Multiuser Detection in Multiple Input Multiple Output Orthogonal Frequency Division Multiplexing Systems by Blind Signal Separation Techniques

Transcription

1 Florda Internatonal Unversty FIU Dgtal Commons FIU Electronc Theses and Dssertatons Unversty Graduate School Multuser Detecton n Multple Input Multple Output Orthogonal Frequency Dvson Multplexng Systems by Blnd Sgnal Separaton Technques Yu Du Florda Internatonal Unversty, dyu00@fu.edu DOI: /etd.FI Follow ths and addtonal wors at: Recommended Ctaton Du, Yu, "Multuser Detecton n Multple Input Multple Output Orthogonal Frequency Dvson Multplexng Systems by Blnd Sgnal Separaton Technques" 01. FIU Electronc Theses and Dssertatons Ths wor s brought to you for free and open access by the Unversty Graduate School at FIU Dgtal Commons. It has been accepted for ncluson n FIU Electronc Theses and Dssertatons by an authorzed admnstrator of FIU Dgtal Commons. For more nformaton, please contact dcc@fu.edu.

2 FLORIDA INTERNATIONAL UNIVERSITY Mam, Florda MULTIUSER DETECTION IN MULTPLE INPUT MULTPLE OUTPUT ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING SYSTEMS BY BLIND SIGNAL SEPARATION TECHNIQUES A dssertaton submtted n partal fulfllment of the requrements for the degree of DOCTOR OF PHILOSOPHY n ELECTRICAL ENGINEERING by Yu Du 01

3 To: Dean Amr Mrmran College of Engneerng and Computng Ths dssertaton, wrtten by Yu Du, and enttled Multuser Detecton n Multple Input Multple Output Orthogonal Frequency Dvson Multplexng Systems by Blnd Sgnal Separaton Technques, havng been approved n respect to style and ntellectual content, s referred to you for judgment. We have read ths dssertaton and recommend that t be approved. Ymn Zhu Deng Pan Jean H. Andran Kang K. Yen, Major Professor Date of Defense: March 6, 01 The dssertaton of Yu Du s approved. Dean Amr Mrmran College of Engneerng and Computng Dean Lashm N. Redd Unversty Graduate School Florda Internatonal Unversty, 01

4 DEDICATION I dedcate ths thess to my parents, who gve me confdence and unlmted love to fnsh my degree. I dedcate ths thess to my wfe, who taes care of my lfe, loves my famly and me, and supports my research. I dedcate ths thess to my parents-n-law, who gve me a beautful and smart wfe. I dedcate ths thess to all of my relatves and frends. The completon of ths wor wll not be possble f I do not have support from all of you.

5 ACKNOWLEDGMENTS I want to express my grattude to my advsor, Dr. Kang K. Yen, for hs contnuous support and patence. From the very begnnng, he beleves n my research abltes to complete a degree wth ntellgence. Dr. Kang K. Yen s partcularly helpful n gudng me to solve plenty of problems durng my research process. Hs academc advce and sprtual supports facltate the accomplshment of my dssertaton. I also apprecate the long-term support from my co-advsor Dr. Jean Andran. Furthermore, I convey my gratefulness to my commttee members Dr. Deng Pan and Dr. Ymn Zhu for ther valuable contrbuton to my dssertaton. Fnally, I am thanful to the efforts of Florda Internatonal Unversty, whch provdes me wth a great research envronment. Once a Panther, forever a Panther! v

6 ABSTRACT OF THE DISSERTATION MULTIUSER DETECTION IN MULTPLE INPUT MULTPLE OUTPUT ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING SYSTEMS BY BLIND SIGNAL SEPARATION TECHNIQUES by Yu Du Florda Internatonal Unversty, 01 Mam, Florda Professor Kang K. Yen, Major Professor Ths dssertaton ntroduces three novel multuser detecton approaches n Multple Input Multple Output MIMO Orthogonal Frequency Dvson Multplexng OFDM systems by blnd sgnal separaton BSS technques. The conventonal methodologes for multuser detecton have to retransmt channel state nformaton CSI constantly from the transmtter n MIMO ODFM systems at the cost of economc effcency, because they requre more channel resources to mprove the communcaton qualty. Compared wth the tradtonal methodologes, the proposed BSS methods are relatvely effcent approaches wthout the unnecessary retransmsson of channel state nformaton. The current methodologes apply the space-tme codng or the spatal multplexng to mplement an MIMO OFDM system, whch requres relatvely complex antenna desgn and allocaton n the transmtter. The proposed Spatal Dvson Multple Access SDMA method enables dfferent moble users to share the same bandwdth smultaneously n dfferent geographcal locatons, and ths scheme requres only one v

7 antenna for each moble user. Therefore, t greatly smplfes the antenna desgn and allocaton. The goal of ths dssertaton s to desgn and mplement three blnd multuser detecton schemes wthout nowng the channel state nformaton or the channel transfer functon n the SDMA-based upln MIMO OFDM system. The proposed scenaros nclude: a the BSS-only scheme, b the BSS-Mnmum Mean Square Error MMSE scheme, and c the BSS-Mnmum Bt Error Rato MBER scheme. The major contrbutons of the dssertaton nclude: a the three proposed schemes save the commercally expensve cost of channel resources; b the proposed SDMA-based upln MIMO OFDM system smplfes the requrements of antennas for moble users; c the three proposed schemes obtan hgh parallel computng effcency through paralleled subcarrers; d the proposed BSS-MBER scheme gans the best BER performance; e the proposed BSS-MMSE method yelds the best computatonal effcency; and f the proposed BSS-only scenaro balances the BER performance and computatonal complexty. v

8 TABLE OF CONTENTS CHAPTER PAGE CHAPTER 1 INTRODUCTION Research Bacground Objectve of the Dssertaton Dssertaton Outlne... 5 CHAPTER SDMA-BASED UPLINK MIMO OFDM SYSTEMS Proposed SDMA-based Upln MIMO OFDM Systems Wreless Channel Large-scale Fadng Model Small-scale Fadng Model MIMO Technques ODFM Technques... 8 CHAPTER 3 BLIND SIGNAL SEPARATION TECHNIQUES Blnd Sgnal Separaton Theory ICA Classfcatons Nature Gradent Algorthm JADE Algorthm FastICA Algorthm CHAPTER 4 BLIND MULTIUSR DETECTION SCHEMES BSS-only Scheme BSS-MMSE Scheme BSS-MBER Scheme CHAPTER 5 SIMULATION AND PERFORMANCE ANALYSIS Smulaton Envronment BER Performance Analyss Computatonal Complexty Analyss CHAPTER 6 CONCLUSIONS Major Outcomes Prospectve Research Endeavors Summary LIST OF REFERENCES...90 VITA...97 v

