FREQUENCY-DOMAIN EQUALIZATION OF SINGLE CARRIER TRANSMISSIONS OVER DOUBLY SELECTIVE CHANNELS DISSERTATION Presented in Partia Fufiment of the Requirements for the Degree Doctor of Phiosophy in the Graduate Schoo of The Ohio State University By Hong Liu, B.Sc., M.Sc. * * * * * The Ohio State University 2007 Dissertation Committee: Approved by Prof. Phiip Schniter, Adviser Prof. Hesham E Gama Prof. Randoph L. Moses Adviser Graduate Program in Eectrica and Computer Engineering
ABSTRACT Wireess communication systems targeting at broadband and mobie transmissions commony face the chaenge of fading channes that are both time and frequency seective. Therefore, design of effective equaization and estimation agorithms for such channes becomes a fundamenta probem. Athough muti-carrier transmissions demonstrate prominent potentia to combat douby seective fading, severa factors may retard their appications, such as: high peak-to-average power ratio, sensitivity to phase noise, etc. Meanwhie, singe-carrier transmission is a conventiona approach and has important appications, such as HDTV broadcasting, underwater acoustic communication. In this dissertation, we focus on receiver design for singe-carrier transmissions. Our goa is to design and deveop a group of channe estimation and equaization agorithms in the frequency-domain, which enabe high performance and ow compexity reception of singe-carrier transmissions through douby seective channes. For singe-carrier transmissions over moderatey fast fading channes with ongdeay spread, we present an improved iterative frequency-domain equaization (IFDE) agorithm based on soft-interference-canceation (SIC) and propose a nove adaptive frequency-domain channe estimation (AFDCE) based on soft-input Kaman fiter, where soft information feedback from the IFDE can be expoited in the channe estimator. Simuation resuts show that, compared to other existing schemes, the ii
proposed scheme offers ower MSE in channe prediction, ower BER after decoding, and robustness to non-stationary channes. We extend the IFDE/AFDCE scheme to accommodate the appication of digita teevision (DTV) signa reception. Compared with the traditiona joint decision feedback equaization (DFE) /decoding pus frequency-domain east-mean-square (FDLMS) channe estimation approach, the proposed scheme achieves better performance at a fraction of the impementation cost. For very fast fading arge-deay-spread channes, traditiona FDE methods fai, because channe variation within a FFT bock induces significant off-main-diagona coefficients in the frequency domain. To conquer the probem, we appy Dopper channe shortening to shape the energy distribution of those coefficients and derive a piot-aided MMSE estimator to estimate them for SIC. We aso propose a nove IFDE by everaging both the sparse structure of shortened channe and finite-aphabet property of transmitted symbos. Numerica resuts show that the proposed scheme has advantages over the we-known FIR-MMSE-DFE/RLS-CE scheme in both performance and compexity. iii
To my famiy iv
ACKNOWLEDGMENTS First of a, I woud ike to thank my advisor, Prof. Phi Schniter, for his vauabe advice, guidance and hep throughout this academic experience. Without his critica feedback on my research and technique writing, it woud not be possibe for me to accompish this work. I thank Prof. Hesham E Gama for his vauabe comments and his Wireess Communication cass and paper discussion seminars motivated me to aways keep a open mind towards research. I aso thank Prof. Randoph L. Moses and Prof. Andrea Serrani for serving in my candidacy and dissertation committees and their constructive feedback. I am gratefu to the Department of ECE for the financia support and Nationa Science Foundation for its funding support under Grant No. 0237037. I am aso gratefu to ATI Research Inc. for offering me a chance to turn my research into practice. I particuary thank Dr. Rau. A. Casas for mentoring and supporting me throughout the internship and serving in my fina defense committee. Without his inspirations, enthusiasm and strong support, this dissertation coudn t have been competed. I aso thank Dr. Troy Schaffer, Haosong Fu and a the other members in the system group, for their coaboration and hep, which makes my internship a wonderfu experience. I thank my abmates in the IPS ab for the stimuating discussions, and for providing the fun environment in which we earn and grow. I thank Ms. Jeri McMichae, v
IPS administrative assistant, for her efforts to make IPS ab a big happy famiy. I am thankfu to a my good friends - that I met in America and in China. Wherever you are, without your mora support, I coud not go through those difficut moments and achieve the goa. Finay, I woud ike to thank my famiy for their unconditiona ove and support throughout my ife. Especiay, I want to thank my husband Jun, for his endess patience and encouragement. Both as a coeague and my dearest friend, he accompanies me throughout this journey a aong. vi
VITA February, 1976... Born - Wuhan, P. R. China Sept. 1994 - June 1998... B.Sc. Eectrica Engineering, Wuhan University, Wuhan, P. R. China Sept. 1998 - June 2001... M.Sc. Eectrica Engineering, Wuhan University, Wuhan, P. R. China Sept. 2002 - Aug. 2003... Graduate Feow, Dept. of Eec. & Computer Eng. The Ohio State University Coumbus, OH. Sept. 2003 - Mar. 2004 Juy 2004 - Sept. 2004...Graduate Research Associate, Dept. of Eec. & Computer Eng. The Ohio State University Coumbus, OH. Apr. 2004 - June 2004 Sept. 2004- June 2005... Graduate Teaching Associate, Dept. of Eec. & Computer Eng. The Ohio State University Coumbus, OH. Juy 2005 - Dec. 2005... System Engineer Intern, ATI Research, Inc. Yardey, PA. Jan. 2006 - June 2006... Graduate Teaching Associate, Dept. of Eec. & Computer Eng. The Ohio State University Coumbus, OH. vii
