Orthogonal Frequency Division Multiplexing modulation and inter-carrier interference cancellation

Transcription

1 Louisiana State University LSU Digital Commons LSU aster's Theses Graduate Shool 23 Orthogonal Frequeny Division ultiplexing modulation and inter-arrier interferene anellation Yao Xiao Louisiana State University and Agriultural and ehanial College, Follow this and additional works at: Part of the Eletrial and Computer Engineering Commons Reommended Citation Xiao, Yao, "Orthogonal Frequeny Division ultiplexing modulation and inter-arrier interferene anellation" (23). LSU aster's Theses This Thesis is brought to you for free and open aess by the Graduate Shool at LSU Digital Commons. It has been aepted for inlusion in LSU aster's Theses by an authorized graduate shool editor of LSU Digital Commons. For more information, please ontat

2 ORTHOGONAL FREQUENCY DIVISION ULTIPLEXING ODULATION AND INTER-CARRIER INTERFERENCE CANCELLATION A Thesis Submitted to the Graduate Faulty of the Louisiana State University and Agriultural and ehanial College in partial fulfillment of the requirements for the degree of aster of Siene in Eletrial Engineering In The Department of Eletrial and Computer Engineering by Yao Xiao B.S., Dalian University of Tehnology, 998.S., Institute of Automation, C.A.S, 2 ay 23

3 Aknowledgments The author wishes to thank Dr. Wu for his invaluable guidane, kindness and understanding during this researh. ii

4 Table of Contents Aknowledgments...ii Abstrat...v Chapter Introdution and otivation.... Introdution....2 otivation Appliations... 5 Chapter 2 OFD and PAPR Problem Prinipal OFD odel... 6 A. Overview... 6 B. OFD odulation... 7 C. Orthogonal Subarriers... 8 D. Bandpass Signaling... 9 E. OFD Demodulation odern OFD model... A. Overview... B. IDFT and Orthogonality... C. Guard Interval and Cyli Prefix... D. A Pratial OFD System- HiperLAN/ PAPR Problem... 4 Chapter 3 Wireless Channel AWGN and Fading Channel Rayleigh Channel Simple Loal odel COST 27 Fading odel ultipath Fading with CFO Chapter 4 Interarrier Interferene Problem and Solutions Fators Induing ICI... 3 A. Doppler Effet:... 3 B. Synhronization Error C. ultipath Fading Interarrier Interferene and Signal-to-interferene Ratio A. ICI in Simple Loal odel B. ICI in ultipath odel C. Signal to Interferene Ratio Solutions for ICI A. CFO Estimation iii

5 B. Windowing Chapter 5 Clustering Detetion and ultiple Codebook Clustering Interarrier Interferene Canellation... 4 A. Justifiation of Slowly Time-varying... 4 B. Clustering ethod... 4 C. Pilot Bits D. Simulation Results ultiple-codebook A. General Struture of ICI Self-anellation B. Comparison of Codebooks Summary and Further Work Referenes Vita iv

6 Abstrat The Orthogonal Frequeny Division ultiplexing (OFD) tehnique, wireless hannel models, and a pair of new interarrier interferene self-anellation methods are investigated in this thesis. The first hapter addresses the history of OFD, along with its priniples and appliations. Chapter two onsists of three parts: the prinipal, the modern OFD models, and the Peak to Average Power Ratio (PAPR) problem. Chapter two also summarizes possible PAPR solutions. Chapter three disusses a series of well-known wireless hannel models, as well as the general formula for wireless hannels. In Chapter four, ICI problem has been disussed, along with its existing solutions. Chapter five fouses on two new ICI self-anellation shemes, namely the lustering method and the multi-odebook method. These two new methods show promising results through the simulations. A summary of this thesis and the disussion of future researh are also provided in Chapter five. v

7 Chapter Introdution and otivation This hapter onsists of three parts: the introdution of OFD history, the researh motivation, and the appliations of OFD tehnique.. Introdution Orthogonal frequeny division multiplexing (OFD) is one of the multi-arrier modulation (C) tehniques that transmit signals through multiple arriers. These arriers (subarriers) have different frequenies and they are orthogonal to eah other. Orthogonal frequeny division multiplexing tehniques have been applied in both wired and wireless ommuniations, suh as the asymmetri digital subsriber line (ADSL) and the IEEE 82. standard. It is well known that Chang proposed the original OFD priniples in 966 [], and suessfully ahieved a patent in January of 97. Later on, Saltzberg analyzed the OFD performane and observed that the rosstalk was the severe problem in this system. Although eah subarrier in the prinipal OFD systems overlapped with the neighborhood subarriers, the orthogonality an still be preserved through the staggered QA (SQA) tehnique. However, the diffiulty will emerge when a large number of subarriers are required. In some early OFD appliations, the number of subarriers an be hosen up to 34. Suh 34 symbols will be appended with redundany of a guard time interval to eliminate intersymbol interferene (ISI) [2]. However, should more subarriers be required, the modulation, synhronization, and oherent demodulation would indue a very ompliated OFD requiring additional hardware ost. In 97, Weinstein and Ebert proposed a modified OFD system [3] in

8 whih the disrete Fourier Transform (DFT) was applied to generate the orthogonal subarriers waveforms. Their sheme redued the implementation omplexity signifiantly, by making use of the IDFT modules and the digital-to-analog onverters. In their proposed model, baseband signals were modulated by the inverse DFT (IDFT) in the transmitter and then demodulated by DFT in the reeiver. Therefore, all the subarriers were overlapped with others in the frequeny domain, while the DFT modulation still assures their orthogonality, as shown in Fig... oreover, the windowing tehnique was introdued in this paper to attak the inter-symbol interferene (ISI) and inter-arrier interferene (ICI) problems. Thanks to these evolutions, modern low-ost OFD systems have beome plausible. Fig.. Frequeny spetrum of OFD subarrier signals Cyli prefix (CP) or yli extension was first introdued by Peled and Ruiz in 98 [4] for OFD systems. In their sheme, onventional null guard interval is substituted by yli extension for fully-loaded OFD modulation. As a result, the orthogonality among the subarriers was guaranteed. With the trade-off of the transmitting energy 2