9 LIST OF TABLES TABLE PAGE Table 1-1 Mnmum dstance between two adjacent antennas... 3 Table 3-1 Elements of the random complex mxed matrx H Table 4-1 Total number of the calculatons for the cross-correlaton... 6 Table 5-1 Man parameters for the proposed SDMA-based upln MIMO OFDM system Table 5- Relatve BER mprovement Table 5-3 Comparson among three proposed schemes n terms of the error probablty for a varety of frame szes at SNR = 5 db Table 5-4 Analytcal computatonal complexty among three proposed schemes... 8 Table 5-5 Comparson among three proposed schemes n terms of the runnng tme for a varety of frame szes at SNR = 15 db... 8 v

10 LIST OF FIGURES FIGURE PAGE Fgure -1 Moble Users n Dfferent Geographcal Locatons... 7 Fgure - SDMA-FDMA-based MIMO OFDM System... 9 Fgure -3 SDMA-TDMA-based MIMO OFDM System Fgure -4 Schematc Dagram of the Proposed SDMA-based Upln MIMO OFDM System... 1 Fgure -5 Wreless Modes Fgure -6 Fadng and Multpath Fgure -7 Large Scale Fadng Model Fgure -8 General Channel Model Fgure -9 Flat Fadng vs. Frequency-Selectve Fadng... 0 Fgure -10 Rcan Dstrbuton wth K < 0... Fgure -11 Rcan Dstrbuton wth K > Fgure -1 Antenna System Models... 4 Fgure -13 Closed-Loop MIMO System... 5 Fgure -14 Comparson of the MIMO Channel Capacty wth Dfferent Amount of Antennas... 8 Fgure -15 OFDM Sgnal Spectrum vs. Conventonal FDM Sgnal Spectrum Fgure -16 OFDM Symbols wth Cyclc Prefx Fgure -17 OFDM Transmtter Module Fgure -18 OFDM Recever Module Fgure -19 BER Performance of the BPSK/QPSK/QAM Modulatons n the AWGN Channel x

11 Fgure -0 BER Performance of the BPSK/QPSK/QAM Modulatons n the Raylegh Fadng Channel Fgure -1 Real Part of OFDM Sgnals wth the BPSK Modulaton and N = Fgure - Imagnary Part of OFDM Sgnals wth the BPSK Modulaton and N = Fgure -3 OFDM Baseband Sgnals wth the BPSK Modulaton and N = Fgure -4 OFDM Baseband Sgnals wth the BPSK Modulaton and N = Fgure 3-1 Model for BSS by ICA Fgure 3- Separaton Procedure by BSS... 4 Fgure 3-3 A Comparson of G 1, G, G 3 Functons Fgure 3-4 Real Parts of Fve Complex Source Sgnals wth Bnomal dstrbuton, Gamma dstrbuton, Posson dstrbuton, Hyper-geometrc dstrbuton and Beta dstrbuton Fgure 3-5 Real Parts of Fve Complex Source Sgnals wth Sne Wave, Square Wave, Funny Curve, Saw-tooth, and Impulsve Nose... 5 Fgure 3-6 Whtened Sgnals for the Souce Sgnals Shown n Fgure Fgure 3-7 Separated Sgnals for the Real Part of Fve Complex Source Sgnals wth Sne Wave, Square Wave, Funny Curve, Saw-tooth, and Impulsve Nose Fgure 4-1 BSS-only Scheme for the SDMA-based Upln MIMO OFDM System Fgure 4- Flowchart of the BSS-only Scheme for the SDMA-based Upln MIMO OFDM System Fgure 4-3 Schematc Dagram of How to Calculate the Correlaton for the Permutaton61 Fgure 4-4 BSS-MMSE Scheme for the SDMA-based Upln MIMO OFDM System Fgure 4-5 Schematc Dagram of the BSS-MMSE Method Fgure 4-6 Schematc Dagram of the MMSE Estmaton Fgure 4-7 BSS-MBER Scheme for the Subcarrer n the SDMA-based Upln MIMO OFDM System Fgure 4-8 BSS-MBER Structure for the SDMA-based Upln MIMO OFDM System. 70 x

12 Fgure 4-9 Flowchart for the MBER Detecton n the Subcarrer Fgure 5-1 BER Performance for Three Proposed Schemes n the Upln SDMA-based MIMO OFDM System Fgure 5- Error Probablty for a Varety of Frame Szes at SNR = 5 db for the Three Proposed Schemes Fgure 5-3 Runnng Tme for a Varety of Frame Szes at SNR = 15 db for the Three Proposed Schemes x

13 LIST OF ABBREVIATIONS AM AWGN BER BPSK BSS CIR CP CSI DAB DS-CDMA DSP DFT FastICA FDM FDMA FFT FPGA FM GSM HOS ICA IDFT Ampltude Modulaton Addtve Whte Gaussan Nose Bt Error Rate/Rato Bnary Phase Shft Keyng Blnd Sgnal Separaton Channel Impulse Response Cyclc Prefx Channel State Informaton Dgtal Audo Broadcastng Drect-Sequence Code Dvson Multple Access Dgtal Sgnal Processng Dscrete Fourer Transform Fast Independent Component Analyss Frequency-Dvson Multplexng Frequency Dvson Multple Access Fast Fourer Transform Feld Programmable Gate Array Frequency Modulaton Global System for Moble Communcatons Hgher-Order Statstcs Independent Component Analyss Inverse Dscrete Fourer Transform x

14 IEEE IFFT Insttute of Electrcal and Electroncs Engneers Inverse Fast Fourer Transform IS-95 Interm Standard 95 ISI JADE LOS MBER MIMO MISO MMSE MSE OFDM pdf PCA PLL PSK QAM QPSK RF SDMA SER SIMO SISO Inter Symbol Interference Jont Approxmate Dagonalzaton of Egenmatrces Lne of Sght Mnmum Bt Error Rato Multple Input Multple Output Multple Input Sngle Output Mnmum Mean Square Error Mean Square Error Orthogonal Frequency Dvson Multplexng Probablty Densty Functon Prncpal Component Analyss Phase-Loced Loop Phase Shft Keyng Quadrature Ampltude Modulaton Quad Phase Shft Keyng Rado Frequency Spatal Dvson Multple Access Symbol Error Rate Sngle Input Multple Output Sngle Input Sngle Output x

