where T s the duraton of an OFDM symbol ncludng the guard and wndowng ntervals, and F denotes the frequency spacng between adjacent OFDM sub-carrers. The channel model s ntroduced n the analyss by consderng respectvely the spaced-tme and spaced-frequency correlaton functons of the (wde-sense statonary uncorrelated scatterng WSSUS; see Chapter and [], [], [3]) channel. For descrbng the frequency-varablty, the frequency-doman channel model s used (see Secton.3). Thereby, we confne ourselves to the case of the exponentally decayng delay power spectrum, where a drect relaton can be gven between the channel parameters {P average power, K Rcean factor, and τ rms RMS delay spread} and the channel correlaton functon φ * P + + H ( f ) E{ H ( f ) H ( f f )} K K + + jπ fτ rms K. (4-3) In ths equaton, K ( K + ) K +, f s the frequency-lag, and * denotes the complex conjugate. The normalzed receved power (average power) s defned as P E{ h k }. To model the tme-varablty, the so-called Jakes Doppler spectrum can be used [4], j( πf ρt+ θ ρ ) augmented by a lne-of-sght (LOS) component ρ e at a gven Doppler frequency f ρ. Such a Doppler spectrum corresponds to a spaced-tme correlaton functon

135 4.3 Performance of an Uncoded OFDM System j πf ρ t ( K e + J (πf m t) ) * P φh ( t) E{ H ( t) H ( t + t)}, (4-3) K + where J ( ) denotes the zero-th order Bessel functon of the frst knd, t s the tmelag, and f m s the maxmum Doppler frequency. ( f v λ v f c, where v m s the m m moble s velocty, λ s the wavelength, f c s the carrer frequency, and c s the speed-oflght.) 4.3. Analytcal Evaluaton of the BER Analytcal expressons for the BER are derved n ths secton. Followng [], we start our analyss wth defnng the symbol transmtted as x k,, whch s an element of the symbol set {x k,m }, m {,, M}. (M s the order of the modulaton scheme.) At the recever s ste, an optmum detector wll choose the symbol x k,n {x k,m }, whch mnmzes the dstance metrc M x y hˆ x. (4-3) d ( k, n ) k k k, n Ths symbol s assumed to be most lkely the transmtted symbol. The term h ˆ k x n k, n ths equaton accounts for the channel estmaton. An error occurs when the metrc calculated for a symbol x k,n x k, s smaller than the metrc for the transmtted symbol x k,. The probablty for ths event s wrtten as Pe Pr{ M d ( xk, n ) < M d ( xk, )} Pr{ D < }, (4-33) where D M d (x k,n ) M d (x k, ) s called the decson varable. Usng (4-3), D becomes ˆ * * * * ˆ ( ) ˆ D y h ( x x ) + y h x x + h ( x x ). (4-34) k k k, k, n k k k, From the channel and system models, y k s known to be a complex Gaussan random varable. The same holds for ĥ k, whch s an estmate of the transfer functon H(f,t). Thus, the decson varable D s a specal case of the generc quadratc form (see Appendx B n []) D k, n k k, n L * * * ( A X l + B Yl + CX lyl + C X l Yl ) l, (4-35) where X l and Y l are complex-valued Gaussan random varables, and A, B, and C are constants. In our case L, consderng one transmtted symbol over one (sub-) channel. The error probablty s the probablty that D <, whch s evaluated n Appendx B of []. Ths probablty s denoted as the ntegral over the pdf of D m c k, The equaton for L > allows for the evaluaton of dversty schemes [], [5] [7].

136 Chapter 4 OFDM Introducton and System Modelng < ) ( } Pr{ dd D p D P e. (4-36) For L, the soluton to ths ntegral s wrtten [] ) ( ) ( / / ), ( b a e e ab I b a Q P + + υ υ υ υ, (4-37) where I n (x) s the n-th order modfed Bessel functon of the frst knd and Q (a,b) s the Marcum s Q functon, whch can be expressed n terms of Bessel functons as ( ) + ) ( ) ( / ), ( n n n b a ab I b a e b a Q, b > a >. (4-38) The parameters a, b, υ, and υ must be related to the moments of X l and Y l, and to the constants A, B, and C. As gven n [], these are obtaned from / / ) ( ) ( ) ( ) ( υ υ α α υ υ υ υ υ α α υ υ υ b a ) )( 4( ) )( 4( * *, AB C C C B A w w AB C w xy yy xx xy xy yy xx xy yy xx ψ ψ ψ ψ ψ ψ ψ ψ ψ ψ υ # (4-39) * * * * * * ) )( ( Y X C Y CX Y B X A Y X Y X Y X AB C xy xy xx yy α ψ ψ ψ ψ α These equatons are appled to our problem by comparng eqs. (4-34) and (4-35). Lettng Y y k and k h X ˆ n (4-34), the constants,, k n x k x A, B, and k n x k x C,, are found, representng the propertes of the modulaton scheme. The behavors of the channel and of the channel estmaton technque wll be expressed by the frst and second moments of the random varables X and Y. These are ] } { ˆ [ ] } { [ ] } ˆ { [ } { } { ˆ * * Y X y h E Y y E X h E y E Y h E X k k xy k yy k xx k k ψ ψ ψ. (4-4) The dervaton of these parameters from the channel and system defntons s gven n

137 4.3 Performance of an Uncoded OFDM System 3 the followng sub-secton. Coherent and dfferental detecton are nvestgated Applcaton of the Mathematcal Models Coherent detecton wth perfect channel estmaton The k-th symbol receved s defned n eq. (4-8) as y k x k h k + n k. Perfect channel estmaton means that the recever has exact knowledge about the attenuaton factor h k, denoted by k k h h ˆ. Consderng the transmtted symbol x k, as a constant yelds θ ρ ρ j h k e E X } {, θ ρ ρ j k k k k k k k e x n E h E x n h x E Y + +,,, } { } { } {, ] [ ] } { [ ρ ψ P X h E k xx, (4-4) ] ) ( [ ] } { [,, N k k k k yy P x Y n h x E σ ρ ψ + +, ] [ ] } ) ( { [ *, * *, ρ ψ + P x Y X n h x h E k k k k k xy, where ρ ρ jθ e s the LOS-component, wth arbtrary phase θ ρ and wth an ampltude defned by ) ( K + K P ρ. Dfferental detecton Wth dfferental detecton, the decson for the receved symbol y k s made based on the adjacent symbol y k x k h k + n k. For phase modulaton schemes, ths can be seen as a detecton based on the channel estmate k k k k k k k k n h x n h x y h ' / ˆ + +, where E{ n' k } N ' σ. Note that ' N N σ σ, f the magntude of x k s one. The parameters Y and ψ yy are then equal as n eqs. (4-4). The addtonal nose term n' k, the correlaton between h k and h k, and the Doppler shft of the LOS-component are expressed n ) ( } ' { T f j k k e n h E X ρ θ ρ π ρ +, ] [ ' ρ σ ψ + N xx NRP, and (4-4) ] } { [ * *, T f j k k k xy e h h E x ρ π ψ ρ. For evaluatng dfferental detecton n the frequency-drecton, let T. Usng the channel correlaton functons gven n Secton 4.3., the correlaton ψ xy between the attenuaton factors at two adjacent symbols becomes + n tme ) ( J n frequency *, T f K F j K P x m rms k xy π τ π ψ. (4-43) Note that the nfluence of the channel-varablty s expressed by ths correlaton-value only, whch s defned by the parameter-products τ rms F and f m T, for the two cases un-

138 4 Chapter 4 OFDM Introducton and System Modelng der consderaton. Performance results are gven n Secton It wll be shown that dfferental detecton n the tme-drecton s more robust than the frequency-doman varant, for the OFDM system under consderaton,.e., for a wde-band ndoor wreless LAN Applcaton to Dfferent Modulaton Schemes Assgnng dfferent constellaton values to the varable x k,n x k,, the probablty can be calculated that an erroneous symbol x k,n has been detected whle the symbol x k, was transmtted. Ths allows for many modulaton schemes an exact calculaton of the BER and for others the evaluaton of close approxmatons. In the followng analyss we assume that all possble transmtted symbols x k, {x k,m } occur wth equal probablty. BPSK and QPSK Exact results can be obtaned for BPSK and QPSK modulaton. The sgnal constellatons for these technques are depcted n Fgure 4-. For both schemes t s suffcent to consder (any) one transmtted symbol, due to symmetres. Ths symbol wll be the +, taken from the set {x k,m } {, } for BPSK, and from {x k,m } {, j,, j} for QPSK. Note that x k,m for both modulaton types. BPSK s analyzed by evaluatng the parameters A and C for x k, and x k,n. The bt error probablty s equal to the symbol error probablty P e (see eq. (4-37)). Gray-coded QPSK transmts two bts per symbol on orthogonal carrers (I- and Q- components). Thus, the error probabltes can be analyzed ndependently and the BER equals ther average. Sutable parameters for A and C are found by (e.g.) assgnng x k, and x k,n {j, j}. Calculatng the probablty that x k,n has been detected, provded x k, was transmtted, the I/Q-plane s dvded n two parts. An error occurs when the receved symbol falls wthn the half plane beng closer to x k,n than to x k,. No error occurs otherwse (see Fgure 4-). Note that for the case of QPSK t s not necessary to evaluate the twoerror-event explctly. The overlappng one-error-events account for one error each n BPSK: Q QPSK: () Q x k,n j one error () x k,n () x k, Error regon, when x k, was transmtted I () two errors () () I x k, x k,n j one error Fgure 4-: Selecton of x k, and x k,n for the performance evaluaton of BPSK and QPSK.