June 2006 - June 2007...Graduate Feow, Dept. of Eec. & Computer Eng. The Ohio State University Coumbus, OH. PUBLICATIONS Research Pubications 1. H. Liu and P. Schniter, Iterative Frequency-Domain Channe Estimation and Equaization for Singe-Carrier Transmissions without Cycic-Prefix, IEEE Transactions on Wireess Communications, submitted Apr. 2007. 2. P. Schniter and H. Liu, Iterative Frequency-Domain Equaization of Singe- Carrier Transmissions over Douby Dispersive Channes, IEEE Transactions on Signa Processing, under revision. 3. H. Liu and P. Schniter, Iterative Frequency-Domain Channe Estimation and Equaization for Singe-Carrier Transmission without Cycic Prefix, Proc. Conference on Information Sciences and Systems, (Batimore, MD), Mar. 2007. 4. H. Liu, P. Schniter, H. Fu, and R. A. Casas, Frequency Domain Turbo Equaization for Vestigia Sideband Moduation with Punctured Treis Coding, Proc. IEEE Workshop on Signa Processing Advances in Wireess Communications, (Cannes, France), Juy 2006. 5. P. Schniter and H. Liu, Iterative Frequency-Domain Equaization for Singe- Carrier Systems in Douby Dispersive Channes, Proc. Asiomar Conf. on Signas, Systems, and Computers, (Pacific Grove, CA), pp. 667-671, Nov. 2004. 6. P. Schniter and H. Liu, Iterative Equaization for Singe-Carrier Cycic-Prefix in Douby Dispersive Channes, Proc. Asiomar Conf. on Signas, Systems, and Computers, (Pacific Grove, CA), vo. 1, pp. 502-506, Nov. 2003. PATENT: H. Liu, R. A. Casas, H. Fu, A frequency-domain Turbo Equaizer for DTV signas, fied January 2006. viii
FIELDS OF STUDY Major Fied: Eectrica and Computer Engineering Studies in: Comm. and Signa Proc. Comm. and Signa Proc. Comm. and Signa Proc. Contro Theory Prof. Phiip Schniter Prof. Hesham E Gama Prof. Randoph L. Moses Prof. Vadim Utkin ix
TABLE OF CONTENTS Page Abstract....................................... Dedication...................................... Acknowedgments.................................. Vita......................................... List of Tabes.................................... List of Figures................................... ii iv v vii xiii xiv Chapters: 1. Introduction.................................. 1 1.1 Motivation............................... 1 1.2 Background............................... 3 1.2.1 Douby Seective Channes................... 3 1.2.2 System Mode......................... 5 1.2.3 Channe Equaization..................... 7 1.2.4 Turbo Equaization....................... 10 1.2.5 Channe Estimation...................... 12 1.3 Contribution and Outine....................... 14 1.4 Notation and Abbreviations...................... 16 2. Frequency-Domain Equaization of Moderatey Fast Fading Frequency- Seective Channes.............................. 20 2.1 Introduction.............................. 20 2.2 System Mode.............................. 22 x
2.3 Receiver Structure........................... 23 2.4 Cycic Prefix Reconstruction...................... 25 2.5 Iterative Frequency-Domain Equaization.............. 26 2.6 Soft-Decision-Directed Channe Estimation............. 29 2.6.1 Soft-Decision-Directed Time-Domain Channe Estimation. 30 2.6.2 Soft-Decision-Directed Frequency-Domain Channe Estimation 32 2.7 Impementation Considerations.................... 38 2.7.1 Bock Overapping....................... 38 2.7.2 Compexity Anaysis...................... 39 2.8 Numerica Resuts........................... 41 2.8.1 Simuation Setup........................ 41 2.8.2 Performance Assessment.................... 42 2.9 Concusion............................... 47 2.A Derivation of Conditiona Mean and Variance............ 48 2.B State-Space Mode for Time-Domain Kaman Fiter......... 49 2.C State-Space Mode for Frequency-Domain Kaman Fiter...... 50 2.D Performance Bound of Channe Estimator.............. 52 3. Frequency-Domain Turbo Equaization for Digita TV Transmission Systems 55 3.1 Introduction.............................. 55 3.2 Treis Coded Vestigia Sideband Moduation............. 56 3.3 System Mode.............................. 60 3.4 Frequency-Domain Turbo Equaization................ 62 3.4.1 MMSE Estimation of Virtua Subcarriers.......... 62 3.4.2 Generation of MAP Inputs.................. 64 3.4.3 Update of Virtua Subcarrier Statistics............ 65 3.5 Modified Adaptive Frequency-Domain Channe Estimation..... 66 3.6 Numerica Resuts........................... 69 3.6.1 Simuation Setup........................ 69 3.6.2 Performance Assessment.................... 70 3.7 Concusions............................... 72 3.A Derivation of Conditiona Mean and Variance............ 78 3.B 8-VSB Pue Shape........................... 80 3.B.1 Root-Raised Cosine Puse................... 80 3.B.2 Raised Cosine Puse...................... 81 4. Frequency-Domain Equaization of Very Fast Fading Frequency-Seective Channes.................................... 82 4.1 Introduction.............................. 82 4.2 System Mode.............................. 85 xi
4.3 Max-SINR Window Design...................... 89 4.4 Piot-Aided Channe Estimation.................... 92 4.5 Symbo Detection............................ 94 4.5.1 Intrabock Processing..................... 95 4.5.2 Interbock Processing..................... 99 4.6 Fast Agorithm and Compexity Anaysis............... 101 4.7 Numerica Resuts........................... 102 4.7.1 IFDE with Perfect CSI..................... 102 4.7.2 IFDE with PACE....................... 103 4.8 Concusion............................... 105 4.A Signa Energy Distribution....................... 115 4.B Conditiona Mean and Variance.................... 116 4.C Fast-IFDE Detais........................... 117 4.C.1 Derivation of (4.57)...................... 120 4.C.2 Derivation of (4.60)...................... 122 5. Concusion................................... 124 5.1 Summary of Origina Work...................... 124 5.2 Possibe Future Work......................... 126 Bibiography.................................... 128 xii
LIST OF TABLES Tabe Page 1.1 A Comparison of Anti-mutipath Schemes [1].............. 9 1.2 Abbreviations............................... 18 2.1 Computationa Compexity........................ 41 3.1 DTV Propagation Modes......................... 72 3.2 Computationa Compexity (per N d symbos).............. 76 4.1 Summary of Iterative Symbo Detection................. 112 4.2 Fast Impementation of the Iterative Symbo Detector......... 113 4.3 Reative Agorithm Compexity (Per Symbo).............. 114 4.4 Recursive Update of (R (n) k ) 1...................... 123 xiii