9 effiieny, this new sheme an result in a phenomenal ICI redution. Hene it has been adopted by the urrent IEEE standards. In 98, Hirosaki introdued an equalization algorithm to suppress both ISI and ICI [5], whih may have resulted from a hannel distortion, synhronization error, or phase error. In the meantime, Hirosaki also applied QA modulation, pilot tone, and trellis oding tehniques in his high-speed OFD system, whih operated in voie-band spetrum. In 985, Cimini introdued a pilot-based method to redue the interferene emanating from the multipath and o-hannels [6]. In 989, Kalet suggested a subarrier-seletive alloating sheme [7]. He alloated more data through transmission of good subarriers near the enter of the transmission frequeny band; these subarriers will suffer less hannel distortion. In the 99s, OFD systems have been exploited for high data rate ommuniations. In the IEEE 82. standard, the arrier frequeny an go up as high as 2.4 GHz or 5 GHz. Researhers tend to pursue OFD operating at even muh higher frequenies nowadays. For example, the IEEE 82.6 standard proposes yet higher arrier frequenies ranging from GHz to 6 GHz..2 otivation The demand for future higher data rate ommuniations always provides the impetus for this researh. It is obvious that a parallel system is apable of arrying more information than a asade system, simply beause it uses a variety of frequeny bands. However, the signifiant advantage of OFD is that it is robust in frequeny-seletive hannels, whih result from either multipath fadings or other ommuniation 3

10 interferenes. The interferene problem is severe espeially for some systems working in the Unliensed National Information Infrastruture (U-NII) operating frequeny range, suh as the IEEE 82.a standard. Under any of these onditions, the hannel has nonuniform power gains, as well as nonlinear phases aross frequenies. An example is provided in Fig..2. Fig..2 agnitude response of a fading hannel In order to deal with frequeny-seletive fadings, the transmitted OFD signals are divided into many sub-hannels so that those sub-hannels an be onsidered frequeny-flat approximately as the number of the sub-hannel N is large enough. Hene the OFD signals will suffer hannel distortion less than the onventional modulated signals. Under OFD modulation, the symbol duration beomes N times longer. For example, if the input data rate is 2bps, then, the symbol duration is 5 ns; however, in an OFD system with 28 subarriers, the symbol duration ould beome 6.4 us. If these two kinds of symbols are modulated and transmitted through a hannel with a partiular rms value--say, rms = 6 ns, it is lear that the system with a longer symbol duration would perform better. In pratie, the DVB-T standard suggests to use 2,48 subarriers, or 8,92 subarriers [8]. In these ases, the symbol duration an be even inreased by several thousand times. 4

11 .3 Appliations The OFD tehniques had been applied for ANDEFT and KINEPLEX [9], sine 96s. After the IFFT/FFT tehnique was introdued, the implementation of OFD beame more onvenient. Generally speaking, the OFD appliations may be divided into two ategories-wired and wireless tehnologies. In wired systems suh as Asymmetri Digital Subsriber Line (ADSL) and high speed DSL, OFD modulation may also be referred as Disrete ultitone odulation (DT). In addition, wireless OFD appliations may be shown in numerous standards suh as IEEE 82. [] and HiperLAN []. OFD was also applied for the development of Digital Video Broadasting (DVB) in Europe, whih was widely used in Europe and Australia. In the DVB standards, the number of subarriers an be more than 8,, and the data rate ould go up as high as 5bps [2]. At present, many people still work to modify the IEEE 82.6 standard, whih may result in an even higher data rate up to bps. 5

12 Chapter 2 OFD and PAPR Problem In this hapter, prinipal and modern OFD systems will be disussed. The prinipal model, as well as mathematial formulae, will be addressed to demonstrate the advantages of the OFD tehnique. In addition, speial problems will be explored, whih might our in OFD systems. Finally an overview of the Peak-to-average-power Ratio (PAPR) problem will be provided in this hapter. 2.. Prinipal OFD odel A. Overview Sine the original OFD model was proposed in the 96s [], the ore struture of OFD has hardly hanged. The key idea of OFD is that a single user would make use of all orthogonal subarrier in divided frequeny bands. Therefore, the data rate an be inreased signifiantly. Sine the bandwidth is divided into several narrower subhannels, eah subhannel requires a longer symbol period. Therefore OFD systems an overome the intersymbol interferene (ISI) problem. As a onsequene, the OFD system an result in lower bit error rates but higher data rates than onventional ommuniation systems. Nevertheless, OFD tehnique has ertain drawbaks [3], suh as the inreased system omplexity, whih is assoiated with the generation of orthogonal subarriers, and other new problems, whih might not our in other modulation shemes. Suh new problems inlude the peak to average power ratio (PAPR) and inter-arrier interferene (ICI). The PAPR problem will be disussed in Chapter 2, and the ICI problem will be further disussed in Chapter 4 and Chapter 5. 6

13 B. OFD odulation Fig 2. Prinipal OFD modulation blok diagram As depited in Fig 2., the input data stream is onverted into N parallel data streams through a serial-to-parallel port. The duration of the data is elongated by N times. Serial-to-parallel onversion is depited in Fig 2.2. Fig 2.2 Serial to Parallel onversion 7