15 SNR SOS SSE TDMA UWB W-F WMAX Sgnal Nose Rato Second-Order Statstcs Sum of Square Errors Tme Dvson Multple Access Ultra-Wdeband Wreless Fdelty Worldwde Interoperablty for Mcrowave Access xv

16 LIST OF SYMBOLS + Pseudo-nverse * Complex conjugaton Eucldean norm α arg β Arbtrary postve constant Argument on a complex value Large-scale fadng parameter Complex space C Channel capacty r γ Inverted dagonal matrx for P r D d 0 d Pea ampltude of the LOS sgnal Reference dstance Bnary bt vectors n the subcarrer ˆ d Estmated data bt sequences n the subcarrer D E e E x Δf f f c Unnown scalng n the subcarrer Expectaton Error vector n the subcarrer Energy of the transmtted sgnals Dfference between subchannels Non-lnear sgmod functon for the complex doman Carrer frequency xv

17 f Raylegh r Probablty densty of the Raylegh dstrbuton f Rcan r Probablty densty of the Rcan dstrbuton G g g' H Smooth even functon Dervatve of G Dervatve of g Channel transfer matrx H Hermtan transpose ˆ H Estmated channel matrx n the subcarrer Hf ht I I Im JW K l M Channel response n the frequency doman Channel response n the tme doman Unt matrx Modfed Bessel functon of the frst nd Imagnary part of a complex value Objectve functon Rcan factor Subcarrer ndex number Number of transmttng antennas Modulaton order µ Step sze for MBER n N N 0 Vector for the AWGN nose Number of subcarrers Power spectral densty of the addtve nose xv

18 N Total numbers of the cross-correlaton cross correlaton N d p P BER P d Number of bnary bt vectors d Number of elements for an antenna array n the recever Bt error probablty Average power at a dstance d P e _ AWGN Probablty of error for the AWGN channel P e _ Raylegh Probablty of error for the Raylegh channel P P SER P t Q r Rf Re Unnown permutaton at the subcarrer Symbol error probablty Average transmtted power Standard Q-functon Magntude of the receved sgnal Receved sgnals n the frequency doman Real part of a complex value R Cross-correlaton matrx between r ˆ r S, X S and ˆ r X rt R xx Receved sgnals n the tme doman Autocorrelaton of the transmtted sgnal vector R Autocorrelaton matrx X ˆ r ˆ r X, X ˆ r n the subcarrer r s st Sf Vector for the source sgnals Source sgnals n the tme doman Source sgnals n the frequency doman {S n } Data symbols xv

19 ˆ S Estmated vector of the source vector S n the subcarrer sgn σ Sgn functon Average power σ n Standard devaton for the varance ofσ n σ n T Varance for the AWGN nose Symbol tme 1/T Frequency of subcarrers T Transpose T g Tr v V Length of the guard nterval Squared Frobenus norm Path loss exponent Whtened mxed matrx H v j Unnown phase for each source s j V Nose free sgnal vector n the subcarrer W W W H W MMSE W MBER x OFMD bandwdth Separaton matrx for mxed real source sgnals Separaton matrx for mxed complex source sgnals MMSE separaton matrx n the subcarrer MBER separaton matrx n the subcarrer Vector for the receved sgnals x Noseless component for x z Whtened mxed vector xv

20 Ф JADE [ ] Contrast functon for the JADE algorthm ξ Smple formula of w w H H w V σ n n the subcarrer xx

21 1.1 Research Bacground CHAPTER 1 INTRODUCTION In recent years, the technques of MIMO OFDM systems, whch are the leadng trends of future wreless communcaton, have been adopted by the fourth generaton of wreless communcaton standards [1], []. For any recever of MIMO OFDM systems, the channel state nformaton or some pror parameters, whch normally nclude the characterstcs of users and nose, the tmng nformaton of users and nose, the relatve ampltude and the tranng sequences, are regularly requred for the conventonal multuser detecton methods contanng matched flter detecton, optmum detecton, decorrelaton detecton and adaptve detecton [3]. It s obvous that those pror parameters occupy expensve communcaton resources, and the conventonal multuser detecton methods are undoubtedly neffcent ways of wreless communcaton. In addton, there are some dsadvantages of the conventonal detecton methods. Frstly, the CSI s typcally dffcult to be obtaned n MIMO OFDM systems. Secondly, the transmsson of the CSI s not often effectve for the fast tme-varyng channel of MIMO OFDM systems. Furthermore, the attenuaton of the CSI may cause a wrong multuser detecton n MIMO OFDM systems [4]. At last, the conventonal methods reduce the channel capacty n MIMO OFDM systems. 1

22 One of the attractve solutons s whether we can fnd a method to separate or recover multusers wthout the CSI or pror parameters n MIMO OFDM systems. Multuser detecton by blnd sgnal/source separaton [5-8] technques, whch s also called blnd multuser detecton, s chosen as a novel and effcent approach wthout pror parameters n MIMO OFDM systems. Accordng to the lterature revew, there are some researchers [9-14] who have appled BSS technques n the space-tme codng [15], [16] or spatal multplexng [17-] MIMO OFDM systems. However, for an upln transmsson from moble devces to a base staton, ether the space-tme codng scheme or the spatal multplexng scheme requests two or more antennas for every moble devce to transmt ther source sgnals. In other words, each moble devce has to be equpped wth at least two antennas n the space-tme codng or spatal multplexng MIMO OFDM systems. The antenna elements must be separated from each other roughly between 10 λ and 40 λ for the purpose of a low spatal correlaton [3]. Table 1-1 shows the mnmum dstance between two adjacent antennas under dfferent frequences. It s obvous that there s almost no possblty for a moble devce wth a lmted sze to be equpped wth two or more antennas under those frequences. Even for a 5 GHz frequency band, the mnmum dstance between two adjacent antennas s at least 0.6 meters n ths case. A useful soluton for the upln transmsson from moble users to the base staton n an MIMO OFDM system s that one moble devce should be equpped wth only one antenna. Otherwse, to desgn and allocate two or more antennas for every moble devce wll be very complex.