139 4.3 Performance of an Uncoded OFDM System 5 (a): sgnal constellaton Q () (b): approxmaton Q ε less () () () () ε 3ε ε ε x k, ε ε ε () () I ε more ε less x k,n e -j3π/4 3ε ε more ε ε ε ε ε ε x k,n e +jπ/4 x k, x k,n e -jπ/4 I () Fgure 4-: Error regons for 8-PSK, when x k, was transmtted. (a) Sgnal constellatons and correct number of errors for each decson range. (b) Approxmaton by evaluatng error probabltes from the three error-states x k,n shown. In some error regons, one extra error s consdered, n other regons, one error s mssed (ndcated as ε more and ε less). ths regon, thus the two-error-event s ncluded automatcally. Ths may seem as an advantage because computatonal complexty reduces, however, when evaluatng hgher order modulaton schemes, many of those half-planes wll overlap and t s sometmes not possble to obtan the exact number of errors for all decson regons. Ths wll be seen n the followng case. 8-PSK Upper and lower bounds on the BER can be calculated for 8-PSK. An exact calculaton s not possble, because the eght sgnal states are not separable n the two orthogonal dmensons of the I/Q-plane. Due to symmetres t s agan suffcent to consder one transmtted symbol, x k,. Fgure 4- llustrates how errors occur n estmatng error probabltes. The sgnal constellatons are shown n Fgure 4-a together wth the exact numbers of errors for each decson regon. (Errors are denoted by ε.) Fgure 4-b shows the actual numbers of errors for each of these regons, when three dfferent error states x k,n are evaluated and averaged. Clearly, too few errors are consdered n some of the decson regons, whle too many are consdered n others. Thus the computatonal results are a (close) approxmaton. The most lkely errors, however, are approprately treated. 6-Quadrature Ampltude Modulaton (QAM) 6-QAM can be evaluated wthout any error. Four dfferent transmtted symbols occurrng wth equal probabltes and 4 error events must be consdered. Some of them must be subtracted n order to account for overlappng decson regons. A possble set of symbols x k, and x k,n to be used are lsted n Table 4-. The complex sgnal constellatons x k are denoted (Re{x k },Im{x k }). Error events whose probablty must be subtracted n the fnal result are wrtten (Re{x k },Im{x k }). All values must be dvded by to have an average power of one. Fgure 4- llustrates the sgnal constellatons

140 6 Chapter 4 OFDM Introducton and System Modelng and error events for the symbol x k, ( 3,3), whch carres the data symbol (). Table 4-: Transmtted symbols and error events for the evaluaton of 6-QAM modulaton. Transmtted symbol Error symbols x k,n x k, ( 3,3) (,3), (3,3), (7,3) -, ( 3,), ( 3, 3), ( 3, 7) - (,3) ( 3,3), (,3), (5,3), (,), (, 3), (, 7) - ( 3,) (,), (3,), (7,) -, ( 3,3), ( 3, ), ( 3, 5) (,) ( 3,), (,), (5,), (,3), (, ), (, 5) Q () () () () ε ε ε xk,n (3,3) x k, (-3,3) x k,n (-,3) () ε () ε () 3ε () ε x k,n (-3,) () () () () ε 3ε 4ε 3ε x k,n (7,3) - error prob. to be subtracted! I () ε () ε () 3ε () ε x k,n (-3,-3) error prob. to be subtracted! x k,n (-3,-7) - Fgure 4-: Illustraton of the error events n 6-QAM, when the symbol x k, ( 3,3) was transmtted. 6 Star-QAM 6 Star-QAM can be treated as a combnaton of 8-PSK and a bnary ampltude modulaton. The bnary AM s evaluated by transformng the I- and Q-varables to an r I + Q varable, resultng n smlar expressons to the above defned ones. Ths s descrbed n [6] and [7].

141 . 4.3 Performance of an Uncoded OFDM System 7 5 BER for QPSK wth coherent demod. (sold) and dff. demod. (dashed) e 3 e e Rcan K factor K [db] e 6. e E b /N [db] Fgure 4-3: Performance of QPSK for coherent detecton (perfect channel estmaton) ( ) and for dfferental detecton wth F,.e., wth perfect correlaton between adjacent sub-carrers (flat fadng) ( ) Performance Results Some observatons can be made from the mathematcal expressons derved above (eqs. (4-4) (4-43)): () For coherent detecton, the statstcal parameters and thus the performance results only depend on P, ρ, and σ N. In other words, the performance depends on the average sgnal-to-nose rato (SNR) SNR P / σ N and on the Rcean K- factor K ρ /(P ρ ). () The same holds n the lmts F or T (.e., for flat fadng) for dfferental detecton. () The performance of dfferental detecton degrades for F > (or T > ), because of a systematc estmaton error n h ˆ k hk + n' k, snce h k h k. The parameter products τ rms F and f m T defne the degradaton, accordng to eq. (4-43). Performance results (average BER) for () and () and QPSK modulaton are shown n Fgure 4-3, as a functon of the average SNR per bt (denoted E b /N ) and as a func- Several sgnal-to-nose rato (SNR) parameters are used n ths thess: The SNR denoted E b /N s the average SNR per data bt. It thus depends on the order M of the modulaton scheme. The average SNR of the subcarrer symbols, beng ndependent of the modulaton scheme, s wrtten as SNR SC (see Secton 6..7.). In Secton 6..3, the SNR of the tme-doman OFDM sgnal s defned, wrtten as

142 8 Chapter 4 OFDM Introducton and System Modelng ton of K, where E N E{ x } P. (4-44) σ b k, m log ( M ) It s observed from the fgure that the SNR requred to acheve a certan BER-performance s dramatcally ncreased for small K-factors (for Raylegh channels). A 3-dB dsadvantage of SNR s evdent for the dfferental detecton method, snce two nose processes wth equal varance are present, the nose of the channel estmate and the nose of the data symbol to be detected. N A performance comparson of dfferent modulaton schemes s presented n Fgure 4-4. Note that the result for 6-QAM (dfferental) s a theoretcal one, because dfferental demodulaton for ths scheme s hard to accomplsh. Agan the advantage of a hgh K-factor s seen. Wth coherent detecton, equvalent performance s obtaned for BPSK and QPSK. Ths s not the case for dfferental detecton on AWGN or Rcean channels, where BPSK has an addtonal advantage of db over QPSK (see also []). It s mportant to note that twce the symbol energy s used wth QPSK, because two bts are transmtted per symbol. The hgher order modulaton schemes (8- PSK and 6-QAM) requre approxmately 3 4 db more sgnal power than QPSK. Takng nto account the channel varablty, rreducble error floors arse (see Fgure 4-5). Both versons of dfferental detecton have been evaluated for Raylegh fadng channels, QPSK modulaton, and for the followng parameters. For detecton n the frequency-drecton, the channel s RMS delay spread τ rms was assumed to be three samples, whch corresponds to a maxmum delay spread of about thrty samples, assumng an exponentally decayng channel delay profle (see Secton.3.3.3). For 8 FFT-ponts, ths value corresponds to about one quarter of the FFT-tme, whch s also about the tme duraton that would be selected for the guard nterval. It s seen that the rreducble error floor assocated wth such qute realstc parameters (τ rms F 3/8) les around (curve { { ). The tme-varablty for dfferental detecton n tme-drecton corresponds to a moble movng at m/s, to a carrer frequency of 6 GHz, and to a symbol length of.3 µs. Accordng to the system model, nter-carrer-nterference (ICI) due to the Doppler spreadng has been neglected 3. Whle the symbol duraton assumed s rather short, the moblty consdered s by an order of magntude hgher than the expected moblty SNR. Ths value s dfferent to the prevous ones, because not all FFT-ponts are used for data subcarrers. In Chapter 8, the codng scheme s ncorporated n some other SNR parameters. 3 That ICI truly s neglgble for the system parameters selected s suggested from the comparson of the maxmum Doppler frequency and the OFDM sub-carrer spacng. The former, beng 4 khz s just.4 % of the latter, whch s MHz. An approxmate equaton for the SNR-degradaton due to moblty can be found for nstance n [7]. Its evaluaton leads to the same concluson (see Secton ).