LIST OF FIGURES Figure Page 1.1 Base band transmission system mode.................. 5 2.1 Receiver structure............................. 24 2.2 Adaptive frequency-domain channe estimator.............. 30 2.3 The bock-overapping scheme....................... 38 2.4 BER versus SNR for AR channes.................... 43 2.5 MSE versus SNR for AR channes.................... 44 2.6 BER versus SNR for WSSUS Rayeigh channes............. 45 2.7 Channe-estimate-MSE versus SNR for WSSUS Rayeigh channes... 46 2.8 Channe-estimate-MSE and BER versus bock index at SNR= 7dB for a non-stationary Rayeigh channe which transitions from f d T s = 0.00001 to f d T s = 0.00005......................... 46 2.9 BER versus SNR for WSSUS Rayeigh channes............. 47 3.1 The spectrum of VSB moduated signa [2]................ 58 3.2 8-VSB root raised cosine puse shape.................. 58 3.3 8-VSB raised cosine puse shape..................... 58 3.4 frequency-domain transform of root raised cosine and raised cosine puse shapes................................ 59 xiv
3.5 Treis encoder, precoder, and symbo mapper [2]............ 59 3.6 BER performance comparison for DFE-VD/FDLMS versus FDTE/AHKCE. 73 3.7 BER performance comparison for FDTE/AHKCE versus FDTE/FDLMS. 73 3.8 MSE performance comparison for FDTE/AHKCE versus FDTE/FDLMS. 74 3.9 MSE of CPR with perfect CSI, estimated channes at SNR=20dB... 75 3.10 Computationa compexity (per symbo)................. 76 3.11 Computationa compexity (per symbo)................. 77 4.1 Frame structure of transmitted signa.................. 85 4.2 Desired banded structure of matrix H(i, 0).............. 89 4.3 Exampe window shapes for PN = 256, N h = 64, SNR=10dB and (a) f d T s = 0.001, (b) f d T s = 0.0075...................... 91 4.4 Intrabock interference canceation.................... 95 4.5 Truncated observation mode....................... 96 4.6 Interbock detection process for P = 2. Soid arrows pass fina hard estimates; dashed arrows pass soft initiaizations............ 101 4.7 Symbo error rate for various PN when M = 10............. 106 4.8 Symbo error rate for various M when N h = 64 and f d T s = 0.003... 107 4.9 MSE of FIR-MMSE-DFE versus at f d T s = 0.003, SNR= 10, and N f = N h.................................. 107 4.10 MSE of FIR-MMSE-DFE versus N f when f d T s = 0.003, N h = 64, and = N f 1................................. 108 4.11 SER versus SNR for N h = 64 and various f d T s with perfect CSI... 108 xv
4.12 SER of IFDE/PACE versus SNR for various N h and f d T s....... 109 4.13 MSE of PACE versus SNR for various N h and f d T s.......... 109 4.14 SER versus SNR for N h = 32 and various f d T s............. 110 4.15 Computationa compexity ratio of FIR-MMSE-DFE/RLS-CE to IFDEnoBDFE-2/PACE............................. 110 4.16 Computationa compexity ratio of FIR-MMSE-DFE/RLS-CE to IFDEnoBDFE-10/PACE............................ 111 4.17 Contour of theoretica MSE of PACE................... 111 xvi
CHAPTER 1 INTRODUCTION 1.1 Motivation In mobie wireess and digita teevision (DTV) transmission, time-varying mutipath phenomenon is generay induced by the randomy changing propagation characteristics as we as the refection, diffraction and scattering of the transmitted signas from the buidings, arge moving vehices, mountains, etc. Such phenomenon distorts received signas and poses critica chaenges in the design of communication systems for high-rate and high-mobiity wireess communication appications. High rate information symbos, after transmitting through mutipath channe, often spread into neighboring symbo periods, and cause serious inter-symbo interference (ISI) at the receiver side. In addition, reative mobiity between the transmitter and receiver eading to fast channe variations, aong with osciator drifts and phase noise, gives rise to time seectivity. The combined time-frequency seectivity induces Dopper-deay spreading, which significanty affects communication system performance. Therefore, the design of effective equaization and estimation agorithms for such channes becomes a fundamenta probem of communication systems. 1
In order to impement commerciay competitive communication systems, owcompexity and ow-cost systems are highy desirabe. Among various proposed candidates for the new system design, the diversity reception with mutipe transmitter and receiver antennas [3,4] and the muti-carrier transmission [5] combined with advanced signa processing agorithms to estimate and equaize the dynamic channes are considered to be the most promising. However, the introduction of mutipe antennas demands dedicated ampifiers in a configurations. Muti-carrier transmission exhibits very high peak-to-average-power ratio (PAPR) and utiizes a combination of highy inear power ampifiers, ampitude cipping and ampifier backoff to mitigate the probem [6]. Since a big portion of the cost of terminas in communication systems is due to the transmitter power ampifier, singe-carrier (SC) moduation system is a favorabe aternative for commercia success. In addition, in some appications such as HDTV transmission, the transmitter is standardized to adopt SC moduation, which aso motivates the receiver design for SC transmission systems. This dissertation considers receiver design for effective and efficient reception of singe-carrier transmission through time-varying mutipath channes. Our goa is to design and deveop a group of channe estimation and equaization agorithms in the frequency domain, which enabe high performance reception of SC transmission with ow computationa compexity. 2