14 C. Orthogonal Subarriers When the parallel symbol streams are generated, eah stream would be modulated and arried at different enter frequenies as the traditional FD sheme. The subarriers entered at frequenies f, f, f 2,... f N in Fig.2. must be orthogonal to eah other. The definition of the orthogonality was given in [4] as T os(2π f t) os(2πf t) dt = δ (n - m), (2..) where δ(n-m) is the Dira-Delta funtion. n m In OFD modulation, the subarrier frequeny f n is defined as f n = n f, (2..2) where f s f = = (2..3) N NT Here f s = is the entire bandwidth, and N is the number of subarriers. T Substituting Eq and Eq.2..3 into Eq.2.., Orthogonality an easily be justified for all f, f, f 2,... f N. Fig 2.3 illustrates an example of subarrier waveforms. Fig 2.3 An illustration of subarrier waveforms 8

15 D. Bandpass Signaling After the modulation by orthogonal sub arriers, all N subarrier waveforms were added together to be up-onverted to the pass-band. This resulting signal waveform will be transmitted with a arrier frequeny at 2.4G Hz, 5G Hz, G Hz or 6 G Hz. Then the band-pass OFD signal waveform would be sent to power amplifier and antennas. Thus, the transmitted OFD signal x(t) an be expressed as: x ( t) = N n= exp ( j2π ( f n f ) t ) + s ( n ) T, (2..) where the s(n) represents the input data stream, T the symbol duration and f the arrier frequeny. Traveling through a wireless hannel, the distorted x ( t) results in r ' ( t) shown in Fig.2.4. E. OFD Demodulation, as P/S Fig 2.4 OFD reeiver At the reeiver, the reeived signal is down-onverted to form a base-band signal first. Then, low-pass filters and de-subarriers are applied to separate subarrier waveforms. Orthogonality of sub-arriers will ensure that only the targeted subarrier 9

16 waveform will be preserved in eah sub-band. Ideally, the final deteted symbols will be idential to those transmitted in Fig odern OFD model A. Overview It was a ompliated proess to ahieve N subarrier osillators, espeially when the N was large. Therefore, the prinipal OFD model ould not been widely used. Thanks to IDFT/DFT-based algorithms introdued in 98 [3], OFD has beome a popular wireless modulation tehnique sine after. The modern OFD model is depited in Fig 2.5. Fig 2.5 odern OFD system

17 B. IDFT and Orthogonality After the parallel symbol streams are generated, IDFT operator substitutes the aforementioned loal subarrier osillators. IDFT operation, F( n) f ( k), an be written as [5]: IDFT f N N n= ( k ) = F( n) exp j 2πkn N (2.2.) The orthogonality of disrete-time Fourier bases an be desribed as follows: N- os k= 2πkn N 2πkm os = δ (n - m) N (2.2.2) Clearly, the output sequenes of the IDFT are orthogonal to eah other. With the absene of loal osillators, the OFD system omplexity has been greatly redued. C. Guard Interval and Cyli Prefix In Fig 2.5, the blok denoted as Add Cyli Prefix atually should be alled the Add Guard Interval in general. The yli prefix (CP) is the most ommon guard interval (GI). The GI is introdued initially to eliminate the inter blok interferene (IBI). Sine one blok of input data symbols are assoiated with a single transmitted waveform in an OFD system, most people refer IBI as ISI. Fig 2.6 demonstrates how to use the GI to eliminate the ISI. However, multipath fading hannel models are onerned in most situations. Therefore, many time-delayed visions of the transmitted waveform might be found at the reeiver [6]. Without GI, these waveforms would interfere with eah other, just as demonstrated in the top half of Fig.2.6. Nevertheless, in those ases where the GI was employed, the portions of waveforms reeived in the GI duration would be totally disarded, as shown in the bottom half of Fig.2.6. Thus, the ISI ould be ompletely

18 eliminated aordingly. It is noted that the GI duration must be larger than the maximum hannel delay time. Otherwise, it ould not entirely remove the ISI. ISI Signal Signal2 GI Signal Signal Signal GI Signal2 ISI Disard Fig.2.6 Guard Interval Elimination of the ISI There are several options for GI. One hoie of GI is zero padding. In this sheme, no waveform is transmitted in the GI duration. However, the zero-padded waveform would destroy the orthogonality of subarriers and results in interarrier interferene (ICI). The yli prefix (CP) is a good substitute of the zero-padding GI. In the CP sheme, the GI is a opy of the partial waveform. Based on the fat that the Fourier bases are periodi funtions, the orthogonality of subarriers an be preserved onsequently. As depited in Fig 2.7, an end-portion of waveform is opied and inserted prior to the beginning of waveform. The time duration of CP, denoted as T G in the Fig 2.7, is often hosen aording to the following: 2

19 CP T G T Fig 2.7 Generate Cyli Prefix Let k be an integer in Eq T G T =. (2.2.3) K 2 For example, in the IEEE 82.a standard, k = 2 is hosen; in Europe DVB (Digital Video Broadasting) standards, k =,2,... 6 an be employed. As aforementioned, k should also depend on the maximum delay time of the hannel. When CP is applied instead of zero-padding GI, both ICI and ISI are eliminated. D. A Pratial OFD System- HiperLAN/2 Even though there are many appliations of the OFD tehnique, the orresponding parameters vary from one to another and depend on the pratial purposes. Fig 2.8 illustrates the simplified version of a pratial OFD system--the HiperLAN/2 system. As a wireless LAN model, the HiperLAN/2 standard an provide servies at 54 bps data-rate. The European Teleommuniation Standards Institute (ETSI) and Broadband Radio Aess Network (BRAN) originally proposed this standard. At present, it has been widely applied in airports, homes, and universities in Europe, Australia and Japan. In this standard, many tehniques suh as QA, onvolution 3