23 Table 1-1 Mnmum dstance between two adjacent antennas Frequency 10 λ 40 λ 900 MHz 3.33 m 13.3 m 1800 MHz 1.67 m 6.68 m 5 GHz 0.60 m.40 m Currently, to acheve an MIMO OFDM system, we also have other technques, such as beamformng, SDMA, and networ [1]. From those canddate schemes, the SDMA-based MIMO OFDM systems are chosen for upln MIMO OFDM systems n ths dssertaton. The SDMA technques can greatly smplfy the desgn and allocaton of antennas for moble devces, because each moble devce only needs to be employed by one antenna. Compared wth other types of MIMO OFDM systems, there are some benefts of the SDMA-based MIMO OFDM systems [4-8]. Frst, the coverage area by a base staton can be extended by the SDMA technques. Second, the SDMA technques are able to reduce the nterference n MIMO OFDM systems. Another mert s that the multpath propagaton can often be mtgated by the SDMA technques. The channel capacty ncrement s another advantage of the SDMA technques. Fnally, the SDMA technques are capable of worng wth almost any modulaton method, bandwdth, frequency band ncludng Global System for Moble Communcatons GSM, Interm Standard 95 IS- 95, OFDM, et al. Therefore, the SDMA technques are a sutable choce for upln MIMO OFDM systems wth many advantages. 3

24 To evaluate the performance for multuser detecton n MIMO OFDM systems, there are two mportant aspects, whch contan the Bt Error Rate/Rato BER performance and the computatonal complexty. However, the current BSS approaches [9-14] n MIMO OFDM systems not only cannot fnd the best BER performance but also cannot fnd the best computatonal effcency. In all, the current research has four problems: 1 the conventonal multuser detecton schemes have drawbacs of the transmsson of the CSI and waste channel resources; the current blnd multuser detecton methods n space-tme codng or spatal multplexng MIMO OFDM systems are not sutable for the upln transmsson from moble users to the base staton; 3 the exstng BSS schemes [9-14] cannot provde the best BER performance n MIMO OFDM systems; 4 the current BSS approaches [9-14] cannot gan the best computatonal effcency n MIMO OFDM systems. 1. Objectve of the Dssertaton Accordng to the research bacground, the objectve of ths dssertaton manly conssts of four aspects. 1 Apply blnd multuser detecton technques to have hgher channel utlzaton and save the channel resources, compared wth the conventonal detecton schemes n MIMO OFDM systems. Propose a SDMA-based upln MIMO OFDM system to solve the transmsson problems from moble devces to the base staton. 3 Propose a BSS only method, whch s referred to as BSS-only, to compromse on both the BER performance and the computatonal complexty. 4 Propose a BSS scheme combned wth a lnear Mnmum Mean Square Error scheme, whch s referred to as 4

25 BSS-MMSE, to mnmze the computatonal complexty. 5 Propose a BSS joned wth a lnear Mnmum Bt Error Rate algorthm, whch s referred to as BSS-MBER, to obtan the best BER performance. To dsplay the performance of all proposed schemes, the mplementaton, smulaton and performance analyss are developed by MATLAB and the software verson s R008a. Varous condtons of the proposed SDMA-based upln MIMO OFDM system are consdered to smulate the three proposed blnd multuser detecton schemes for ther BER performance or computatonal complexty. 1.3 Dssertaton Outlne In Chapter 1, four problems of the current research are revealed about multuser detecton n MIMO OFDM systems. The objectve of ths dssertaton s ntroduced accordng to those current problems. Three proposed blnd multuser detecton schemes promse three dfferent performance goals n the proposed SDMA-based upln MIMO OFDM system. The proposed SDMA-based upln MIMO OFDM system s ntroduced n Chapter. To acheve a sutable system wth our dfferent desgn goals, some mportant aspects ncludng the wreless channel, the MIMO technques and the OFDM technques, need to be analyzed, dscussed and consdered n ths chapter. In addton, the fadng channels, the capacty analyss of MIMO systems, and OFDM base band sgnals are also smulated and analyzed. 5

26 Chapter 3 llustrates the blnd sgnal separaton technques. The development of BSS and ndependent component analyss ICA technques s demonstrated frst, and then sgnfcant BSS algorthms are ntroduced. Accordng to our analyss, the Fast Independent Component Analyss FastICA algorthm s selected and modfed for three proposed blnd multuser detecton schemes n the SDMA-based upln MIMO OFDM system. Several types of complex FastICA algorthms are also smulated n ths chapter. Chapter 4 proposes BSS-only, BSS-MMSE, BSS-MBER schemes for dfferent desgn goals, n whch the merts for all of the schemes are provded and dscussed. Wth these schemes, the researchers are able to decde whch one should be chosen for a specal desgn objectve. The dscusson focuses on ther BER performance and computatonal complexty. The smulaton results are dscussed and analyzed n Chapter 5. It provdes how to set up the smulaton envronment and shows the smulaton results about the BER performance for three proposed methods. In addton, the nfluence by a dfferent number of frames s also dscussed. Fnally, the computatonal complexty s smulated through the runnng tme. Chapter 6 summarzes the major outcomes of ths dssertaton and proposes new endeavors for researchers to extend the prospects for ndustral applcatons further. In retrospect, ths research establshes three new schemes for the SDMA-based upln MIMO OFDM system wth a varety of performances. 6

27 CHAPTER SDMA-BASED UPLINK MIMO OFDM SYSTEMS The research of MIMO OFDM was started n the early 000s [1]. The MIMO based OFDM schemes may smultaneously mprove the transmsson rate, the transmsson range and the transmsson relablty of a wreless system. Because MIMO OFDM s more effcent than MIMO combned wth other modulatons [1], a combnaton of both MIMO and OFDM can tap ther potentals at the same tme. The MIMO OFDM technques have been appled n the Insttute of Electrcal and Electroncs Engneers IEEE 80.11n or Wreless Fdelty W-F networs [9], [30]. Fgure -1 Moble Users n Dfferent Geographcal Locatons 7