1.2 Background 1.2.1 Douby Seective Channes Wireess communications operate through eectromagnetic radiation from the transmitter to the receiver. The communication medium, commony referred as the channe, usuay distorts the signa based on its propagation characteristics. Two important factors which characterize the distortion effects of the channe are mutipath fading and Dopper effect. Mutipath fading is the phenomenon in which the transmitted signa arrives at the receiver via mutipe propagation paths at different deays due to refection, diffraction and scattering of the radio waves. It resuts in a wide variation of the received signa strength, since the mutipe signas arriving at the receiver may add up constructivey or destructivey. The Dopper effect, named after Christian Dopper, is the change in frequency and waveength of a wave that is perceived by an observer moving reative to the source of the waves [7]. In mobie wireess communication scenario, Dopper effect is attributed to the reative movement of the surrounding objects as we as the transmitter and receiver. It eads to fast phase osciation of the received signas on mutipe paths, thus acceerates the time variation of the channe distortion. Future wireess communication services featuring high-data-rate and high-mobiity can aggravate the mutipath and Dopper effect. In digita communication systems, for most of the channes, the discrete information bearing symbos are moduated with a continuous puse shape and transmitted across the channe [8]. In most cases, the puse shapes are ocaized in time and frequency so that transmission of each symbo consumes a sma tie in the time-frequency pane. For high data rate transmission, the duration of the puse becomes sma and comparabe to the mutipath deay, thus 3
ISI occurs and the channe distortion is caed frequency-seective. In high-mobiity scenarios, the channe response varies significanty in the signaing duration due to Dopper effect, thus the channe distortion becomes time-seective within a singe processing bock. Channes whose response are both time and frequency seective are commony referred as douby-seective channes. Theoreticay, the douby seective channe can be modeed as a inear time-varying system [9]. When the surrounding objects are stationary, the input and output reationship between transmitter and receiver can be represented as a inear time-invariant system with the impuse response N c(τ) = c δ(τ τ ), (1.1) =1 where c and τ are the attenuation and propagation deay of the -th path respectivey. This mode is widey adopted for description of mutipath frequency-seective channe. When there is reative movement between the surrounding objects incuding transmitter and receiver, the attenuation and deay of the -th path vary with time. Therefore the impuse response of the channe becomes N c(t, τ) = c (t)δ(τ τ (t)). (1.2) This is the continuous time mode for a douby seective channe. =1 Dopper spread and deay spread are two important quantities that measure the time seectivity and frequency seectivity of the channe respectivey. The Dopper shift of the -th path is defined as f c dτ (t) dt, where f c is the carrier frequency. The Dopper spread f d is defined as the argest difference between the Dopper shift of a paths. dτ i (t) f d = max f c i,j dt dτ j(t) dt (1.3) 4
Larger f d impies that the channe varies more rapidy in time. The deay spread (or mutipath spread) is defined as the difference in the propagation time between the ongest and shortest path. Thus, When T d is arger, the mutipath effect is more evident. 1.2.2 System Mode T d := max τ i (t) τ j (t). (1.4) i,j r(t) r n s n s k a(t) s(t) c(t, τ) a ( t) T Equaizer h µ(t) Channe Estimator Figure 1.1: Base band transmission system mode. The continuous time transmission system mode is depicted in Fig. 1.1, where the information signa is first moduated by a puse shaping fiter (PSF) a(t) and then transmitted through time-varying frequency-seective channe c(t, τ), the received signa is distorted by AWGN noise µ(t) and then passes through matched PSF a (t). The base-band transmitted symbo sequence and moduated signa waveform of data rate 1/T symbos/sec depicted in Fig. 1.1 are given by s T (t) = k s k δ(t kt), (1.5) s(t) = s T (t) a(t) = k s k a(t kt), (1.6) where {s k } are the transmitted symbos. 5
To incude the transmitter PSF a(t) and receiver PSF a ( t), the composite channe impuse response can be defined as h(t, τ) = a(τ) c(t, τ) a ( τ) = c(t, τ) b(τ) (1.7) N = c (t)b(τ τ (t)), (1.8) =1 where b(τ) = a(τ) a ( τ). As impied by (1.3), when f d f c, we can assume τ (t) = τ for a ong time period (approximatey proportiona to fc 2f d f s, where f s is the samping frequency). In this case, we can rewrite (1.8) as N h(t, τ) = c (t)b(τ τ ). (1.9) =1 In genera, the received signa r(t) is defined as r(t) = h(t, τ) s T (t) + ν(t) = = k s k N N c (t)b(τ τ (t)) =1 k s k δ(t τ kt)dτ + ν(t) (1.10) c (t)b(t kt τ (t)) + ν(t), (1.11) =1 where ν(t) = µ(t) a ( t) and µ(t) is the AWGN noise. Samping r(t) with period T, we obtain r(nt) = k = c (nt)b(nt kt τ (nt)) + ν(nt) (1.12) s k N =1 s n N c (nt)b(t τ (nt)) + ν(nt) (1.13) =1 Define r n = r(nt), ν n = ν(nt) and h n, = N =1 c (nt)b(t τ (nt)), then discrete time system mode is given by: r n = L s n h n, + v n, (1.14) =0 6
where we assume h n, has finite support [0 L]. Generay, the PSF is assumed to be a Nyquist fiter of bandwidth f s, therefore {v n } can be treated as AWGN noise. Whie for North America terrestria digita TV transmission, the PSF is a root raised cosine fiter of bandwidth f s /2, therefore {v n } is a coored noise. However in this thesis we woud sti treat it as AWGN simiar as in [10, 11], and extension to the coored noise case can be done with a itte bit more efforts. 1.2.3 Channe Equaization In this section, we give a brief retrospection on channe equaization schemes. First, we consider channe equaization schemes for moderatey fast-fading channes, where the channe can be viewed as static within one processing bock and varying across bocks, then we move on to discuss channe equaization agorithms for vary fast-fading channes, where the channe s time-variation within a singe bock can not be ignored. In traditiona ow-mobiity communication appications, the dominant factors which degrade the performance of communication systems are the mutipath fading and noise. A conventiona anti-mutipath approach, which was pioneered in voiceband teephone modems, is to transmit a singe carrier moduated by data symbos and a time-domain equaizer is appied at the receiver to compensate for ISI [12]. Various equaization methods, ranging from optima approaches such as maximum a posteriori probabiity (MAP) symbo detection, maximum-ikeihood (ML) sequence detection to suboptima inear equaization such as zero-forcing (ZF), minimum mean square error (MMSE) symbo estimation, and noninear minimum mean square error decision feedback equaization (MMSE-DFE) have been proposed and researched in various 7