20 oding, punture, and interleaver might be used. At the reeiver, there are de-interleaver, zero-inserting, and Viterbi deoder omponents orrespondingly. The OFD modulation in the HiperLAN/2 system is similar the prinipal one, exept that four pilot bits were used for the time and frequeny synhronization, and CP is inserted prior to the OFD information symbols, as depited in Fig 2.5 and 2.7. As a matter of fat, the HiperLAN/2 standard is nearly the same as the IEEE 82.a standard at the physial layer; both standards use 64 subarriers with 6 yli prefix bits per blok. 2.3 PAPR Problem One of the new problems emerging in OFD systems is the so-alled Peak to Average Power Ratio (PAPR) problem. The input symbol stream of the IFFT should possess a uniform power spetrum, but the output of the IFFT may result in a nonuniform or spiky power spetrum. ost of transmission energy would be alloated for a few instead of the majority subarriers. This problem an be quantified as the PAPR measure. where PAPR is defined as the peak signal power versus the average signal power. X i is the 2 { X i } { X } 2 i ax PAPR =, E th i bit in an IFFT output stream This high PAPR is undesirable, beause it generally would result in out-of-band (OOB) distortion power. The PAPR problem an be illustrated in Fig 2.9. In this example, the average power is, and peak power is about 5. 4

21 5 Fig 2.8 An example of pratial OFD system

22 Choosing ommuniation hardware omponents with extremely broad linear range ould mitigate this OOB power, but that would also badly derease system effiieny, or introdue exess noise. Those drawbaks an be explained as follows Fig.2.9 A PAPR example Beause of PAPR problem, a large dynami range of the D/A and A/D onverters will be required; otherwise, the peak values ould be lipped, whih would result in a signal distortion. On the other hand, if A/D and D/A onverters with large working ranges are hosen, the quantization noise will inrease and the system performane will degrade. In addition, the hoies of power amplifier and up-onverters will also be ruial when PAPR problem ours. A large working range is required to ensure that the nonlinear distortion would not be introdued. As a result, power effiieny is dereased signifiantly due to PAPR problem. For example, the maximum power effiieny of a Class B power amplifier drops from 78.5% to 4.6%, when the PAPR inreases db to 7dB, as stated in the IEEE 82.a standard. Power effiieny is pivotal in mobile ommuniations suh as laptop and PDA over the wired ommuniations. Sine the PAPR problem is not the fous of this thesis, only an overview of existing solutions for PAPR is provided here. In fat, there are many approahes, suh as 6

23 oding [7], partial transmit sequenes [8], seletive mapping [9], lipping [2], random phase updating algorithm [2], and sub-blok phase weighting [22]. 7

24 Chapter 3 Wireless Channel In this hapter, four hannel models are disussed, namely additive white Gaussian noise (AWGN) hannel, Rayleigh hannel, loal model, and general multi-path fading with arrier frequeny offset (CFO). In addition, the European COST 27 fading model is introdued. 3. AWGN and Fading Channel The AWGN hannel is the simplest hannel model used in most ommuniation systems. The thermal noise in the reeivers an be haraterized as an additive white Gaussian proess. Although there are other fators induing hannel noise, suh as antenna temperature, reeiver filter, and multipath fading [23], only multipath fading will be studied in this hapter. Channel fading is generally ategorized into large-sale and small-sale fadings, whih often our simultaneously. Large-sale fading results from shadowing terrain ontours suh as hills, forests, or buildings, relative to the distane between transmitter and reeiver. Small-sale fading, also known as Rayleigh fading, is not determined by the distane in ommuniation. The small-sale fading is manifest in two ways: the signal spreading and the time variation. 8

25 3.2 Rayleigh Channel A Rayleigh model is widely used to model wireless multipath fading hannels in pratie. Rayleigh model is frequently used to desribe a wireless hannel with AWGN but without Light of Sign (LOS), where the power gain is subjet to a random Rayleigh distribution. The omplex hannel impulse response Y(t) an be given as: Y ( t) = g ( t) ( wt + ϑ ( t) ) + jg ( t) sin ( wt + ϑ ( t) ) i os, (3.2.) q where g, i g are Gaussian random variables, ϑ ( t) is uniformly distributed in [,2π ] q. Then, the gain amplitude of the reeived signal an be expressed as: It an be proved that g = g + g (3.2.2) r 2 i 2 q g r is a Rayleigh distribution as in Fig. 3., and its pdf is 2 r r exp < r p = 2 2 σ 2σ (3.2.3) otherwise Fig. 3. Rayleigh distribution 9

26 Aording to the Jake s model [24], there are many transmission paths, and any of these path gains an be onsidered a Gaussian random variable. Then, the gross gain an be formulated as: = 2 r g l l= g (3.2.4) It has been proved that g is still a Rayleigh distributed proess. However, when a r LOS path exists, a Riean model instead of a Rayleigh model should be onsidered. 3.3 Simple Loal odel A simple loal model means that there is only a single path from the transmitter to the reeiver. Some indoor environments an be modeled as simple loal models, beause their hannel time delays are negligible. In suh a irumstane, only arrier frequeny offset needs to be onsidered. Aording to Armstrong s OFD hannel analysis [25], a wireless hannel an be haraterized as a vetor C, and the demodulated signal an be alulated by the onvolution of C and the input data stream. It is noted that the white Gaussian noise is ignored in this model. The vetor C is defined as follows: [ ] C L = 2 N l = N N k= ( l ε ) j2πk + exp N 2