28 The SDMA-based MIMO OFDM system s a specfc subclass of MIMO OFDM systems that should be able to enable dfferent moble users to share the same bandwdth smultaneously n dfferent geographcal locatons. Fgure -1 llustrates the bloc dagram of moble users n dfferent places. We assume that there are l transmttng antennas for l users sgnals and a p-element antenna array s nstalled n the recever. Although the transmtters are equpped wth multple antennas, the unqueness of the SDMA technques s that these transmsson antennas cannot be shared by dfferent moble users and each of them belongs to one user only. In other words, because of the lmted space of moble devces, each moble user can only be equpped wth one antenna. The transmsson of OFDM sgnals cannot be coordnated or allocated, compared wth the specal multplexng or space-tme codng scheme n whch all of users are capable of sharng every antenna n the transmtters..1 Proposed SDMA-based Upln MIMO OFDM Systems The proposed SDMA-based upln MIMO OFDM system can be ncluded n all nds of exstng multple-access standards wth some enhancements of system capacty. There are two types of SDMA-based MIMO OFDM systems: the SDMA-FDMA Frequency Dvson Multple Access scheme and the SDMA-TDMA Tme Dvson Multple Access scheme. If the SDMA-based MIMO OFDM scheme s combned wth a conventonal FDMA scheme n Fgure -, n moble users OFDM sgnals wll share the same tme slot. The other case n Fgure -3 llustrates n moble users OFDM sgnals share the same frequency band. It s clear that both of them boost up the system capacty. Generally, the SDMA-TDMA scheme s more popular, because t only employs one 8

29 sngle carrer frequency, whch saves lmted and expensve frequency resources. Moreover, the SDMA-TDMA scheme s able to maxmze the number of users supported. If there s no specal menton, the followng SDMA scheme refers to the SDMA-TDMA scheme n ths dssertaton. Therefore, ths scheme wll be appled to the proposed SDMA-based upln MIMO OFDM system for three proposed blnd multuser detecton schemes. Fgure - SDMA-FDMA-based MIMO OFDM System There are manly two parts for the proposed SDMA-based upln MIMO OFDM system, whch are the transmtter and the recever. Fgure -4 shows the schematc dagram of the proposed SDMA-based upln MIMO OFDM system. We assume there are l users and each user transfers ts source bt sequences nto OFDM sgnals through an 9

30 10 OFDM transmtter module. After ths procedure, l antennas smultaneously transmt the OFDM sgnals to the recever. The recever, whch s equpped wth a p-element antenna array, s to receve the lnearly mxed complex OFDM sgnals. Fnally, the OFDM recever modules demodulate the mxed OFDM sgnals nto the mxed bt sequences of l users. Fgure -3 SDMA-TDMA-based MIMO OFDM System The transmtter and recever relatonshp of the proposed SDMA-based upln MIMO OFDM system n one of OFDM subcarrers can be descrbed by [1] + = p l lp p l p n n s s H H H H x x M M L M O M K M.1

31 where x are mxed source sgnals at the recever, s are ndependent source sgnals at the transmtter, n are addtve whte Gaussan noses AWGN that are added at the recever, and H j denote the elements of the frequency doman channel transfer matrx H wth p l dmenson. If s omtted for the sae of notatonal convenence and the vectors x, s, and n are gven by x = [x 1, x,, x p ] T. s = [s 1, s,, s l ] T.3 n = [n 1, n,, n p ] T.4 where T denotes transpose. The frequency doman channel transfer matrx H wth p l dmenson s gven by H = [H 1, H,, H l ] T.5 where H = 1,,, l are the set of the channel transfer functon vectors of the l users to each element of the p-element recever, whch s express as H = [H 1, H,, H p ] T, = 1,,, l..6 The compact expresson of the proposed SDMA-based upln MIMO OFDM system n the subcarrer can be expressed by the followng equaton x = H s + n = x + n.7 11

32 where x denotes the noseless component for x n the subcarrer. It s easy to understand that the number of antennas can decde the dmenson of the channel transfer matrx. The hgher the number of antennas s ncreased, the more the number of dmensons of transfer matrx s estmated. Transmtters Recevers H 11 n 1 S 1 OFDM Transmtter... s 1 H 1p... H l1... x 1 OFDM Recever... X 1 n p S l OFDM Transmtter s l H lp x p OFDM Recever X p Fgure -4 Schematc Dagram of the Proposed SDMA-based Upln MIMO OFDM System There are some assumptons n the desgned SDMA-based upln MIMO OFDM system. We assume that t s an nstantaneous lnear mxture model. The complex source sgnals are ndependent and have non-gaussan dstrbuton, and AWGN noses have zero mean and a varance of σ n. In addton, the frequency channel transfer functon H s statonary and has Gaussan dstrbuton. To desgn a sutable SDMA-based upln MIMO OFDM system for the proposed multuser detecton schemes, some sgnfcant specfcs should be consdered, and they 1

33 nclude: the fadng analyss of the wreless channel, the selecton and capacty analyss of MIMO technques, and the mplementaton of the OFDM transmtter module and the OFDM recever module. The followng of ths chapter focuses on these mportant aspects to mplement a proposed SDMA-based upln MIMO OFDM system.. Wreless Channel The term wreless s a generc word, whch llustrates that electromagnetc waves or rado frequences RF transmt nformaton through a part of or the whole communcaton paths. Wreless communcaton s able to transfer nformaton over both short dstances and long dstances. Furthermore, t s commonly employed n telecommuncaton wth an mpractcal or mpossble use of wres. The users n the next generaton wreless communcaton need hgher nformaton transmsson rate and better transmsson qualty, however, wreless resources are correspondngly lmted. Therefore, t s very sgnfcant to analyze the propertes of the wreless modes and the wreless fadng channel models, whch are able to support us to desgn the proposed upln MIMO OFDM system wth such lmted and expensve telecommuncaton resources. The wreless modes nclude pont-to-pont communcaton, pont-to-multpont communcaton, multpont-to-multpont communcaton, broadcastng, and others. Fgure -5 shows several wreless modes. The wreless devces, such as a cellphone, a wreless router, a laptop wth W-F, an ampltude modulaton AM or Frequency Modulaton FM rado, and so on, utlze the electromagnetc spectrum from 9 Hz to 300 GHz n wreless communcaton. However, the frequences are consdered as a publc 13

34 resource by most of countres and dfferent ranges can be used for dfferent purposes. For example, the frequency band of a common GSM cellphone s 900 MHz or 1800 MHz. The regular frequency band for a plot to communcate wth the control tower of an arport s around 900 MHz as well. If a passenger s usng a cellphone durng taeoff or landng, the passenger s phone call may nterfere wth plot s communcaton wth the control tower. Therefore, the effcent utlzaton of the lmted channel resources s very meanngful. Fgure -5 Wreless Modes 14