ways of trading of compexity for performance. However for severe mutipath channes, which is more evident in wireess high-data-rate transmission, a these singe carrier time-domain equaization (SC-TDE) schemes suffer from heavy computation compexity due to the ong deay spread. Muti-carrier moduation with frequency-domain equaization (FDE) techniques are proposed as aternative anti-mutipath approaches for such kind of channes, and orthogona frequency division mutipexing moduation (OFDM) with FDE system can be viewed as a successfu exampe. OFDM transmits symbos through a arge number of cosey-spaced orthogona sub-carriers, which is essentiay using many sowy-moduated narrow band signas rather than one rapidy-moduated wide-band signa [13], therefore it transfers a severe frequency-seective channe into an parae array of frequency-fat channes on each sub-carrier. As a favorabe resut, the channe equaization is simpified to a channe inversion operation on each sub-carrier, and the computationa compexity of OFDM-FDE is approximatey proportiona to the ogarithm of deay spread per symbo, which is much ower than the SC-TDE schemes. However, the transmitted OFDM signa is the sum of a arge number of moduated sub-carriers, so OFDM suffers from high PAPR. This drawback increases the cost of power ampifiers. In addition, OFDM can be sensitive to carrier frequency offset and phase noise [6]. Singe carrier FDE (SC-FDE) schemes are proposed as a promising aternatives to sove the high PAPR issue associated with OFDM [1]. SC-FDE transfers the FFT modue from transmitter to receiver, thus avoids the high PAPR, but sti inherits the ow compexity advantage attributed to frequency-domain signa processing. In addition, it has some merits not shared by OFDM system. For exampe, coding, 8
whie desirabe, is not necessary for combating frequency seectivity, as it is in OFDM. Meanwhie, SC moduation is a we-proven technoogy in many existing wireess and wireine appications, and its radio frequency (RF) system inearity requirements are we known [1]. As shown in tabe 1.1, SC-FDE scheme possesses attractive features and especiay fits appications with constraints on PAPR and power. Furthermore, SC-FDE shares a number of common signa processing functions with OFDE-FDE, thus SC and OFDM modems can easiy be configured to coexist. In this dissertation, we conduct investigation of new equaization schemes to combat the douby seective channes in the framework of SC-FDE. Tabe 1.1: A Comparison of Anti-mutipath Schemes [1]. OFDM SC-FDE SC-TDE Signa PAPR High Low Low Computationa Compexity Low Low High Coding Requirement Strict Fexibe Fexibe With the increasing appication/depoyment of high-mobiity and high-rate wireess communication, Dopper spread becomes an important factor in the system design. When the channe varies significanty within one OFDM symbo duration, sub-carriers are no onger perfecty orthogona, severe ICI wi degrade system performance substantiay. The same diemma aso pagues SC-FDE schemes, since the resuting frequency-domain (FD) channe matrix is not diagona any more, therefore the simpe one-tap equaizer is not viabe. Effective equaization for rapid timevarying frequency-seective channes is a chaenging probem. In recent years, various approaches to suppress ICI for muti-carrier systems are investigated. Choi proposes 9
a MMSE successive detection agorithm [14] to cance ICI, but the computation compexity is too high if the number of subcarrier is arge. Assuming that some sma ICI coefficients can be directy ignored, severa ICI suppression agorithms with ower compexity are proposed in [15 17]. However, such assumption may not be vaid as shown in [18], where a maximizing signa to noise pus interference ratio (SINR) window is derived to restrict ICI infuence and then an iterative MMSE estimator is appied to cance ICI as we as estimate finite-aphabet frequency-domain symbos. Rugini appies banded LDL factorization [19] to further reduce the compexity of estimation step in [18]. Besides, some parametric modes are adopted to describe the douby seective channe, various equaization agorithms based on those modes are expored. Gorokhov [20] uses Tayor series expansion to ineary approximate timedomain channe variations and achieves ow compexity channe equaization based on the structura property of data mode. Barhumi proposes a frequency-domain pertone equaizer based on compex exponentia basis expansion mode (CE-BEM) [21]. Motivated by the ow-compexity ICI suppression scheme for OFDM systems in [18], we studied the FDE with anaogous ICI suppression for SC systems and proposed iterative FDE schemes for both cycic prefixed (CP) and non-cycic prefixed (NCP) SC systems with the desired ogarithmic per-symbo processing compexity. 1.2.4 Turbo Equaization Turbo codes are first introduced by Berrou, Gavieux and Thitimajshima in [22]. They present stunning resuts that performance near the theoretica imits of shannon can be achieved with reativey simpe code structure and decoding agorithm. 10