27 = ( l + ε ) ( N )( l + ε ) sin π exp jπ N l + ε N sin π N, (3.3.) where ε is the normalized frequeny offset and N is the IFFT length. If ε is zero in Eq. 3.3., whih means that no CFO exists, l = δ (l) results in no ICI. When CFO is present ( ε ), l will dereases as l inreases. In other words, the interarrier interferene is aused mostly by neighboring subarriers. This phenomenon is shown in Fig 3.2a. N N Phases among subarrier signals also vary in this model. We an approximate to in Eq.3.3., when N is large. Then phases will hange about π from a subarrier to next. Whenever l inrements by, the sign of π ( l +ε ) sin will be inverted. In summary, the neighboring subarriers have nearly the same phase, as illustrated in Fig. 3.2 b. Let C N N N N 2 = 2 n L N 3 2 L L L L L. Then the demodulated signal an be reformulated as Y=CX; 3.4 COST 27 Fading odel The COST 27 model was presented as an outdoor wireless hannel model in Europe [27], whih power gains, time delays, and Doppler spreading ategories were speified for four typial environments. 2

28 These parameters were evaluated by numerous measurements performed in many ountries, inluding the United Kingdom, Frane, and Sweden. The four typial environments were rural area (RA), typial urban area (TU), bad urban area (BU), and hilly terrain (HT). COST 27 standard provided both the ontinuous time formula and disrete taps model a b Fig 3.2 Amplitudes and phases of subarriers. (N=64, CFO=.2) Their power distributions are haraterized as follows: RA: TU: P ( τ ) ( 9.2τ ) exp τ.7µ s = otherwise 22

29 P ( τ ) ( τ ) exp τ 7µ s = otherwise BU: P ( τ ) exp =.5 exp ( 9.2τ ) ( 5 τ ) τ 5µ s 5 τ µ s otherwise HT: P ( τ ) exp =.exp ( 3.5τ ) ( 5 τ ) τ 2µ s 5 τ 2µ s otherwise The COST-27 models are due to wide sense stationary unorrelated sattering (WSSUS), with four types of Doppler spreading ategories haraterized by the maximum delays. Tapped delay-line models are often adopted to simplify the aforementioned ontinuous-time models. For example, the following table desribes the tapped delay-line COST 27 RA model: Table 3. COST27 RA tapped delay-line model Tap number Delay [us] Power [db] Doppler Category RICE Class Class Class (RICE means Riean distribution, while Class means lassial (Jake) Doppler distribution in Table 3.) 23

30 3.5 ultipath Fading with CFO The hannel is often modeled as a multipath fading in reality. Also, the COST27 models an be adopted to obtain multipath power gains and time delays for hannel simulations. Different paths are represented as the taps in table 3., eah path with a different power gain and a different time delay. The Doppler frequeny shift and CFO are also onsidered in the hannel simulations. A general multipath framework for all hannel environments is designed, suh environments inluding Rayleigh fading, simple loal hannel with CFO, COST 27 hannels and so on. The following symbols are used in the formulation of the general multipath framework. Table 3.2 List of symbols Symbol Denotation Note N Length of IFFT and FFT In IEEE 82.a 64 N Length of Cyli Prefix In IEEE 82.a 6 T Duration of all N samples In IEEE 82.a 3.2 µ s f Carry frequeny In IEEE 82.a 5G f Sub-arrier s frequeny spae In IEEE 82.a.325Hz k k i th k sample in ertain blok th i blok, inlude N samples Number of paths 24

31 p th p of paths τ p Time delay of th p path (table on d ) f p a k, i Frequeny offset of Input data th p path x ( t) Output of IFFT r ( t) Reeived signal y ( t) Output of FFT y l, i th l sample of th i blok z m, i m th output of th i blok A pulse-shaping funtion an be defined as t < P T ( t) =. (3.5.) otherwise Other pulse-shaping waveforms suh as raised-osine funtion an also be applied [26]. The transmitted signal waveform onsists of two parts. The first part is the OFD modulated signal, and the seond part is its yli extension. It is assumed that the first blok of data an ahieve perfet time synhronization. Under the assumption that the power amplifier and antenna is ideal, the OFD modulated signal with CP is exatly the signal in the air. Suppose there are paths, and eah path has different gain, time delay, and frequeny offset. Then, the reeived signal an be written as: 25

32 r ( t) g px( t p, f + f p ) = p= τ, (3.5.2) where x ( t) is the transmitted signal. Then, the reeived r( t) form a baseband signal y ( t). will be down-onverted to Define L = N N, then y where r(t) is as in Eq ( t) = r( t ) [ j2 f ( t i( L ) T )] exp π, (3.5.3) + In addition, the low pass filter is assumed to be ideal, and no aliasing is introdued here. Substituting Eq into the equation 3.5.3, then, sampling y ( t) at the time instants as follows: T t = i( + L ) T + l. (3.5.4) N Then, the disrete-time data stream of the FFT an be written: y, will be sent for FFT operation. The output l i N m zm. i = yl+ N, i exp 2π jl (3.5.5) N l= N Eq an be simplified as: N = k= z = a (3.5.6) m, i k, i k, l, m Generally, it an be divided into two parts, the signal part and the interferene part, and it an be rewritten as follows: z m i = am, im, l, m + ak, ik, l, m k m,, (3.5.7) 26

33 27 where m l k,, is defined as: = = + + = p N i p p p p p m l k T k f f T L f j g N,, 2 exp τ τ τ π ( ) + N l T f m k 2πj p exp NT N lt P p T τ ( ) ( ) = = + + p N i p p p p p T k T f f T L f j g N 2 exp τ τ τ π ( ) + N l T f m k 2πj p exp + NL T N NL T lt P p T τ. (3.5.8) Sine m l k,, depends on m k, and l only, it is noted that ( ) l i f m l k,,, = an be stated, where m k i = in Eq Compared with the simple loal model where any row in the matrix an be determined by a yli shift of the first row, the new hannel model doesn t have suh a yli struture. This differene is shown in Fig 3.3. a. Loal simple model b. multipath fading model Fig. 3.3 Two Channel odels (N=64, CFO=.2)