143 4.3 Performance of an Uncoded OFDM System 9 Performance of OFDM wth perfect channel estmaton BPSK, K BPSK, K 4 BPSK, K QPSK 8 PSK 6 QAM average BER E /N b (a) OFDM wth dfferental detecton and flat fadng (F ) BPSK, K BPSK, K 4 BPSK, K QPSK 8 PSK 6 QAM average BER E b /N (b) Fgure 4-4: Performance of dfferent modulaton schemes. (a): Coherent detecton wth perfect channel estmaton. (b): Dfferental detecton wth F,.e., perfect correlaton between adjacent sub-carrers (flat fadng). n an ndoor wreless-lan system. Despte ths, the error-floor s much lower for ths method of dfferental detecton (curve. The other results depcted analyze the nfluence of synchronzaton errors. In the frequency-doman results, ICI and ISI have been neglected, whch s exact as long as the

144 3 Chapter 4 OFDM Introducton and System Modelng Performance of dfferental detecton; QPSK; Raylegh channel average bt error rate (BER) 3 4 τ rms 3 smp.; δt smp. τ rms 3 smp.; δt 3 smp. τ rms 3 smp.; δt 3 smp. v m/s; δf v m/s; δf 3% of F; w/o ICI v m/s; δf 3% of F; ncl. ICI statc channel; perfect sync average E /N [db] b Fgure 4-5: The channel varablty s leadng to rreducble error floors for the dfferental modulaton schemes. Dfferental QPSK s evaluated over Raylegh fadng channels. channel mpulse response remans wthn the guard nterval. In other words, the performance mpact results from the systematc phase rotatons only that are as seen from the extended system model (Secton 4..4) due to the tme-synchronzaton error. Such phase rotatons mean for the dfferental detecton technques that the sgnal constellaton ponts compared typcally move closer together, whch mples a performance degradaton. Note however, that a negatve tmng offset equal to the channel s τ rms slghtly mproves the performance. Ths s because the channel as well nduces some systematc phase rotaton, whch s n the case dscussed cancelled by the phase rotaton due to tmng-offset 4. The mpact on the performance s small, however, for the offsets evaluated. In the curves depctng the performance for the detecton scheme n tme-drecton, the mpact of ICI due to a frequency-offset s shown as well. ICI has been ncluded usng the approxmaton from [7]. It s seen that the mpact of the phase dstorton s evdent at all SNR-values, whle ICI determnes the error floor at hgh SNR. In Fgure 4-6, the performance of dfferental QPSK (n frequency-drecton) s 4 The progressve phase rotaton due to a tmng-offset can be utlzed for tmng synchronzaton (see Secton 6..7). Thereby, the systematc phase rotaton due to the channel leads to a bas n the estmate. If ths based estmate s used for tmng-synchronzaton, optmum performance s acheved, because the systematc phase rotatons due to the channel and due to the bas compensate each other.

145 . 4.4 Conclusons and Recommendatons 3 Rcan K factor K [db] 5 5 BER for QPSK wth dff. demod. T m { (dotted),. (sold),.7 (dashed)}.... e 6. e. e 3 e e E b /N [db] Fgure 4-6: Performance of QPSK wth dfferental detecton n frequency-drecton. The maxmum excess delay of the channel s related to the FFT-tme, expressed by T m. shown as a functon of E b /N and K, where τ rms s a parameter. Snce the maxmum excess delay of the channel whch should not exceed the guard nterval s a functon of τ rms and K, all these parameters are nterrelated. The followng defntons are ntroduced to get a set of general results. The FFT duraton and GI-duraton are connected by a fxed factor, whch s usually n the range of 4. The maxmum excess delay of the channel can be wrtten τ max τ rms K, accordng to the defnton of Secton (see eq. (-4)). Ths leads to the normalzed excess delay, defned as Tm τ max TFFT τ rmskf. In Fgure 4-6, the performance of dfferental QPSK s shown for T m {,.,.7}. The curves for T m allow a comparson wth Fgure 4-3. Especally for severely fadng channels (low K-factors), the performance degradaton s sgnfcant for the delay spreads consdered. 4.4 Conclusons and Recommendatons The dervaton of the OFDM system model has confrmed that data symbols can be transmtted ndependently over multpath fadng rado channels. It has to be assumed, however, that the channel s maxmum excess delay s shorter than the guard nterval, and that the system has been synchronzed suffcently. Small synchronzaton errors lead to systematc phase rotatons of the data constellaton ponts a property whch can be exploted for estmatng synchronzaton offsets. If the tmng- or frequencysynchronzaton error becomes too large, the orthogonalty of the sub-carrers s partly lost and the sgnal-to-nose rato of the system s degraded. That s, nter-carrer-nter-

146 3 Chapter 4 OFDM Introducton and System Modelng ference (ICI) and nter-symbol-nterference arse. ICI can also result from very fast channel varatons (Doppler spreads) or from carrer phase jtters. The system models presented can be utlzed n analytcal studes of varous aspects of the OFDM technque, as, for nstance, n the performance evaluaton. The basc model ntroduced assumes perfect synchronzaton, whle an extended model consders the phase rotatons due to small synchronzaton-offsets. The performance analyss of an uncoded OFDM scheme s based on the classc formulas gven by Proaks ([]: Appendx B). Expressons are derved for the evaluaton of dfferent modulaton schemes and for coherent and dfferental detecton. The frequency-doman channel model (see Chapter ) for Rcean fadng channels has been appled. It allows to show performance results as a functon of the channel parameters {P, K, τ rms } the normalzed receved power, the Rcean K-factor, and the RMS delay spread. Assumng perfect channel estmaton, or f dfferental schemes are appled complete channel correlaton, the performance s determned by P and K. These parameters specfy the average sgnal power and the depth of the fades. Better performance s thus acheved over channels havng a hgher K-factor, because the fades are shallower. Performng dfferental detecton n the frequency-doman, a degradaton of the results s seen, due to the small dfferences of the channel transfer functon at adjacent subcarrers (whose data symbols are compared). Snce, for small frequency-lags, there s a very strct relatonshp between ths correlaton functon and the RMS delay spread, τ rms, of the channel (n partcular for Raylegh fadng channels see Appendx A), t s concluded that the performance degradaton s well characterzed by τ rms. (To be exact, the performance s defned by the product τ rms F, where F s the sub-carrer spacng.) Imperfect tmng-synchronzaton also has an mpact, because systematc phase offsets are ntroduced between adjacent sub-carrers. For the low-moblty OFDM based WLAN system under nvestgaton, the correlaton of subsequent symbols n tme-drecton s much hgher than the correlaton of symbols on adjacent sub-carrers. Therefore, t s recommended to apply dfferental detecton n tme-drecton, not n frequency drecton. In ths case, systematc phase offsets are nduced by mperfect carrer frequency-synchronzaton. By extendng the OFDM system model, t becomes possble to analyze mperfectons of OFDM systems. Frequency synchronzaton-offsets, for example, gve rse to ntercarrer-nterference, whch can be accounted for by an addtonal nose term []. In a smlar fashon, the mpact of Doppler spreads, phase nose, or channel estmaton errors can be ncorporated. The evaluaton of such mperfectons s a topc for future work. Usng the orgnal equatons of [], t s also possble to nvestgate dversty technques (see e.g. [5] [7]).