35 Several mportant types of wreless fadng channels related to the proposed SDMA-based MIMO OFDM channels need to be consdered. Fadng means a nd of attenuaton and t may possbly happen when transmttng modulated sgnals over some propagaton meda. In wreless communcaton, fadng may be due to ether multpath propagaton or shadowng. Cloud Scatterng Plane Reflecton Drect Path LOS lne-of-sght Dffracton Cellphone Reflecton Tower House Fgure -6 Fadng and Multpath 15

36 Fgure -6 shows that the obstacles such as buldng, cloud, tress or plane can reflect, scatter, or dffract the transmtted waves. The drect path for the transmtted waves between the transmtter and the recever s called lne of sght LOS. The transmtted waves by none-los paths are usually destructed by those obstacles. Therefore, the receved sgnals through the LOS are generally stronger than others from none-los paths. Dfferent tme, frequency or locaton could change the fadng, and common fadng channel models nclude two aspects: large-scale fadng and small-scale fadng [31]. The large-scale fadng, whch s also called attenuaton or path loss, relates to large dstances or tme-average characterstcs of transmtted sgnals. On the contrary, smallscale fadng, whch means fadng for short, s the fast fluctuaton of the ampltude or power of the transmtted sgnals corresponds to short dstances or short tme ntervals. Attenuaton and several fadng channels contanng flat fadng, frequency-selectve fadng, slow fadng, fast fadng, Raylegh fadng, Rcan fadng, et al should be consdered...1 Large-scale Fadng Model Large-scale fadng, or attenuaton, llustrates the path loss by propagaton ncludng reflecton, scatterng and dffracton n an open space envronment. The average power at a dstance d from the transmtter s gven as P d =β d/d 0 -v P t.8 16

37 where β s a large-scale fadng parameter dependng on antenna gan, frequency, wavelength, and other factors, d 0 s the reference dstance, P t s the average transmtted power, and v s the path loss exponent. 10 Large-scale Fadng Model, f c =1800MHz, Path loss[db] free space v= 30 urban cellular rado v=3 shadowed urban cellular rado v= Dstance[m] Fgure -7 Large Scale Fadng Model The path loss exponent s usually equal to n an open space envronment and s greater than n an envronment wth obstacles as shown n Fgure -6. In a practcal or emprcal stuaton le the cellphone n Fgure -6, the measurement for P d of the phone may not be the same value n dfferent places at the same dstance from the transmttng 17

38 tower or the base staton, because these obstacles can randomly nfluence the path loss. It s so called shadowng. The probablty densty functon pdf of the average power for a large-scale fadng wll submt to Gaussan dstrbuton [31]. Fgure -7 llustrates the large scale fadng model by Equaton.8. The carrer frequency s set to 1800 MHz and the reference dstance d 0 s 100 m. There are three types of stuatons consdered n ths model: v s for an open space cellular rado, 3 for an urban cellular rado, and 5 for a shadowed urban cellular rado, respectvely. The horzontal axs s log-dstance, and the vertcal one s path loss measured by db. When there s no shadow, t s obvous that the path loss ncreases wth the v. However, the random shadow may mae an mpact on the path lose. Thus, we can see t s not a straght lne n ths fgure compared wth the envronment wthout shadow, and t vares wth the random shadowng effect... Small-scale Fadng Model Small-scale fadng, or fadng, llustrates a fast fluctuaton of the power of the transmtted sgnals when the recevers are moved wthn a slghtly small area. It s caused by the multpath waves of the transmtted sgnals and these waves reach the recevers at moderate dfferent tmes. As mentoned before, scatterng, dffracton, and reflecton can generate the multpath waves and ths s nown as multpath fadng. In order to research the behavor of dfferent fadng channels, a general channel model s depcted n Fgure -8. In the tme or frequency doman, the source sgnals, the channel response, and the receved sgnals are st or Sf, ht or Hf, and rt or Rf, respectvely. 18

39 Fgure -8 General Channel Model Fgure -9 shows two types of wreless channels that are flat fadng channel and frequency-selectve fadng channel. Flat fadng channel means the coherence bandwdth of the channel s larger than the bandwdth of the source sgnal, whch s depcted n the frequency doman on the left sde of the fgure. Here the coherence means the mnmum frequency or tme requred for the magntude change of the channel. On the other hand, f the opposte assumpton wth a larger bandwdth of the source sgnal compared wth a smaller coherence channel bandwdth n the frequency doman as shown on the rght sde of the fgure, the receved sgnals wll be dstorted. If we consder Sf as a symbol bandwdth n the frequency doman for the proposed SDMA-based upln MIMO OFDM system, t ndcates that Inter Symbol Interference ISI exsts. Therefore, the channel bandwdth Hf n the frequency doman should be equal to or larger than the coherence channel bandwdth n the frequency doman to avod ISI. Compared wth the delay restrcton of the transmsson channel, slow fadng wll happen f the coherence tme of ths channel s not small. The shadowng mentoned above can lead to slow fadng. The rate of the channel wll be much slower than that of the transmtted sgnal. Then the varatons of ampltude and phase can be consdered statc over one or several bandwdth ntervals. On the other hand, f the coherence tme of 19

40 the channel s relatvely less than the delay restrcton of the transmsson channel, the fast fadng wll tae place. In ths case, t s worthy to notce that the change of the ampltude and phase s not statc anymore, and the channel response alters fast nsde the symbol perod. Fgure -9 Flat Fadng vs. Frequency-Selectve Fadng In all, the flat or frequency-selectve fadng channel and the slow or fast fadng channel are modeled by a lnear tme-varyng mpulse response. But the nature or practcal envronment of the multpath channels s mpossble to eep such an deal mpulse response. Thus, statstcal models are necessarly consdered to explore the performance of the receved sgnals and the most essental models are Raylegh fadng channel model, Rcan fadng channel model and others [31]. 0

41 There are manly two cases n a flat fadng channel. If there s no LOS path between the transmtter and the recever, t s a Raylegh fadng model. Otherwse, t s a Rcan fadng channel. The probablty densty functons of ether a Raylegh random varable or a Rcan random varable are gven by Equaton.9 and Equaton.10, respectvely [31]: r r r = exp, r 0.9 σ σ f Raylegh r r + D Dr f Rcan r = exp I 0, r 0, D 0.10 σ σ σ where r s the magntude of the receved sgnal, σ s the average power, D ndcates the pea ampltude of the LOS sgnal, I s the modfed Bessel functon of the frst nd, and I 0 s the zero-order of I. The Rcan dstrbuton wll approach the Raylegh dstrbuton when there s no LOS path n the channel. In other words, D s very close to zero. In addton, another quanttatve descrpton of the Rcan dstrbuton s the Rcan factor, K, and t s defned as [3] log D K =.11 σ Fgure -10 shows the smulatons of the Rcan dstrbuton when the value of K s less than zero.e. K s -35 db or -15 db n ths smulaton. The Rcan dstrbuton comes close to the Raylegh dstrbuton n ths fgure. Ths case happens frequently, 1