34 In the Fig.3.3 b, even though the peak values of subarriers are different, the following rules still hold: first, the peak values always our at diagonal loations; seond, interferene is mostly due to the neighboring subarriers. A Fourier transform matrix an be defined as: where L jw jw( N ) e e F = ( ) ( ), (3.5.9) 2 jw N jw N e e 2π w =. N The signal soure vetor is denoted as S ] T = [ s s L s N. Then the IFFT-modulated signal vetor an be written as: X * = F S, (3.5.) where * F is the omplex onjugate of matrix F. Let the hannel impulse response be h ( l). The reeived signal vetor Y an be formulated as Y ( l) = X h. (3.5.) After down-onversion, where the CFO needs to be onsidered, the FFTdemodulated signal an be written as, ( EY ) R = F, (3.5.2) jε 2 jε j( N ) ε where E = diag([, e, e, L, e ]). Finally, the reeived signal vetor R an be expressed as follows: * R = FEF HS + FN AWGN, (3.5.3) 28

35 where diag( fft( h( l), N) ) white noise H =, is the frequeny response of the hannel; and N AWGN is the 29

36 Chapter 4 Interarrier Interferene Problem and Solutions Inter-arriers interferene (ICI) is a speial problem in the OFD system. In this hapter, the fators induing ICI and the solutions will be investigated. 4. Fators Induing ICI ICI is different from the o-hannel interferene in IO systems. The o-hannel interferene is aused by reused hannels in other ells [28], while ICI results from the other sub-hannels in the same data blok of the same user. Even if only one user is in ommuniation, ICI might our, yet the o-hannel interferene will not happen. There are two fators that ause the ICI, namely frequeny offset and time variation. As disussed in [29], some kinds of time variations of hannels an be modeled as a white Gaussian random noise when N is large enough, while other time variations an be modeled as frequeny offsets, suh as Doppler shift. Only frequeny-offset is disussed in this hapter. ICI problem would beome more ompliated when the multipath fading is present. The following figure shows the relationship between CFO and ICI. Fig. 4-. Relationship of CFO and ICI. CFO 3

37 A. Doppler Effet: The relative motion between reeiver and transmitter, or mobile medium among them, would result in the Doppler effet, a frequeny shift in narrow-band ommuniations. For example, the Doppler effet would influene the quality of a ell phone onversation in a moving ar. In general, the Doppler frequeny shift an be formulated in a funtion of the relative veloity, the angle between the veloity diretion and the ommuniation link, and the arrier frequeny, as shown in Fig. 4.2 path v Fig. 4.2 Doppler Effet The value of Doppler shift ould be given as v f d = 2π os( θ ), (4..) λ where θ is the angle between the veloity and the ommuniation link, whih is generally modeled as a uniform distribution between and 2 π, v is the reeiver veloity, and the λ is the arrier wavelength. Let us assume that eletromagneti wave veloity is C, the wavelength of arrier an be written as C λ =, (4..2) f 3

38 where f is the arrier frequeny. Three kinds of Doppler effet models are generally disussed in existing literatures: the lassial model, the uniform model, and the two-ray model. The lassial model is also referred as Jake model, whih was proposed in 968 [24]. In this model, the transmitter was assumed to be fixed with vertially polarized antenna. There was no Light of Sight (NLOS) path, and all path gains were subjet to idential statistis. It had been proved in 972 [6] that the spetrum of this kind of Doppler shift ould be given as: P J ( f ) = πf m k f f f m 2, (4..3) where k was fixed onstant to given hannel and antenna, f m was the maximum Doppler shift as in Eq. 4.. and f was defined in Eq The uniform model is muh simpler. Both veloity and angle are supposed to be uniformly distributed [3]. In this ase, the power spetrum ould be written as: f f d P ( ) U f = 2 f (4..4) d otherwise The two-ray model assumed that there were only two paths between the transmitter and reeiver. Aordingly, the resulting power spetrum is given as [3] P T d + 2 ( f ) = [ δ ( f f ) + δ ( f f )] d (4..5) B. Synhronization Error It an be assumed that most of the wireless reeivers annot make perfet frequeny synhronization. In fat, pratial osillators for synhronization are usually 32

39 unstable, whih introdue frequeny offset. Although this small offset is negligible in traditional ommuniation systems, it is a severe problem in the OFD systems. In most situations, the osillator frequeny offset varies from 2 ppm (Parts Per illion) to ppm [3]. Provided an OFD system operates at 5 GHz, the maximum offset would be KHz to 5 KHz (2- ppm.). However, the subarriers frequeny spaing is only 32.5 KHz. Hene; the frequeny offset ould not be ignored. In most literatures, the frequeny offset an be normalized by the reiproal of symbol duration. For example, if a system has a bandwidth of Hz, and the number of subarriers is 28, then the subarrier frequeny spaing would be /28= 78 KHz. If the reeiver frequeny offset is KHz, then the normalized frequeny offset will be /78=.3%. If the normalized frequeny offset is larger than, only the deimal part needs to be onsidered, as shown in Fig. 4.. C. ultipath Fading The influene of multipath fading on ICI is seldom disussed before. As a matter of fat, the multipath fading does not ause ICI, but it will make the ICI problem worse. Sine ICI annot be negleted in pratie, the impat of multipath fading should be disussed. It is reognized that the yli prefix has been used to eliminate ISI entirely and therefore only ICI needs to be onerned. Beause there are many time-delayed versions of reeived signals with different gains and different phase offsets, the ICI is more ompliated to alulate. There are many multipath hannel models. Even in the European COST 27 standard, there are four different typial models. In addition, Rayleigh and Riean hannels ould also be onsidered as multipath models. 33