147 4.5 References References [] J. G. Proaks, Dgtal Communcatons, 3 rd edton. New York: McGraw Hll, 995. [] R. Prasad, Unversal Personal Communcatons. Boston: Artech house, 998, ch.. [3] R. van Nee and R. Prasad, OFDM for Wreless Multmeda Communcatons. Boston: Artech House,. [4] O. Edfors, M. Sandell, J. J. van de Beek, D. Landström, F. Sjöberg, An Introducton to Orthogonal Frequency-Dvson Multplexng, Research Report TULEA 996:6, Dvson of Sgnal Processng, Luleå Unversty of Technology, csee/sp/publcatons.html. [5] O. Edfors, Low-complexty algorthms n dgtal recevers, Ph.D. Thess, Luleå Unversty of Technology, Sept [6] M. Sandell, Desgn and Analyss of Estmators for Multcarrer Modulaton and Ultrasonc Imagng, Ph.D. Thess, Luleå Unversty of Technology, Sept [7] M. Speth, S. A. Fechtel, G. Fock, and H. Meyr, Optmum Recever Desgn for Wreless Broad-Band Systems Usng OFDM Part I, IEEE Trans. Commun., vol. 47, no., pp , Nov [8] S. B. Wensten and P. M. Ebert, Data Transmsson by Frequency-Dvson Multplexng Usng the Dscrete Fourer Transform, IEEE Trans. Commun. Techn., vol. COM-9, no. 5, pp , Oct. 97. [9] A. Peled and A. Ruz, Frequency Doman Data Transmsson Usng Reduced Computatonal Complexty Algorthms, n Proc. IEEE Int. Conf. Acoust., Speech, Sgnal Processng, Denver, CO, 98, pp [] P. Pollet, M. van Bladel, and M. Moenclaey, BER Senstvty of OFDM Systems to Carrer Frequency Offset and Wener Phase Nose, IEEE Trans. on Commun., vol. 43, no. /3/4, pp. 9 93, Feb./March/Aprl 995. [] P. H. Moose, A technque for orthogonal frequency dvson multplexng frequency offset correcton, IEEE Trans. Commun., vol. 4, no., pp , Oct [] P. A. Bello, Characterzaton of randomly tme-varant lnear channels, IEEE Trans. on Commun. Systems, vol. CS-, pp , Dec [3] R. Steele, Moble Rado Communcatons. New York: John Wley & Sons, 99. [4] W. C. Jakes Jr., Mcrowave Moble Communcatons. New York: John Wley & Sons, 974.

148 34 Chapter 4 OFDM Introducton and System Modelng [5] J. Lu, T. T. Tjhung, F. Adach, and C. L. Huang, BER performance of OFDM- MDPSK systems n frequency-selectve Rcean fadng wth dversty recepton, IEEE Trans. Veh. Technol., vol. 49, no. 4, pp. 6 5, July. [6] X. Dong, T. T. Tjhung, and F. Adach, Error Probablty Analyss for 6 STAR- QAM n Frequency-Selectve Rcean Fadng wth Dversty Recepton, IEEE Trans. on Veh. Techol., vol. 47, no. 3, pp , Aug [7] T. T. Tjhung, F. Adach, K. H. Tan, X. D. Dong, and S. S. Ng, BER Performance of 6 STAR-QAM n Rcean Fadng wth Dversty Recepton, n Proc. PIMRC 94, The Hague 994, pp

149 Chapter 5 OFDM System Proposal and Emulaton System 5. Introducton Man parts of ths Ph.D. research have been performed under the framework of a cooperatve research project between Korea Telecom and Delft Unversty of Technology, as mentoned n the ntroducton. One of the goals of ths project was the development of an OFDM based wdeband communcatons system operatng at up to 55 Mbt/s n 6 GHz rado channels. Wreless asynchronous transfer mode (ATM) transmsson was consdered n ndoor and low-range (and low moblty) outdoor envronments. The frst part of ths chapter (Secton 5.) gves an overvew of the proposed OFDM system. Most of the parameters gven and choces made are motvated n the text; others have been selected rather ntutvely. One purpose of the system proposal was to specfy an OFDM system that could be used as a benchmark system n analytcal studes and smulaton studes of several aspects of the OFDM technque. These studes are descrbed n the remanng chapters of ths thess. They mostly concern mplementaton ssues of OFDM, lke synchronzaton and channel estmaton, and ther performance evaluaton. Some of the conclusons have been ncorporated n the system proposal gven here. That s, although some parameters may have been selected adhoc, ther sutablty was nvestgated and confrmed afterwards. The proposed system conssts of a central base staton (BS) and several moble termnals (MT). The base staton acts as an nterface between the physcal transmsson meda of the wred ATM backbone network and the broadband rado ar-nterface. Therefore, t must be optmzed for operatng robustly and effcently n these two very dssmlar communcatons meda, the hghly relable optcal fber network and the ran- 35

150 36 Chapter 5 OFDM System Proposal and Emulaton System domly fadng rado channel. The target bt-rate of 55 Mbt/s s reached under deal condtons, and when the uplnk and down-lnk data rates are added up. Channel bandwdths n the order of MHz are requred; n mult-cell systems, several of these channels must be avalable for adjacent base statons. Such large bandwdths may be avalable n the 6 GHz frequency-band. The ar-nterface s the man research topc of ths Ph.D. thess, hence the system proposal s focused on the physcal layer. Orthogonal frequency dvson multplexng (OFDM) s consdered to be the key enablng technology for such hgh data rates n multpath fadng, moble channels. One ATM cell was assumed to be the smallest nformaton entty to be transmtted at a tme. A multple access scheme havng both tme- and frequency dvson multple access components (TDMA and FDMA), maps the ATM cells on the OFDM symbols, after nterleavng and error correcton codng. Perodc tranng symbols are transmtted on the down-lnk for synchronzaton and channel estmaton. These tranng symbols are followed by sgnalng symbols, whch are used by the medum access control (MAC) protocol to negotate transmsson capacty. On the up-lnk, pre-equalzaton and tme-dvson duplexng (TDD) are proposed for mnmzng the sgnal processng requred and for enablng asymmetrc data rates. Recprocty of the channel s assumed. Pre-equalzaton allows the effcent transmsson of nformaton enttes as short as a sngle ATM cell on the up-lnk, wthout addng vast amounts of overhead for synchronzaton and channel estmaton. It also reduces the sgnal processng needed at the base staton for servng multple moble termnals. Slow tme-varablty of the rado channel s a necessty, however. Another prmary goal of the cooperatve research project was the demonstraton of the proposed ar-nterface on a hardware platform to be developed. Unfortunately, the techncal specfcatons of the nvestgated systems are so demandng that an mplementaton s almost mpossble for a small research team, as real-tme DSP of two data streams s requred at samplng frequences of ~ MHz. A drastcally downscaled hardware platform s therefore used, whch s presented n Secton OFDM Based System Proposal A hghly effcent multple access scheme s one of the man requrements of the proposed, OFDM-based, multmeda communcatons system. In order to mnmze delays n low-rate applcatons and n automatc repeat request (ARQ)-schemes, whch are needed to meet defned qualty-of-servce (QoS) requrements, the system should be able to transmt small data enttes (sngle ATM cells) wthout the need for excessve sgnalng and synchronzaton overhead. Ths desgn target becomes crtcal because of the hgh data rate of up to 55 Mbt/s.

151 5. OFDM Based System Proposal 37 Another mportant aspect was to consder an opton for smultaneously accessng the system wth low-complexty termnals that can only cope wth one quarter of the system bandwdth. Such transcevers have smplfed RF front-ends and baseband processng unts, whch both lead to reduced power consumpton. Moreover, the lmted bandwdth mples a 6-dB advantage n ther lnk-budgets. Adaptablty to current channel condtons s provded by two mechansms. Two transmsson modes (modes I and II) wth dfferent delay spread robustness can be used accordng to the typcal channel propertes of the envronment. Ther man dfference s the length of the guard nterval and the number of FFT-ponts and sub-carrers. A set of codng and modulaton technques allows for a trade-off between the range and the bt-rate. I.e., Usng more effcent codng technques and more robust modulaton schemes, the range can be extended at the cost of a decreased data rate. The key specfcatons and desgn paradgms consdered are: up to 55 Mbt/s ATM data rate operaton n the 6 GHz (mm-wave) frequency-band ndoor pco-cells and short range outdoor envronments (< m dameter) lmted moblty (max. 5 m/s) fulfll defned QoS and delay requrements provde hgh spectral effcency low mplementaton complexty (to cope wth the hgh data rates) low power consumpton hgh robustness aganst delay spread and nterference provde adaptablty to changng channel condtons (e.g. fall-back modes) Ths secton ntroduces the OFDM system proposal, whch takes the above lsted requrements nto consderaton. It s organzed as follows. In Secton 5.., the man transmsson modes are explaned, and the selected tme-dvson duplex (TDD) frame structure and OFDM symbol confguraton are ntroduced. The multple access scheme havng tme and frequency dvson multple access (TDMA, FDMA) components s descrbed n Secton 5... Secton 5..3 presents the hardware archtecture of base statons and moble termnals n the form of block dagrams. Interleavng and codng schemes are outlned n Secton 5..4, followed by lnk budget consderatons n Secton In Secton 5.4, the system proposal s summarzed and prelmnary conclusons are drawn. 5.. Ar Interface Physcal Layer The OFDM modulaton technque s consdered a strong canddate for the ar-nterface of hgh-speed wreless LANs and smlar systems. The man advantages of OFDM n ths context are ts hgh spectral effcency and robustness aganst multpath delay