42 because t s very common that there s no LOS between moble users to a base staton n urban areas. If the value of K s a postve number.e. K s 10 db, 15dB or 5 db, the smulaton for the Rcan dstrbuton s shown n Fgure -11. The Rcan dstrbuton approaches the Gaussan dstrbuton when K s postve. In addton, we assume that the number of channel realzaton s 10,000, and the vertcal axs measures the ncdence for the Raylegh or Rcan dstrbuton n both Fgure -10 and Fgure Rcan approaches Raylegh Raylegh Rcan, K=-35dB Rcan, K=-15dB 700 Incdence r Fgure -10 Rcan Dstrbuton wth K < 0

43 Rcan approaches Gaussan Rcan, K=10dB Rcan, K=15dB Rcan, K=5dB 700 Incdence r Fgure -11 Rcan Dstrbuton wth K > 0.3 MIMO Technques A conventonal wreless system s a Sngle Input Sngle Output SISO antenna system that s lmted by the channel capacty. Whatever modulaton scenaros are chosen, there s stll a physcal restrcton by only one sngle wreless channel. To ncrease the channel capacty, more base staton, transmsson power, or bandwdth wll be requred. Thus, an antenna array or several ndependent antennas can be appled n the recever to ncrease the recevng dversty whle the transmtter s stll equpped wth one antenna. 3

44 Ths s called Sngle Input Multple Output SIMO system. An antenna array or several ndependent antennas can also be n the transmtter and the recever s equpped wth only one antenna to decrease the complexty of the recever. Ths type s so-called Multple Input Sngle Output MISO system. Transmtter Recever SISO Transmtter Transmtter Transmtter Recever Recever Recever SIMO MISO MIMO Fgure -1 Antenna System Models Furthermore, both the transmtter and the recever nstalled an antenna array or several ndependent antennas are a so-called MIMO system. The MIMO technques can not only offer a hgher spectral effcency or a hgher data rate, whch ndcates more bts 4

45 per second per hertz of bandwdth, but also have the mert of relablty or dversty. Although the MIMO system s more complex, t s stll a sgnfcant part of the modern wreless communcaton standards such as 4G, Worldwde Interoperablty for Mcrowave Access WMAX, and IEEE 80.11n. Fgure -1 shows these four types of antenna system models from up to down, respectvely. There are two types of MIMO systems: the closed-loop MIMO system and the open-loop MIMO system. When the recever feeds the nformaton about the wreless channel to the transmtter through a feedbac channel, ths s called the closed-loop MIMO system and Fgure -13 llustrates t Transmtter Recever Feedbac channel Fgure -13 Closed-Loop MIMO System Because the transmtters now the channel state nformaton through the feedbac channel n the closed-loop MIMO system, the transmtters can adjust the power of the paths between the transmtters and the recevers. It ndcates that the transmtters do not need to send the source sgnals to all of the drectons covered by the antenna array. Consequently, ths method can dramatcally save the transmsson power and energy. The receved sgnal gan s ncreased by the transmtted sgnals from dfferent antennas; and 5

46 meanwhle, the multpath fadng s reduced by the MIMO channel. The beamformng technque [3] s a type of closed-loop MIMO systems, and t can adjust the phase and the ampltude of each transmtter through the feedbac channel. All of the transmtters are able to drectly generate the correct phase and ampltude for each recever. An opposte case s that the MIMO system does not contan a feedbac loop, and t cannot provde drect access to the channel state nformaton. Ths type of MIMO technques s called an open-loop MIMO system, whch needs more power and energy to transmt sgnals through the antenna array for all of the drectons. It s notceable that the feedbac channel occupes the precous wreless channel resources. In order to save the channel resources, the open-loop type s employed to the proposed SDMA-based upln MIMO OFDM system. Due to the obstacles between the transmtter and the recever, and the nterference from others, the power and Sgnal Nose Rato SNR of the transmtted sgnals n the recever are regularly dropped dramatcally and are very small. There s normally a mnmum SNR requrement at the recever n order to detect and recover the transmtted sgnals. If the SNR value s less than ths mnmum requrement, the recever s unable to do such a detecton and recovery. Therefore, to mantan the requred value of the power and SNR at the recever s another requrement of the proposed upln SDMA-based MIMO OFDM system. The channel capacty s another mportant parameter that should be consdered for the proposed upln SDMA-based MIMO OFDM system. The amount of antennas n the transmtter and n the recever not only nfluences the channel capacty but also decdes 6

47 the computatonal complexty for multuser detecton n the recever. Thus, a sutable choce of the amount of antennas should be consdered. The MIMO channels are not always stable and they often change randomly. If the changng procedure s an ergodc process, the channel capacty s gven by [3] C = E{ C H} = E{ max Tr Rxx = NT log det I N R + N E T x N 0 HR xx H H }.1 where Tr s related to the squared Frobenus norm, R xx s the autocorrelaton of transmtted sgnal vector and equals to E{xx H }, H s Hermtan transpose. We assume that the transmsson power s the same for every transmsson antenna, and then TrR xx s equal to N T. E x means the energy of the transmtted sgnals, and N 0 denotes the power spectral densty of the addtve nose. Fgure -14 llustrates a comparson of, 4 4 and 8 8 MIMO channel capacty. It shows that more antennas we have, more channel capacty wll be generated. Although the 8 8 channel has the best channel capacty performance, the computatonal complexty cannot be accepted for the proposed blnd multuser detecton schemes. The MIMO channel has antennas n transmtter and antennas n recever. Snce the number of antennas s lmted, t s not representatve for the proposed SDMA-based upln MIMO OFDM system. As for how many of them are sutable, t s stll an open queston. There s no statement that the amount of antennas should be as many as possble. Thus, the 4 4 MIMO channel s selected for the proposed blnd multuser detecton schemes n the proposed SDMA-based upln MIMO OFDM system. 7