40 4.2 Interarrier Interferene and Signal-to-interferene Ratio As mentioned in Chapter 3, the hannel an be expressed as a matrix C. The reeived signal an therefore be written as: Y = CS +, (4.2.) N w where S is the input bits, and N input data, is the number of bloks, eah blok onsists of N N w is the white noise. Noise omponents will not be disussed and then will be negleted from now on. Ideally, C is an N N identity matrix. However, with the existene of CFO, the matrix has nontrivial off-diagonal elements. Hene, Eq ould be rewritten as: ( k) = S( k) C + S( l) Y (4.2.2) kk C kl l k The first part in Eq onsists of the information-bearing signals, while the seond part is interarrier interferene. However, C will be different in simple loal models and multipath models. A. ICI in Simple Loal odel response. In this ase, the matrix C is yli as follows: C C CN CN C N N 2 = 2 Cn C L CN 3 C C C 2 L C L L L L C C C In other words, all sub-hannels an be haraterized by the same impulse And the entries of the omplex matrix C an be written as in [32]. This formula is also showed in Chapter 3. 34

41 C i ( ( i + ε ) π ( i ε ) ( N )( i ε ) sin π jπ + = exp + N sin N, (4.2.3) where ε is the normalized frequeny offset and N is IFFT length. Then, Eq an be rewritten as: N l= ( k ) = S( k ) C + S ( l) Y. (4.2.4) C l k B. ICI in ultipath odel The ICI in multipath model is more ompliated, as shown in Chapter 3. We just rewrite the equation here. In this equation, power gains subarrier-dependent. In other words, different subarriers have different power gains. C is not a simple yli matrix here as that in the simple model. C. Signal to Interferene Ratio The signal to interferene ratio (SIR) measure is often quantify ICI. For a simple hannel model, SIR an be written as Eq : 35

42 2 C SIR (4.2.6) = N 2 Ci i= In a multipath ase, SIR of the L th sub-hannels is given as: CLL SIRL =, L =,, 2,..., N (4.2.7) N 2 C i= i L Li 2 The overall SIR of all sub-hannels an be defined as E( ) SIR W = SIR L. 4.3 Solutions for ICI any existing sheme were proposed to attak ICI problem. Three kinds of approahes are addressed here. The first approah is based on CFO estimation and ompensation, whih makes use of pilot sequenes, virtual arriers or blind signal proessing tehniques. The seond approah is based on the windowing tehnique in either time domain or frequeny domain, suh as Nyquist windowing and Hanning windowing. The third one is alled ICI self-anellation, or Polynomial anellation oded (PCC), where the repeated bits are transmitted to mitigate inter-arrier interferene. A. CFO Estimation In order to ompensate CFO, CFO must be estimated at first. One a preise CFO estimate is obtained, a perfet equalizer then an be designed to eliminate ICI. Signal proessing methods are applied to solve this problem. Liu and Tureli proposed USIC-based and ESPRIT-based algorithms to estimate CFO [33]. Basially, their methods are non-blind beause they used virtual arriers, just as in [34, 35]. Other 36

43 researhers proposed aximum Likelihood for CFO estimation [36], whih was proved to be equivalent to usi-based algorithm. Other CFO estimation methods involve with training sequenes [37]. B. Windowing Fig. 4.4 shows the OFD transmitter struture with the windowing tehnique, while the reeiver remains the same as the prinipal OFD reeiver. It is well known that the multipliation operation in the frequeny domain is equivalent to the irular onvolution in the time domain. Different windowing by hoosing parameters w i an result in different digital filtering. Fig. 4.4 Windowing in the transmitter. As stated in [25], there are many kinds of windowing shemes to redue the ICI due to CFO, suh as the Hanning window, the Nyquist window, and the Kaiser window. In [38], the SE Nyquist window is used to mitigate the white noise. C. Interarrier Interferene Self-anellation The ICI self-anellation sheme is a method involving with enoded redundany. Compared with other shemes, only half or less of bandwidth is used for information transmission. In other words, only half or less of full data rate ould be ahieved. Same bandwidth effiieny will be ahieved for ICI self-anellation and ½-rate onvolution 37

44 oding. However, empirial results have shown that ICI self-anellation outperforms the onvolution oding in most hannel environments. The redundant information in an ICI self-anellation enoder an be applied to eliminate the ICI at the reeiver. The priniples of ICI self-anellation an be illustrated in Fig a. The typial hannel gains b. Zhao s ICI self-anel sheme Fig. 4.5 Self-anellation example As shown in Fig. 4.5 (a), only the first and seond subarriers have a large gain differene. The differene between any other neighboring subarriers is muh smaller. The ( l + ) th subarrier arries the inverted signal as the th l subarrier does. The interarrier interferene from th l, and ( ) th l + subarriers an anel eah other. This is the key idea for the ICI self-anellation shemes. Armstrong extended the original ICI self-anellation enoder to any larger amount of redundant repetitions. This new sheme was also referred as Polynomial Canellation Coded (PCC) sheme. Another ICI self-anellation sheme is proposed reently [39]. In 38

45 this new sheme, a different bit enoder is applied, and it will result in a better performane in ertain hannel models than the PCC sheme. In the next hapter, this sheme will be disussed in detail. 39