The magic comes from the decoding agorithm: iterative exchanging soft information between two simpe constituent codes. Inspired by the success of turbo decoding, researchers start investigating the appication of such iterative soft information exchanging agorithms, which is termed turbo principe, to sove other probems. Ever since then, turbo equaization becomes an active research direction. The idea of turbo equaization is first introduced in [23], where a soft-output Viterbi agorithm (SOVA) is appied for soft-in-soft-out channe equaization and decoding. A soft muti-user interference canceation agorithm is proposed for code division mutipe access (CDMA) system in [24]. Such idea is appied to turbo equaization in [25 27], and various techniques to reduce the computationa cost required to compute the equaizer coefficients are discussed. Frequency-domain approaches for MMSE turbo equaization are proposed in [28 30] and [31] for singe-input-singe-output and mutipe-input-mutipe-output systems, respectivey. The key phiosophy behind turbo equaization is to incorporate soft information into the equaization and decoding tasks. Traditionay, the equaizer estimates the symbos, makes a hard decision, and then feeds them to a decoder. This approach actuay destroys information pertaining to how ikey each of the possibe data symbos might have be. However, this additiona soft information can be converted into probabiities that a optima decoding agorithm (such as BCJR agorithm [32]) can expoit for better performance. Another key characteristic of turbo equaization is its iterative treatment. In turbo equaization, once the decoder processes the soft information it can, in turn, generate its own soft information indicating the reative ikeihood of each transmitted bit. This 11
soft information from the decoder is fed back to the equaizer to aid symbo estimation. This process is often termed beief propagation or message passing [33,34] and has connections to methods in artificia inteigence, statistica inference, and graphica earning theory. A cosey reated research topic with Turbo equaization is iterative channe estimation. For coherent detection (detecting transmitted symbos from received signa using an estimated channe impuse response (CIR)), channe estimator pays an important roe. A number of researches consider expoiting the soft output information of turbo equaizer to improve the accuracy of channe estimation. Iterative CIR estimators based on east mean square (LMS), recursive east square (RLS) and Kaman fiter are proposed in [35] and [36] respectivey, which take soft information of data symbo estimates from equaizer as input and update fiter coefficients accordingy. Appication of iterative detection and channe estimation techniques in goba systems for mobie communications (GSM) and enhanced data rates for goba evoution (EDGE) shows a significant performance enhancement in [37]. In this dissertation, we aso consider fitting soft input channe estimation into the turbo equaization framework, giving a receiver with iterative channe estimation, equaization, and decoding. The most reevant references to our work are [25,28,29,36]. 1.2.5 Channe Estimation Channe estimation (CE) for douby seective channe is a chaenging and interesting probem. Generay speaking, CE schemes can be divided into two big famiies, one is training based CE (TB-CE) or decision directed CE (DD-CE) schemes, the other is bind CE schemes. For douby seective channe, TB-CE and DD-CE are 12
more common, which can be roughy categorized into three casses: finite parametric mode based CE schemes, statistica mode based CE schemes and adaptive CE schemes. Finite parametric mode based CE schemes assume that the time variation of each independent channe coefficient can be captured by a inear combination of imited number of basis functions, thus CIR over a time interva can be attained by estimating those basis expansion parameters. Such modes are commony adopted for estimating very fast fading channes over a bock duration. Various CE schemes have been researched for difference parametric modes. Kaman fiter, MMSE and LS channe estimator based on basis expansion mode (BEM), Sepian basis, kernes for Rayeigh fading are investigated in [38 42]. A Tayor expansion based channe mode is proposed in [43] to faciitate the design of ICI canceation fiter. Statistica mode based CE schemes assume the second-order statistics information of the channe is either known or avaiabe through estimation, thus CIR can be obtained by expoiting the correation between received signa and priori known piot symbos/ detected symbos. For very fast fading channes, piot-aided channe estimation for muticarrier moduation are investigated in [44, 45]. For moderatey fast fading channes, various frequency-domain channe estimation (FDCE) schemes have been proposed to track and predict wireess channes for OFDM systems, with or without piot symbos, and with or without knowedge of channe statistics [46 48]. For SC systems, time-domain channe estimation is the typica approach [30, 36, 49], though a few piot-aided FDCE schemes have been proposed [50 52]. A survey about inear channe estimation for systems with mutipe antennas is presented in [53]. 13
Adaptive CE schemes appy an adaptive fiter to track channe variation in time, whie both piot symbos and detected data symbos can be used to update the fiter coefficients. For rapid time-varying channes, adaptive fiters are adopted to estimate the mode parameters with ow computationa compexity for a BEM and poynomia basis in [54] and [55] respectivey. Iterative CIR estimators based on LMS and RLS fiter is investigated in [35]. For modest time-varying channes, a frequency-domain adaptive agorithm is proposed in [56] to track channes for SC transmission systems. Bind CE schemes are adopted in communication system where training symbos are not avaiabe or not sufficient to initiaize channe estimates. Various bind equaization methods have been proposed during the ast ten years. These methods incude higher-order statistica approaches [57], constant moduus agorithm (CMA) [58], subspace method based on second-order statistics [59], etc. In adaptive CE schemes, bind CE can serve as initiaization step. In this dissertation, we focus on FDCE agorithms and deveop adaptive Kaman fiter based per-tone channe estimator to track and predict channes for SC systems. the most reevant references with our work are [36,39,52]. 1.3 Contribution and Outine In the seque, we give the dissertation outine and its main contributions. In Chapter 2, we consider the receiver design for singe carrier transmission systems over moderatey fast-fading frequency-seective channes [60,61]. Particuary we investigate iterative frequency-domain equaization (IFDE) with expicit frequencydomain channe estimation (FDCE). First, an improved IFDE agorithm is presented 14