152 38 Chapter 5 OFDM System Proposal and Emulaton System spread. The latter s obtaned through the ntroducton of a guard nterval. The wellknown, and extensvely studed dsadvantages of ths modulaton technque nclude []: Senstvty aganst frequency offsets and phase jtters Non-constant power envelope (requrng lnear power amplfers to avod dstorton) These ssues have to be solved suffcently, otherwse the orthogonalty among data symbols s partly lost (ICI and ISI arse). To overcome, or at least ease these mparments, some of the desgn consderatons of the proposed OFDM scheme were: Transmt suffcent overhead (tranng-symbols) on the down-lnk to allow the MTs to synchronze to the BS wth low computatonal complexty and to allow for accurate and effcent channel estmaton. Use as lttle carrers as possble, whch s of advantage for the frequency synchronzaton algorthm, for the peak-to-average power rato (PAPR) problem, and for the robustness aganst carrer phase jtter and Doppler spreads Modes of Operaton For dfferent envronments, antenna confguratons and lnk qualtes, several modes of operaton are proposed. There are two ncompatble man modes (mode I and mode II) that wll be permanently assgned to a base staton, dependng on the propertes of the envronment. Mode II has a hgher robustness aganst long delay spreads, whch may be requred n very large rooms (cf. Secton.5.). Ths hgher robustness s obtaned by ncreasng the guard nterval duraton, the symbol length, and the number of FFT ponts and sub-carrers. Mode I allows for maxmum excess delays of about ns (~5 ns RMS delay spread, τ rms ), mode II permts about 5 ns (τ rms 65 ns). Exceedng those maxmum values leads to a gradual performance degradaton that may be tolerable f the sgnal-to-nose rato s suffcent. Mode I has advantages due to the smaller number of FFT ponts, allowng for relaxed hardware requrements. For nstance, the robustness to phase nose and Doppler shfts s enhanced, the PAPR problem s reduced, and the effcency s slghtly hgher, due to a more effcent frame format. These advantages may enable the desgn of cheaper access ponts for small envronments, where mode I s typcally approprate and suffcent. Another desgn goal was to provde the possblty to smultaneously access the network wth full and reduced (one quarter) bandwdth moble termnals, as mentoned above. These two optons are denoted as the full-rate (-fr) and the quarter-rate (-qr) bandwdth modes. Usng four sub-symbols per OFDM symbol, the coded ATM cells are mapped on the transmsson medum n a flexble TDMA/FDMA scheme (see Secton 5..). Table 5- lsts the characterstc parameters of modes I and II,

153 5. OFDM Based System Proposal 39 Table 5-: Characterstc parameters of the transmsson modes I and II for full and quarter bandwdth termnals mode: I II parameter full quarter full quarter Number of FFT ponts Nr. of data + plot sub-carrers FFT tme [µs].. n [samples] Guard + wndowng nterval [µs] n [samples] Bandwdth (- db) [MHz] ~ ~ 8 ~ ~ 8 Samplng frequency [MHz] operatng at full and quarter bandwdth. Quarter rate termnals cannot use the full transmsson rate, however, they have advantages regardng the complexty of the base-band processng unt and the RF frontends, regardng the lnk budget (see Secton 5..5), and regardng the power consumpton. The quarter-rate mode can also serve as a fallback mode for the full-rate users, when shortcomngs are experenced n ther lnk-budgets. (Ths apples partcularly for the up-lnk). But the reduced bandwdth also mples some dsadvantages. Less bandwdth means less frequency-dversty, thus consderng forward error correcton codng the performance s expected to be worse. The bt- and frame-error-rate analyss of a coded and nterleaved OFDM system confrms ths expectaton (see Secton 8.). Frequency hoppng across the four quarter-rate sub-bands would reduce ths performance gap. Another possble remedy s the applcaton of dversty schemes, as proposed n Secton 8.3. The transmsson speed s determned by the modulaton technque and codng scheme used. OFDM allows for hgh flexblty n usng dfferent modulaton and codng technques smultaneously, dependng on the users channel qualtes. The man optons consdered are QPSK and 6-QAM modulaton wth codng rates of approxmately ½ and ¾. However, many other combnatons can be appled as well. These modulaton modes are referred to as sub-modes -H, -L, and -LL. Ther descrpton and the actual transmsson rates acheved are presented n Secton 5...4, Table Frame Format and Modulaton Schemes A tme dvson duplexng (TDD) frame format has been proposed, whch has a fxed total frame length and a flexble boundary between the down-lnk and the up-lnk n order to support asymmetrc data rates. To smplfy the swtchng of the transcevers between transmsson and recepton and to be able to compensate for propagaton de-

154 4 Chapter 5 OFDM System Proposal and Emulaton System Mode I: down-lnk flexble boundary up-lnk tme tranng sequence data symbols down-lnk sgnalng TDD guardsymbol data symbols up-lnk sgnalng free data symbols TDD guardsymbol 69 T 88.4 µs Mode II: down-lnk up-lnk tme t 37 T 94.8 µs Fgure 5-: Frame structure of the tme dvson duplex scheme n modes I and II. Each rectangle ndcates one OFDM symbol. lays, null-symbols are nserted. An llustraton s gven n Fgure 5-; the frame related parameters for the two transmsson modes are lsted n Table 5-. Usng a TDD scheme, most synchronzaton can be done by the moble termnals on the down-lnk. For ths purpose, the base staton transmts a tranng symbol at the begnnng of each frame, beng a unque OFDM symbol. Ths symbol s used for (frame) tmng and frequency synchronzaton, as well as for the dervaton of a channel estmate for the down-lnk channel. The requred sgnal-processng algorthms are descrbed and evaluated n Chapter 6. There s no tranng symbol on the up-lnk, assumng recprocty of the channel. In order to facltate coherent detecton on the up-lnk, pre-equalzaton technques are suggested. I.e., the up-lnk data constellaton ponts are multpled by the nverse of the Table 5-: Frame related parameters of the OFDM system proposal parameter mode I mode II mode II OFDM symbol duraton T [µs].8.56 OFDM symbols per frame frame duraton [µs] frame rate [kframes/s] TDD guard symbols per Frame (overhead) (.8 %) (5.4 %).5 (.8 %) synchronzaton symbols per Frame (.4 %) (.7 %) (.8 %) sgnalng symbols per Frame (.8 %) (5.4 %) (.8 %) sgnalng channels per Frame; up + downlnk (4 per OFDM symbol) up-lnk or 4 down-lnk modulaton for sgnalng BPSK codng rate for sgnalng ~½ data bts per sgnalng channel per Frame sgnalng rate per sgnalng ch. [kbt/s]

155 5. OFDM Based System Proposal 4 channel transfer functon that has been estmated on the down-lnk. Passng the preequalzed OFDM sgnal through the multpath channel, the overall transfer functon becomes flat or phase-lnear. Channel estmaton and synchronzaton on the up-lnk thereby reduce to an estmaton of the magntude of the receved constellaton values, and the estmaton of tmng-offsets and carrer phase-offsets. Chapter 7 explans those technques. In mode II, the number of OFDM data symbols per frame was halved n order to mantan the rate of synchronzaton symbols. (Below, a dscusson on the frame length and channel tme-varablty s gven.) For the sake of smplcty, the overhead symbols (TDD guard, synchronzaton and sgnalng) were adopted from mode I, resultng n an ncreased overhead and a doubled data rate on the sgnalng channel 5. Doublng the perod of the synchronzaton symbol s reasonable because the requrements on the frequency synchronzaton are also doubled. Mode II' ntroduced n the table above s a slghtly more effcent proposal compared to mode II. The effcency s ncreased by alternatngly transmttng sgnalng channels on the up- and down-lnk, and by halvng the TDD guard ntervals. Accordng to mode I, the transcevers have to be able to swtch between up and down-lnk wthn the duraton of one mode I OFDM symbol. Thus extendng the TDD guard symbols s a waste of effcency. It has to be evaluated, however, f the propagaton delays and flter group delays can be ft wthn ths guard perod. The up-lnk transmsson must start slghtly n advance to ensure that the up-lnk symbols FFT-perods arrve at the deal tme-nstants. Channel varablty and moblty In these paragraphs, the speed and character of the tme-varablty of the channel are brefly analyzed. Assumng the maxmum speed n an ndoor envronment to be v m m/s, the maxmum Doppler frequency s f m v m /λ 4 Hz at 6 GHz. Defnng the coherence tme ( t) c as the tme-separaton for whch the spaced-tme correlaton functon of the channel φ H ( t).9, we obtan for the above f m and Jakes fadng model [] ( t) c.5 ms (see eq. (4-3) n Secton 4.3. for K ). For the above defned OFDM system,.5 ms are equal to ~ (mode II: ~) OFDM Symbols or approxmately 3 frames, durng whch the channel s almost constant. Alternatvely, the sutablty of the proposed frame duraton can be evaluated based on the samplng theorem. In order to use the tranng sequence transmtted n the begnnng of each frame for estmatng the channel, the Nyqust crteron has to be fulflled. To track the varatons of a channel wth maxmum Doppler frequency f m, the channel s transfer functon has to be sampled at tme-nstants separated by at most 5 A doubled data rate on the sgnalng channels n mode II can be useful, because mode II may operate n bgger envronments wth hgher numbers of potental users. Thus, a hgher sgnalng data rate mght ncrease the total throughput.