48 MIMO Channel 4 4 MIMO Channel MIMO Channel 50 bps/hz SNR [db] Fgure -14 Comparson of the MIMO Channel Capacty wth Dfferent Amount of Antennas.4 ODFM Technques One of the fundamental objectves of the proposed wreless communcaton system s to support a hgh data rate and to ntegrate multmeda types through a unfed platform. A common scenaro to support ths purpose s the OFDM [33], [34], whch s a frequency-dvson multplexng FDM scheme. Although the concepton of OFDM can be dated bac to the 1950s, hgh cost of mplementaton through analog flters s the major ssue, whch prevented the mplementaton of ths scheme at that tme. Fast Fourer 8

49 transform FFT made ths mplementaton possble later. From then on, OFDM became more and more popular n wreless communcaton. Subsequently, the OFDM technque was appled n IEEE 80.11a n 1999, IEEE 80.11g n 00, and IEEE 80.16e broadband wreless access n 005. In recent years, ths method has been taen as the ey part of 3G and 4G cellular communcaton standard. From a theoretcal standpont, the prncpal advantage of OFDM compared wth sngle carrer schemes s the ablty to dvde data streams nto several parallel narrowband subchannels also called sub-carrers or subcarrers at a low symbol rate, whch means smplfed channel equalzaton. Other advantages of the OFDM technques nclude robustness aganst fadng, low senstvty to tme synchronzaton errors, and so on. In addton, there are some dsadvantages of OFDM systems such as senstvty to the frequency synchronzaton and Doppler shft, poor power effcency, and loss of spectrum caused by the Cyclc Prefx CP [35]. The orthogonal property between subcarrers s vewed as an essental part of the OFDM scheme n order to overlap frequency spectrum, and provde undsturbed channels. Compared wth the OFDM scenaro, the conventonal frequency dvson multplexng requres guard ntervals between dfferent subchannels that do not overlap wth each other. Fgure -15 shows a comparson between these two schemes. Although the realzaton for the conventonal method s a straghtforward tas when the number of subcarrers s less than 64, the dsadvantage s ts low spectral effcency. On the contrary, the OFDM system wth more than 64 subcarrers s able to mae use of the spectrum resource n hgh effcency. 9

50 The OFDM scheme s not only used n the proposed SDMA-based upln MIMO OFDM system but also has become the choce for a lot of hgh profle wreless systems such as WF, WMax and Ultra-Wdeband UWB [36]. The structures of the OFDM transmtter module and the OFDM recever module are provded n ths secton n order to apply them to the proposed SDMA-based upln MIMO OFDM system. 1 OFDM Sgnal Spectrum Ampltude fn fn-1 fn Frequency 1 Convetonal Frequency Dvson Multplexng Spectrum Ampltude fn fn+1 fn Frequency Fgure -15 OFDM Sgnal Spectrum vs. Conventonal FDM Sgnal Spectrum If N subcarrers are used, the OFDM sgnal can be represented as: 30

51 N 1 = s t S ne n=0 jπnt, T 0 t T.13 where {S n } s the data symbols, N s the total number of subcarrers, T s the symbol tme, 1/T s the frequency of subcarrers, and all of subcarrers are orthogonal wth each other durng ths symbol perod T. Fgure -16 OFDM Symbols wth Cyclc Prefx If a guard nterval wth the length T g s added pror to the OFDM sgnal, the sgnal n the nterval -T g t < 0 wll be equal to the sgnal n the nterval T-T g t < T to ncrease the robustness. The length of the guard nterval should be larger than the delay of multpath channels to elmnate ISI. ISI reles on the duraton of the symbol perod. A shorter symbol tme or/and a hgher transmsson data rate may brng a larger ISI. But t s qute clear that to ncrease ths guard nterval wll reduce the spectrum effcency. Thus, there s a trade-off between the guard nterval and the spectrum effcency. The desgn strategy s to ncrease the length of guard nterval as much as possble wth precondtons of enough spectrum effcency and good ant-isi ablty. Fgure -16 shows ths guard nterval and the arrow n ths fgure show ths copy procedure. Then the OFDM sgnal wth guard nterval s 31

52 N 1 = s t S ne n=0 jπnt, T t T.14 T g Assume ths baseband OFDM sgnal s carred by a carrer frequency f c, and then the transmtted sgnal can be expressed as: jπf t T y t = Re{ s t e } = = c N n 1 0 S n cosπ f c + t + arg[ S n ] T.15 where Re denotes the real part of a complex value, and arg stands argument on a complex value. An nverse dscrete Fourer transform IDFT or nverse fast Fourer transform FFT IFFT based OFDM transmtter module s shown n Fgure -17. The IDFT/IFFT procedure s used to produce OFDM transmsson sgnals. IDFT s a conventonal mathematcal method and IFFT s a calculaton applcaton of IDFT n a fast way. In the same way, dscrete Fourer transform DFT and fast Fourer transform have the same relatonshp. For the proposed SDMA-based upln MIMO OFDM system, t s more convenent to apply IFFT and FFT, because they can reduce the computatonal complexty remarably. The followng processes are deemed necessary n order to acheve the OFDM transmtter. - Phase Shft Keyng PSK / Quadrature Ampltude Modulaton QAM encoder transfers the nput bt sequences nto Bnary Phase Shft Keyng BPSK / Quad Phase Shft Keyng QPSK / QAM modulated symbols. 3

53 - S/P model s a seres to parallel converter, whch converts users dscrete-tme BPSK/QPSK/QAM modulated symbols nto parallel data streams. - IDFT/IFFT module transforms the parallel data streams nto N low-rate parallel sub-channels. Assume the carrer frequences are f 0, f 1,, f N-1. The dfference n neghbor carrer frequences s f. So the total bandwdth W s equal to N f. Thus, the symbol duraton s extended by the factor of N and these N sub-carrers are orthogonal wth each other. - Cyclc Prefx, whch avods ISI at the transmtter, s added to each OFDM symbol before transmsson and t s removed at the recever. - P/S model s a parallel-to-seral converter, whch combnes N modulated subcarrers to create the OFDM transmsson sgnal. CP S 0 s 0 Output OFDM sgnal Input bt sequence PSK/ QAM encoder S/P S 1... S N-1 IDFT or IFFT s 1... s N-1 P/S Fgure -17 OFDM Transmtter Module Fgure -18 shows the structure of the OFDM recever module. Through the seral-to-parallel converter at the recever, the OFDM sgnal s demultplexed nto N subchannels agan. After remove the CP, the DFT/FFT module demodulates these OFDM symbols. The baseband BPSK/QPSK/QAM sgnal s then recombned through a parallel- 33