based on soft iterative interference-canceation. Second, soft-decision-directed channe estimation agorithms are derived and anayzed both in time and frequency domain. As it turns out, frequency-domain approach is more computationa efficient than time-domain approach. Therefore a new adaptive FDCE (AFDCE) agorithm based on per-tone Kaman fitering is proposed to track and predict the frequencydomain channe coefficients. The AFDCE agorithm empoys across-tone noise reduction, expoits tempora correation between successive bocks, and adaptivey updates the auto-regressive mode coefficients, bypassing the need for prior knowedge of channe statistics. Finay, a bock overapping idea is proposed which faciitates the joint operation of IFDE and AFDCE. Simuation resuts show that, compared to other existing IFDE and adaptive channe estimation schemes, the proposed schemes offer ower mean-square error (MSE) in channe prediction, ower BER after decoding, and robustness to non-stationary channes. In Chapter 3, we consider a frequency-domain turbo equaization and adaptive frequency-domain channe estimation (FDTE/AFDCE) scheme for the reception of transmissions that empoy treis coded vestigia sideband (TCVSB) moduation, as specified by the ATSC North American terrestria digita teevision (DTV) standard [62, 63]. The proposed FDTE/AFDCE scheme enabes ow-cost and highperformance reception of highy impaired DTV signas. Through numerica simuation, we demonstrate that our FDTE/CE scheme outperforms the traditiona joint DFE/decoding pus frequency-domain east-mean-square (FDLMS) channe estimation approach at a fraction of the impementation cost. 15
In Chapter 4, we consider the receiver design for singe carrier transmission systems over very fast fading frequency-seective channes [64 66]. In these quicky varying arge-deay-spread channes, the traditiona FDE methods fai when the channe response varies significanty over the FFT anaysis window. Here we propose a nove FDE that is based on Dopper channe shortening, soft iterative interference canceation, and bock decision feedback. In addition, we derive a MMSE channe estimator for the piot-aided estimation of significant channe coefficients in frequency domain, which are necessary for FDE. Numerica simuations show that the proposed scheme has advantages over the we-known FIR-MMSE-DFE pus RLS based CE scheme in both performance and compexity. Finay in Chapter 5, we offer some concuding remarks and indicate future research possibiities. To enhance the fow of the dissertation, we coect a detaied derivations in the appendices of each chapter. 1.4 Notation and Abbreviations Matrices (coumn vectors) are denoted by upper (ower) bod face etters. Conjugate, transpose, Hermitian transpose, and inverse of A are denoted by A, A T, A H and A 1, respectivey. The Frobenius norm and 2 norm are denoted by F and, respectivey. The expectation, Kronecker deta, Kronecker product, moduo-n and integer ceiing operations are denoted by E[ ], δ( ),, < > N,, respectivey. The N N identity matrix and unitary discrete Fourier transform (DFT) matrix are denoted by I N N and F N N, i n for the nth coumn of I. C(a) denotes the circuant matrix with first coumn a, and D(a) is the diagona matrix with diagona eements 16
a. Re( ) denotes the rea part, and diag(a) is the vector formed from the diagona eements of square matrix A. Finay, CN(µ, Σ) denotes the muti-dimensiona circuar Gaussian distribution with mean vector µ and covariance matrix Σ. 17
Tabe 1.2: Abbreviations AWGN AFDCE APPLE AR ATCR BER BPSK CE CIR CMA CP CPR CSI CWGN DFE DTV FDCE FDE FDLMS FDTE FFT FIR IBI ICI IFDE i.i.d. ISI LMS LS MAP MF ML MMSE MMSE-DFE MSE OFDM PAPR QPSK RLS SC SCCP Additive White Gaussian Noise Adaptive Frequency-Domain Channe Estimation Approximate Linear Estimation Auto-regressive Across Tone Channe Refinement Bit Error Rate Binary PSK (2-PSK) Channe Estimation Channe Impuse Response Constant Moduus Agorithm Cycic Prefix Cycic Prefix Reconstruction Channe State Information Circuar White Gaussian Noise Decision Feedback Equaizer Digita Teevision Frequency-Domain Channe Estimation Frequency-Domain Equaization Frequency-Domain Least Mean Square Frequency-Domain Turbo Equaization Fast Fourier Transform Finite Impuse Response Interbock Interference InterCarrier Interference Iterative Frequency-Domain Equaization independent and identicay distributed InterSymbo Interference Least Mean Square Least Square Maximum a Posterior Match fiter Maximum Likeihood Minimum Mean Square Error Minimum Mean Square Error Decision Feedback Equaization Mean Squared Error Orthogona Frequency Division Mutipexing Peak-to-Average-Power Ratio Quaternary PSK (4-PSK) Recursive Least Squares Singe Carrier Singe Carrier Cycic Prefix 18
SC-FDE SC-TDE SDD-CE SDD-TDCE SDD-FDCE SER SISO SNR TE TCVSB VSB WSSUS ZF Singe Carrier Frequency-Domain Equaization Singe Carrier Time-Domain Equaization Soft-Decision-Directed Channe Estimation Soft-Decision-Directed Time-Domain Channe Estimation Soft-Decision-Directed Frequency-Domain Channe Estimation Symbo Error Rate Singe Input Singe Output Signa to Noise Ratio Turbo Equaization Treis Coded Vestigia Side-band Vestigia side-band Wide-Sense-Stationary uncorreated scattering Zero-Forcing 19
CHAPTER 2 FREQUENCY-DOMAIN EQUALIZATION OF MODERATELY FAST FADING FREQUENCY-SELECTIVE CHANNELS 2.1 Introduction Broadband wireess access systems offering high data-rates are ikey to face severe mutipath fading, incuding channe deay spreads spanning tens or hundreds of symbo intervas. Whie orthogona frequency division mutipexing (OFDM) is a popuar means of combating these mutipath effects, its drawbacks incude high PAPR and high sensitivity to carrier-frequency offset (CFO). Singe carrier (SC) transmission with FDE presents an aternative to OFDM that retains robustness to channe deay spread without the disadvantages of high peak-to-average power ratio (PAPR) and CFO-sensitivity [1]. When FDE is accompished via turbo equaization (TE) [23, 27], an iterative reception scheme whereby the equaizer and decoder iterativey exchange soft information to jointy expoit channe structure and code structure, significant performance gains resut with ony modest increase in demoduator compexity [28, 29, 62]. Hence, the focus of this chapter is SC transmission with turbo FDE. 20