156 4 Chapter 5 OFDM System Proposal and Emulaton System t plot < ( f m ). Ths yelds t plot <.5 ms for f m 4 Hz. Thus the frame duraton of ~9 µs guarantees suffcent oversamplng of the channel estmates. We antcpate that the proposed OFDM system s sutable for such slowly tme-varant rado channels, but not for (much) faster moblty. Performance results for the ar-nterface over tme-varant channels are gven n Secton 6.5 of ths thess OFDM Symbol Confguraton Sub-bands and OFDM sub-symbols Fgure 5- shows the OFDM symbol confguratons n modes I and II. Several zerocarrers are ntroduced. The zeros at f c, + { 4,, +4} MHz are used to separate the four quarter rate sub-bands, where f c, s the center frequency of the full-rate OFDM channel. The zero at f c, s also requred to avod problems wth carrer feed-through and AD/DA converter offsets, as explaned n Secton For the same reason, zerocarrers are used at the center frequences of the quarter rate channels, whch are located at f c, + { 36,,, 36} MHz. In mode II, the number of (data and plot) sub-carrers s doubled. Three zero sub-carrers are separatng the OFDM sub-bands n order to keep the sub-band center frequences at fxed postons. These extended guard-bands may be of beneft to avod nter-sub-band-nterference, because the requrements on carrer stablty are hgher n mode II. Alternatvely, two of the zero sub-carrers may be used as addtonal plots. Dscusson of plot assgnment and purpose of plots The plots present n the system cannot be used for channel estmaton, because ther frequency spacng s too large. In stead, they are used for synchronzaton purposes and for coherent demodulaton as follows. On the down-lnk and up-lnk, the plots are needed for the estmaton of carrer phase-offsets due to resdual carrer frequency-errors, whch lead to a common phase rotaton of all sub-carrer constellaton values (see Secton 4..4.). On the up-lnk, they are also used for the trackng of up-lnk tme-delays, whch cause a progressve phase rotaton of the sub-carrers (see Secton 4..4.). Mode I; full rate Mode I; quarter rate (sub-band ) plots sub-band 3 sub-band 4 sub-band sub-band frequency f f f c,4 f c, f c,3 f c, c, f f c, + 48 MHz c, f c, + MHz Mode II; full rate Mode II; quarter rate (sub-band ) sub-band 3 sub-band 4 sub-band sub-band frequency f f c,3 f c,4 f c, f c, f c, f c, Fgure 5-: OFDM symbol confguratons n the dfferent operaton modes

157 5. OFDM Based System Proposal 43 Those delays must be known very accurately, when coherent demodulaton s appled. On the one hand, plots should be dstrbuted evenly across the sgnal bandwdth n order to explot frequency dversty when some of them are n deep fades. On the other hand, a constant spacng between adjacent plots can be problematc n a multpath channel wth two man paths. For a two-path channel wth relatve delay tme τ δ, the channel transfer functon has mnma separated by /τ δ. Thus, f the plot spacng f plot /τ δ, all plots mght be n a deep fade at the same tme. A short calculaton s gven to show that the latter problem can probably be neglected n the system under nvestgaton. Dstrbutng the number of plots proposed for the system evenly across the sgnal bandwdth leads to a constant spacng of 8 and 4 MHz among adjacent plots, n modes I and II, respectvely. Such a f plot corresponds to a τ δ of 5 and 5 ns, respectvely, or equvalently, to path-length dfferences of 37.5 and 75 m. Due to the very lmted szes of the rado cells n the proposed system and due to the low transmsson powers, t s rather unlkely that rays wth such large path-length dfference can sgnfcantly nterfere wth each other. Therefore, a constant plot spacng can be used, whch also smplfes the algorthm for extractng the up-lnk tmng-offset (see Secton 7.5.). A plot assgnment wth a non-unform spacng s presented n Secton Spectral shape The spectral shape of the proposed OFDM operaton modes s shown n Fgure 5-3, assumng a perfect power amplfer. That means, out-of-band radaton because of non-lnear dstorton of the sgnal n non-lnear amplfers s not ncluded. Note that the spectra of full rate users power spectrum magntude [db] mode I mode II f n MHz Fgure 5-3: Spectra of the OFDM sgnals n dfferent operaton modes. Null-carrers are used to separate the four sub-bands and to avod data transmsson at the DC-carrer(s).

158 44 Chapter 5 OFDM System Proposal and Emulaton System spectra of mode II are shfted by db n that fgure. It s seen that the spectral shape s very smlar for modes I and II. The steep decay at the band edges s due to the tmedoman wndowng appled (see Fgure 4-, Secton 4...). The purpose of ths type of wndowng s the reducton of out-of-band radaton n order to allow a close spacng of adjacent frequency-bands (channels) used by the system n dfferent rado cells. In the current system proposal, the length of the wndow s qute sgnfcant, beng ~ % and ~5 % of T FFT for mode I and II, respectvely. Whle such a long wndowng nterval can be seen as an extenson of the guard nterval, t also means a loss of effectve transmsson power, addtonal to the loss due to the guard nterval. Consderng a real system, flters are requred for channel-selecton, alasng suppresson (ADC), and sgnal reconstructon (DAC). The specfcatons of those flters can be slghtly relaxed, due to the wndowng Data Transmsson Rates Table 5-3 lsts the data transmsson rates that can be acheved n the dfferent operaton modes wth varous modulaton and codng schemes and for full and quarter bandwdth termnals. It s a topc for further research, whether the proposed modulaton and codng technques are the deal combnatons. The gross data rates lsted n Table 5-3 are the numbers of data bts per OFDM symbol dvded by the duraton of an OFDM symbol. Thus, the overheads ntroduced for sgnalng (sgnalng channels and sgnalng overheads appended to ATM cells), synchro- Table 5-3: Transmsson rates usng dfferent modulaton and codng technques (LL: Very low speed; L: Low speed; H: Hgh speed). Values n brackets are for mode II'. mode bandwdth mode modulaton codng rate OFDM symbols per ATM cell data bts / OFDM symbol gross data rate n Mbt/s ATM bt-rate n Mbt/s I-LL full QPSK ½ quarter I-L full QPSK ¾ quarter I-H full quarter 6- QAM ¾ II-LL full QPSK ½ (5.4) quarter (.6) II-L full QPSK ¾ (75.6) quarter (8.9) II-H full quarter 6- QAM ¾ (5.3) 35.8 (37.8)