46 Chapter 5 Clustering Detetion and ultiple Codebook In this hapter, two kinds of interarrier interferene (ICI) self-anellation shemes will be disussed. First a lustering proedure is applied to improve OFD signal detetion. Then a general oding framework for ICI self-anellation shemes will be introdued. Finally a summary of this thesis and future researh plan will be addressed. 5. Clustering Interarrier Interferene Canellation A. Justifiation of Slowly Time-varying The lustering sheme is based on the assumption that the wireless hannel is a slow-fading hannel, that will be loally time-invariant among a few bloks, as reognized in many literatures, suh as in [3, 4, 4]. It an be manifested in the following justifiations. The definition of slow fading is T >> T s, where T is the oherent time and T s is the symbol duration. T is the parameter used to haraterize the time-varying nature of the Doppler effet. Generally, T is defined as T = 9 6πf m, (5..) where f m is the maximum of Doppler frequeny shift, whih an be obtained through the following equation: f vm vm f = λ, (5..2) m = 4

47 where v m is the maximum veloity, f is the arrier frequeny, and is the speed of light. The oherent time T an be alulated as T = 9 6πv m f. (5..3) B. Clustering ethod The entral idea for the lustering tehnique is that all subarriers have almost idential phase offsets. This is valid beause all subarriers travel through the same paths. Also, suppose that the noise is white Gaussian noise. Beause the data sent is from a finite alphabet set, suh as BPSK, QPSK and QA, the reeived signals will satter around suh a finite alphabet set, as depited in Fig Fig 5. a Reeived BPSK signals b. Reeived QPSK signals 4

48 C. Pilot Bits In IEEE 82.a, there are four sub-arriers reserved for pilot bits. However, in our sheme, only two pilot subarriers are requested. Based on the reeived pilot signals, the hannel gains an be estimated D. Simulation Results The previous ICI self-anellation sheme, onvolution oding, normal (without onvolution oding and self-anellation), and ICI self-anellation with lustering are ompared in Figure 5.2. Fig. 5.2 shows that bit error rates versus the signal-to-noise ratios for different OFD shemes. - BER our new method Zhao Conv-oding Normal SNR Fig Simulation results of loal model, CFO=.2 42

49 The number of subarriers is 256, and the CFO is.2. The onvolution oding in the industrial standard is used in these simulations ( g = 338 and g = 78 rate =/2). The standard Viterbi hard-deision deoder is applied at the reeiver. Obviously, the new sheme outperforms other existing shemes. The Fig 5.3 shows the results for CFO=.5, COST 27 hannel model in rural areas. In both simulations, 2 onte Carlo trials are taken. BER - -2 our new method Zhao Conv-oding Normal SNR Fig. 5.3 Simulation of ultipath model. CFO=.5 43

50 5.2 ultiple-codebook A general framework of ICI self-anellation is presented here. Suh a new framework will inlude not only the existing ICI self-anellation odebooks but also new potential odebooks. A. General Struture of ICI Self-anellation A preoder H of a matrix form, an be design as depited in Fig Sine the ICI self-anellation enoder inserts as many redundant bits as the information bits, the N funtion of H an be written as a N matrix. 2 A. Transmitter B. Reeiver Fig 5.4 Simplified blok diagram of ICI self-anellation sheme An example of H is as follows. Supposedly, the information bit vetor is [ s s s ] T S 2 3 L s N / 2 =. This vetor an be obtained from the serial-to parallel omponent as in Fig 5.4. The length of S is N/2 in this situation. Even only the one-time repeating shemes (rate is /2) will be disussed here, it an be automatially extend to higher repeating shemes. 44

51 45 = L O O L L H Then, aording to Zhao s ICI self-anellation enoder, the OFD-modulated signal will be [ ] T s s s N s s s s S H 2 / 2 2 = L [32]. Similarly, Sathananthan proposed another ICI self-anellation enoder H 2 as follows: = 2 L N O L L H In this sheme, the OFD-modulated signal will be [ ] T s s s s s s L as in [39]. A ( ) 2 matrix S H is defined as a sub-blok in the odebook H, where is the number of olumns in S H. It an be written as Ψ = S I H, (5.2.)

52 where L ψ = and N L I is an identity matrix. The parameter ould be hosen aording to: = N k =,, L log (5.2.2) 2 k 2 2 Then we an reate a odebook H from based on H S as follows: H When we set i HS = O H S O O H S (5.2.3) N N k = log 2, then = and we obtain the odebook H 2.. On 2 2 the other hand, Han be generated by hoosing k =. If we hoose different k, suh as k = 2,4,..., other kinds of odebooks H an be obtained, resulting in multiple odebooks. B. Comparison of Codebooks It is neessary to ompare these ICI self-anellation odebooks among different environments, suh as loal hannel with different CFO, Rayleigh hannel, multipath fading hannel with CFO. In a simple loal model, all odebooks show similar in performane, although Zhao s sheme is better when the CFO is small. When the CFO is as large as.4, all of the shemes demonstrate poor performane. Fig 5.5 provides simulation results for CFO=.3. 46

53 BER = =2 =N/ SNR Fig. 5.5 ulti-odebooks for simple loal model CFO=.3 For Rayleigh Channels, all ICI self-anellation shemes have similar performanes. However, Zhao s odebook is slightly better than others when the SNR is low BER..5 = =2 =N/ SNR Fig 5.6 ulti-odebooks for Rayleigh hannels 47

54 For multipath fading models, suh as COST 27 RA model, Sathananthan s sheme is better when CFO is large. However, when CFO dereases down to.5, a new odebook beomes the best among multiple odebooks, as shown in Fig. 5.7: BER = =3 =N/ Summary and Further Work SNR Fig 5.7 ultiple-codebooks for ultipath hannel. CFO=.5 Sine the lustering sheme greatly improved the ICI self-anellation reeivers, and the multi-odebooks will show robust performane among different hannel environments, it is desirable to investigate a hybrid system integrating these two methods in a variety of environments, suh as the Rayleigh hannel, or the IO fading. Another extension would be ombining the ICI self-anellation sheme with error ontrol odes and RAKE reeivers to ahieve yet-better OFD performane. In addition, new tehniques would be investigated in the future suh as in [42,44]. 48

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