159 5. OFDM Based System Proposal 45 Table 5-4: Summary of all overheads requred for wreless access and ATM. The total values are relatve to the gross data rate,.e., the data rate ncludng codng. descrpton mode I mode II mode II' TDD guard symbols.8 % 5.4 %.8 % synchronzaton tranng sequence.4 %.7 %.8 % sgnalng n sgnalng channels.8 % 5.4 %.8 % total overhead per frame 7. % 3.5 % 8.6 % sgnalng appended to ATM cells (4/57 bytes) 7 % 7 % 7 % total overhead for wreless access 3.7 % 9.6 % 5. % overhead of ATM headers (5/53 bytes) 9.4 % 9.4 % 9.4 % total overhead relatve to gross data rate.9 % 7. % 3 % nzaton, and tme dvson duplexng have not been subtracted. Plots are excluded. The sub-modes -H, -L and -LL use dfferent modulaton and FEC-technques, namely, QPSK and 6-QAM modulaton wth rate ½- and rate ¾-codng, as seen from the table. Dependng on the modulaton and codng scheme, a varyng number of OFDM symbols s requred for the transmsson of one ATM cell (see also Secton 5..). Each ATM cell consstng of 48 data bytes and 5 header bytes s augmented by 4 bytes for the sgnalng requred by the MAC-protocol. I.e., a data entty comprses 456 nformaton bts, whch make 9 and 684 coded bts, respectvely, wth rate ½- and rate ¾- codng. The amount of sgnalng nformaton was estmated based on the work presented n [3]. The ATM bt-rates lsted n the last column stll nclude the overhead of the ATM headers, but none of the overheads ntroduced for the wreless access. Defnng the gross data rate as %, the overheads are summarzed n Table Up- and Down-lnk Multple Access Scheme Ths secton gves an overvew of the above-ntroduced frame structure and OFDM symbol confguratons, whch make up the multple access scheme. TDMA and FDMA components are combned, as ndcated n Fgure 5-4. TDD s proposed as a duplexng scheme. A fxed frame structure of 69 (n mode I; mode II: 37) OFDM symbols results, wth a flexble boundary between the up- and the down-lnk. The FDMA component (sub-bands) s suggested n order to smultaneously allow moble termnals that are usng only one quarter of the full system bandwdth the quarter-rate users. The BS operates n mode I or II, dependng on the present envronment (see Secton 5...). In the begnnng of each frame, a tranng symbol (TS) (a unque OFDM symbol) s broadcast on the down-lnk, whch s used for tme- and frequency synchronzaton

160 46 Chapter 5 OFDM System Proposal and Emulaton System tme frequenc TDMA-TDD/FDMA-OFDM Multple Access Scheme: Mode I: Mode II: OFDM Symbol Nr. Symbol Nr TDD - guard symbol TS: Synchronzaton and channel est. SIG SIG SIG 3 SIG 4 Downlnk sgnallng 3 3 Mode I-H (or II-L); full rate; ATM cell Mode I-L; full rate; ATM cell Mode I-LL; Mode I-H Mode I-L; quarter (or II-L); quarter rate; /4 quarter rate; / ATM cell 3 3 rate; ATM cell 4 4 ATM cell M I-H; qr; 5 5 /4 cell TDD - guard symbol varable poston SIG SIG SIG 3 SIG 4 Uplnk sgnallng Downlnk Uplnk Mode I-H (or II-L); full rate; ATM cell Mode I-H (or II-L); quarter rate; ATM cell Mode I-L; quarter rate; / ATM cell Mode I-H (or II-L); quarter r.; / cell TDD - guard symbol Mode I-L; quarter rate; /4 ATM cell TS: Synchronzaton and channel est. SIG SIG SIG 3 SIG Fgure 5-4: The proposed TDMA-TDD/FDMA-OFDM multple access scheme. Each row represents one OFDM symbol, whch s dvded nto four sub-bands. Note: Frequency hoppng s not shown. and for channel estmaton (see Chapter 6). The TS s followed by four parallel sgnalng channels, each n a separate OFDM sub-band. To ensure hghest possble relablty, BPSK modulaton and rate ½-codng s used for all sgnalng (see Table 5-). The consecutve symbols carry the user data on the down-lnk. The sub-modes -H, -L and -LL use dfferent modulaton and FEC-technques, namely, QPSK and 6-QAM modulaton, wth rate ½- and rate ¾-codng. Dependng on the modulaton and codng schemes, a varyng number of OFDM symbols s requred for the transmsson of one

161 5. OFDM Based System Proposal 47 ATM cell (see Table 5-3). To effcently map ATM cells on ths fxed frame structure, t s consdered to allow the transmsson of half or quarter ATM cells per frame as well. On the up-lnk, another four dedcated sgnalng channels are avalable. No tranng symbols are used there to maxmze the spectral effcency. In stead, the applcaton of pre-equalzaton s suggested n order to facltate coherent detecton, whch requres a recprocal channel. Ths prncple s dscussed n detal n Chapter 7. Super-frame structures should be defned to effcently mplement the mappng of ATM cells on the gven frame-structure usng the multple access schemes descrbed, usng a centralzed, scheduled MAC protocol Archtecture of the Transcevers Base Staton (Access Pont) The archtecture of the base-band system and RF front-end of the base staton s rather smple. However, the MAC and control sub-layers have rather hgh complexty, snce the data streams of multple MTs have to be multplexed n the BS, requrng ARQ, power control, sgnalng, and other functons. And they have to operate at very hgh speed. Usng plots and/or blnd technques, transmsson delays and carrer phase offsets have to be estmated for each user (see Secton 7.5.). A block dagram of the base-band and RF parts s gven n Fgure 5-5. Note that none of the requred flter stages are shown for the sake of smplcty. Base staton: plot symbols, tranng sequence guard nterval, wndowng codng / decodng, nterleav./ denterl. symbol mappng symbol detecton multplexer plot extracton IFFT FFT DSP tmng D/A A/D I/Q mod LO I/Q dmod LO duplexer downconv. W-MAC, W-control, ATM cell multplexng upconv. Fgure 5-5: Archtecture of the base-band system and RF front-end of the base statons Moble Termnal The base-band system of the moble termnals has a somewhat hgher complexty, because synchronzaton, channel estmaton, and pre-equalzaton algorthms have to be mplemented. The block dagram s depcted n Fgure 5-6. Note the hardware feedback sgnal for frequency-synchronzaton. Interestng smplfcatons of the synchronzaton tasks requred (tmng, frequency, samplng frequency)

162 48 Chapter 5 OFDM System Proposal and Emulaton System Moble termnal: LO I/Q dmod LO I/Q mod A/D freq. sync. D/A synchron. DSP FFT tmng sync. IFFT plot ext./ chan. est. s-mappng pre-equal. channel estmate symbol detecton upconv. duplexer downconv. multplexer codng / decodng, nterleav./ denterl. W-MAC, W-control, ATM cell multplexng guard nterval, wndowng plot symbols Fgure 5-6: Archtecture of the base-band system and RF front-end of the moble termnals can be acheved by lockng all local oscllators (LO) and the samplng clocks on one adjustable frequency source. Thereby, synchronzng for one of the frequency-offsets n hardware (usng the feedback sgnal), all other frequency-offsets are cancelled smultaneously, whch smplfes the mplementaton of the proposed OFDM system. Note that ths prncple also requres the oscllators of the base staton to be locked on one another to provde fxed ratos among ther frequences Forward Error Correcton Codng Forward Error Correcton Codng Standard convolutonal codng schemes wth soft decson Vterb decodng can be appled. Possble parameters for the encoder and decoder are a codng rate of ½ and a constrant length of 7. The rate ¾ codng used n modes -L and -H (see Table 5-3) can be derved from the rate ½ code by puncturng. Note that the same codes are used n the IEEE 8. and n the HIPERLAN/ wreless LAN standards [], [4]. Ths was the only reason for selectng these codes for our proposal. No research towards optmzaton of the codng scheme was performed. Error rate results for the codng and nterleavng schemes are presented n Chapter Interleavng Schemes Bt-level nterleavng s used to break-up burst errors nto, deally ndependent, welldstrbuted errors, whch can be corrected more effcently by conventonal codng schemes. Because of the frequency-selectve fadng channel experenced by the OFDM system, errors usually result from the sub-carrers beng attenuated by the channel. Ths often results n burst errors the applcaton of an nterleaver s thus necessary. Block nterleavers are proposed for the nvestgated transmsson system. The convolutonally encoded data bts to be transmtted are wrtten column-wse nto a rectangular array of k columns and n rows, where k denotes the degree (or depth) of the nter-

163 5. OFDM Based System Proposal 49 Interleaver (degree k 4): nterleaver (degree k 3): block structure: wrte matrx read matrx 6 P Z 4 3 P P 5 3 k btnumber sub-carrer number n P: plot SC Z: zero SC wrte matrx read matrx 9 P Z 5 3 P P spreadng of coded bts over sub-carrers (numbers ndcate bt-numbers of coded bts): IL : IL : SC bt/sym b, s b, s b, s k 4 f plot SC bt/sym b, s b, s b, s k 3 f plot zero zero plot plot plot plot Fgure 5-7: Interleavng schemes for transmsson mode I-LL, quarter rate. leaver. The bts to be modulated on the OFDM sub-carrers are read from ths array row-wse. Two consecutve bts of the coded sequence are therefore separated by k sub-carrers n an OFDM symbol. Note that only one bt of the QPSK or 6-QAM constellatons s defned at a tme, because the whole symbol undergoes the same fadng, mplyng that all ts bts have the same error probablty. Thus defnng a whole data symbol (sub-carrer) at once would counteract the goal of breakng up error bursts. Not only the two or four bts transmtted (n one QPSK or 6-QAM symbol) over one sub-carrer undergo the same fadng, but, because we consder slow tme varablty of the channel, sub-carrers of consecutve OFDM symbols are also affected n the same way. Therefore, the nterleavng must be done n the frequency-doman,.e., across the sub-carrers of the OFDM symbols. The block-sze of the nterleaver s determned by the number of sub-carrers of the OFDM scheme. Error correcton codng s done over a whole ATM cell, whch s carred by a number of OFDM symbols as ndcated n Table 5-3. Ths requres that the bts are perodcally wrtten nto the nterleavng matrx and read from t n order to be modulated on dfferent bts of the (QPSK or 6- QAM) data constellatons and on consecutve OFDM symbols. For nstance, n transmsson mode I-LL quarter rate, 4 OFDM symbols are requred to transmt the 9

164 5 Chapter 5 OFDM System Proposal and Emulaton System nterleaver for mode II, quarter rate: wrte matrx (bt nr.) read matrx (SC. nr.) 9 P P P Z 3 P : P : P P: plot SC Z: zero SC nterleaver for mode I, full rate: nterleaver for mode II, full rate: read matrx (SC. nr.) read matrx (SC. nr.) wrte matrx (bt nr.) P P Z P P Z P Z P Z P Z P P Z P Z P P k 9 n wrte matrx (bt nr.) P P P Z P P P Z Z Z P P P Z P P P Z Z Z P P P Z P P P Z Z Z P P P Z P P P k 7 n Fgure 5-8: Interleavng schemes for transmsson modes I; full rate, and II; full and quarter rate. bts of one whole, rate-½ coded ATM cell. Tme-nterleavng s not consdered n order to mnmze throughput delays and memory buffers. However, when frequency hoppng s mplemented n the quarter rate mode, tme-nterleavng over all OFDM symbols on whch an ATM cell s mapped should be added n order to dstrbute the coded bts more evenly over the frequencyband. For the quarter rate opton of transmsson mode I (usng QPSK and rate-½ codng), two possble nterleavng schemes are depcted n Fgure 5-7. One of degree 4 (nterleaver (IL) ), the other one of degree 3 (IL ). Next to the rectangular block-nterleavng matrx, the translaton of coded bts to sub-carrers and OFDM symbols s llustrated. Plot and zero sub-carrers are ncluded n the nterleavng scheme, so that, usng IL, subsequent coded bts are modulated alternately on odd and even sub-carrers. (To obtan ths, the degree of the nterleaver must be odd.) Ths property s desrable wth the transmtter dversty schemes presented n Secton 8.3. For the other transmsson modes, possble nterleaver structures and plot/zero carrer assgnments are depcted n Fgure 5-8. For mode II quarter rate (-qr), mode I full rate

165 5. OFDM Based System Proposal 5 (-fr), and mode II-fr, nterleavers of depth 5, 9, and 7, respectvely, are suggested. Obvously, adjacent coded bts are spread more n the full rate modes, thus we expect better performance from these schemes. Theoretcal and smulaton results are gven n Secton 8.. To mprove the performance of the quarter rate modes, t s suggested to mplement frequency hoppng across the four quarter-rate sub-bands or antenna dversty technques. Some proposals for computatonally effcent dversty schemes are descrbed n Secton Lnk Budget A lnk budget for the 6 GHz frequency band s gven n Table 5-5, assumng that 5 mw transmt power are avalable. Full and quarter rate termnals are consdered n the table. Fgures n Italcs dentfy parameter values used n calculatons, when parameter ranges are specfed. It s evdent from the table that ths lnk budget s rather crtcal. No fadng margns are consdered for the shadowng, for nstance, and a path loss exponent of two was assumed. Several nvestgatons have shown that shadowng s a very crtcal problem n 6 GHz communcatons. The leaves of a tree, for example, or the user hmself may completely block a 6 GHz lnk [5]. The concluson s that a lne of sght (LOS) s needed n most cases. Note that a LOS reduces or elmnates shadowng. And t results n fadng dstrbutons wth hgher Rcean K-factors, whch means that the fades are shallow compared wth Raylegh fadng channels. Both effects do allow for operaton lower average SNR. A loss of the LOS most lkely results n dropouts, however. Multple transmt/receve antennas wthn a room could counteract ths problem, just lke multple lght sources are placed wthn a room to acheve a more unform lght dstrbuton and to reduce shadows (see e.g. [6]). Rado-over-fber lnks were suggested to connect the RF front-ends to the base staton over consderable dstances. A slghtly dfferent (and somewhat more promsng) stuaton s ndcated by the channel measurements conducted by Smulders [7]. Wth and wthout LOS, Smulders reports values of normalzed receved power (transmsson loss ncludng the antenna gans) between 85 and 7 db for rooms of dfferent szes, and for dstances up to about 3 m. The path loss exponents observed are below one, due to the antenna desgn used (cf. Secton.5). Ths would allow for a good coverage wthn the relatvely large rooms nvestgated. It s concluded that the system s feasble, however, only for lmted ranges (maxmum 3 m).

166 5 Chapter 5 OFDM System Proposal and Emulaton System Table 5-5: Lnk budget at 6 GHz for full and quarter rate users parameter quarter rate full rate comments bandwdth ~8 MHz ~ MHz spectrum down by db carrer frequency 6 GHz FFT ponts 3 (64) 8 (56) used sub-carrers 9 (38) 88 (76) n TX mode I (II) Power budget: transmt power P tx 7 dbm.e. 5 mw TX power back-off 6 db Because of sgnal dynamcs HPA power 3 7 dbm TX power plus back-off antenna gans g tx,rx 3 6 db omndrectonal antennas free space prop. loss a p at dstance d 88, 98, 8 db at, 3, m calculated as log(4πd/λ) at 6 GHz (λ 5 mm) other losses a tx ~ db connectors, cables, etc. receved power P rx -67, -77, -87 dbm at, 3, m P tx + g tx + g rx a tx a p Nose budget: nose bandwdth B N.5 MHz 9 MHz 88 (76) sub-carrers of (.5) MHz nose fgure F 5 db assumed value equv. nose temp. T 67 K T (F )T nose densty N -7 dbm/hz N T k nose power P N -97 dbm -9 dbm P N N B N SNR 3,, db 4, 4, 4 db P rx /P N (at, 3, m) Requrement: frame error rate max. - requred E b /N requred E c /N guard nterval a GI mn. db mn. 9 db db wth R c ½, ν 5 codng, QPSK modulaton; n Raylegh fadng channels (see Chapter 8) mplementaton loss 3 5 db phase nose, non-lnearty, channel a mp estm., etc. (estmated) requred SNR approx. 5 db E c /N o a GI a mp 5.3 The Emulaton System A man topc of ths Ph.D. thess s the development of dgtal sgnal processng (DSP) algorthms for OFDM-based wde-band ar-nterfaces. The fnal goal of ths research and development effort s the demonstraton of the proposed ar-nterface technques on a realstc hardware platform.

167 5.3 The Emulaton System 53 OFDM ar-nterface emulator: host PC host PC (data source) audo RS3 transmtter DSP board I/Q (analog) RS3 channel DSP board I/Q f f I/Q mod. IF I/Q dmod. frequ. sync. I/Q recever DSP board 3 audo RS3 host PC (data snk) Provde coded data blocks Interleavng; symbol mappng; plot nserton; IFFT; guard nterv.; wndowng; tranng sequence Tme-varant transversal flter for multpath channel smulaton; channel nose channel sm. I/Q modulaton and demodulaton to smulate frequency synchronzaton; phase nose; etc. AGC, frequency and tme synch.; FFT; plot extracton; channel est.; symbol de-mappng; de-nterleav. Decodng; bt and packet error rate estmaton Fgure 5-9: Archtecture of the emulaton system. Unfortunately, the techncal specfcatons of the nvestgated systems are so demandng that an mplementaton s almost mpossble for a small research team, as real-tme DSP of two data streams (the n-phase and quadrature (I/Q) components of the complex base-band sgnal) s requred at samplng frequences of ~ MHz. A drastcally downscaled hardware platform s therefore presented (Fgure 5-9) that enables the assessment of real-tme DSP for such applcatons at low cost. Moreover, (software) mplementaton dffcultes are largely avoded due to the reduced speed. The transmtter and recever are each mplemented on separate audo frequency (sam- Fgure 5-: Photo of the emulaton system. The osclloscope shows the tme-doman OFDM sgnal and ts spectrum wth a smulated channel. Note that the spectrum s calculated n real-tme by the recever-dsp (DSP board 3). The Korea-Telecom (KT)- verson s depcted.