When targeting practica impementation, accurate and efficient channe estimation (CE) is critica. For OFDM systems, various frequency-domain channe estimation (FDCE) schemes have been proposed to track and predict either sow-fading or fast-fading wireess channes, with or without piot symbos, and with or without knowedge of channe statistics [39,46,47]. For SC systems, time-domain channe estimation is the typica approach [30,36,49], though a few piot-aided FDCE schemes have been proposed [50 52]. With the decision-directed time-domain schemes, it has been observed that performance improvements resut from the use of soft decoder outputs in pace of hard symbo estimates [36,49]. In this chapter, we propose a new joint channe-estimation/equaization scheme for the reception of SC transmissions over wireess channes with moderatey fast fading and ong deay spread. First, an improved iterative FDE (IFDE) agorithm is presented based on a frequency-domain TE idea. Second, soft-decision-directed channe estimation (SDD-CE) is studied both in time and frequency domain. Though the time-domain approach is optima in minimizing the MSE, its heavy computationa compexity prohibit practica appications. Therefore, we focus on frequency-domain approach, where a new adaptive FDCE (AFDCE) agorithm based on soft-input Kaman fitering and across-tone noise reduction is proposed to track and predict the channe in each frequency bin. Our AFDCE agorithm aso expoits the tempora correation between successive bocks and adaptivey updates the channe s autoregressive (AR) mode coefficients in case the channe statistics are unknown. Finay, a bock-overapping scheme is adopted to faciitate the joint operation of IFDE and AFDCE. Our approach differs from reated work in the foowing ways. 21
1. Existing 1 IFDE agorithms [28,29] are derived in the time domain and approximatey transated to the frequency domain using the cycic property of the equaizer. In contrast, our IFDE agorithm is derived in the frequency domain directy. 2. Existing soft-input CE agorithms [36, 49] work in the time domain. We focus on soft-input frequency-domain CE, hoping for ow-compexity operation in the case of ong channe deay spread. 3. Existing FDCEs [39, 46, 52] are piot-aided in nature, even though practica piots may be sparse. To better track time-varying channes, we consider (soft) decision-directed CE. The chapter is organized as foows. Section 2.2 briefy introduces the communication system mode. Section 2.3 summarizes the receiver architecture and section 2.4 describes the CPR procedure. IFDE and SDD-CE are detaied in sections 2.5 and section 2.6, respectivey. Section 2.7 discusses impementation issues, and section 2.8 presents numerica resuts. Finay, section 2.9 concudes. 2.2 System Mode Consider coded singe-carrier transmission where a bit stream {b m } is coded and mapped to symbos {s n } in a finite aphabet S and transmitted over a noisy inear time-varying mutipath wireess channe. For simpicity, we assume {s n } to be uncorreated. The compex-baseband channe can be described by the time-varying ength-n h impuse response {h n, } N h 1 =0, where h n, denotes the time-n response to an 1 The IFDE we proposed in [62], appropriate for vestigia side-band (VSB) moduation, is a specia case of the IFDE described here. 22
impuse appied at time n. The compex-vaued observations {r n } are then given by r n = N h 1 =0 h n, s n + u n, (2.1) where {u n } is zero-mean circuar white Gaussian noise with variance σw 2. Note that (2.1) describes SC transmission without cycic prefix (CP). To impement IFDE and AFDCE jointy, we wi eventuay use overapped bockprocessing with bock ength N and bock shift interva N d. (A detaied discussion is postponed unti section 2.7.) Furthermore, we assume channe variation is sow enough to be modeed as time-invariant within a bock. Thus, in terms of the bockbased quantities r n (i) = r ind +n, s n (i) = s ind +n, u n (i) = u ind +n, and h (i) = h ind + N 2,, the signa received during the ith bock can be expressed as u n (i) + n =0 h (i)s n (i) + N h 1 =n+1 h (i)s <n >N (i 1), 0 n < N h 1, N r n (i) = h 1 u n (i) + h (i)s n (i), N h 1 n < N. =0 (2.2) Note that {r n (i)} N h 2 n=0 contain inter-bock interference (IBI), i.e., symbo contributions from the previous bock. In the seque, we wi make extensive use of the N- dimensiona vectors r(i) := [r 0 (i),...,r N 1 (i)] T, s(i) := [s 0 (i),...,s N 1 (i)] T, u(i) := [u 0 (i),...,u N 1 (i)] T, and h(i) := [h 0 (i),...,h Nh 1(i), 0,, 0] T. 2.3 Receiver Structure The proposed receiver is iustrated in Fig. 2.1 and the corresponding processing steps are described beow (for the ith bock). Since steps 1-5 can be repeated severa times for the same bock, a superscript j is used to denote the iteration index. 23
r(i) y (j) (i) x (j) (i) p (j) (ŝ n (i) s n (i)) ˆb(i) IBI Canceation FFT Equaizer MAP CP Restoration Decoder s (j) (i) ĝ(i + 1) s (j) (i), v (j) s (i) Channe Estimator Priori Info. Generator p (j) ext(s n (i)) Figure 2.1: Receiver structure. 1. Perform IBI-canceation and CP-reconstruction (CPR) on r(i) using the methods of [67,68]. 2. With the aid of FFTs, perform frequency-domain MMSE equaization assuming symbo means and variances obtained through the previous round of decoding. From the time-domain symbo estimates ŝ(i), extract the conditiona probabiities { p (j) (ŝ n (i) s n (i) = s), s S } N 1 n=0 for ater use in decoding. 3. Perform maximum a posteriori (MAP) decoding, and update the extrinsic a priori distribution p (j) ext(s n (i)). 4. Using p (j) ext(s n (i)), generate symbo means s (j) (i) and variances v (j) s (i) to be used as priors in the next round of equaization. 5. Use s (j) (i) and v (j) s (i) to smooth current channe estimates and predict the channe for the next bock. For step 3, we assume that the LOGMAP agorithm [69] is used for MAP decoding and that the standard procedure is used to generate the a priori distribution (see, e.g., [27, 62]). In the foowing three sections, we describe the IBI canceation and 24
CPR (step 1), IFDE agorithm (Steps 2 and 4) and the AFDCE agorithm (Step 5) in detai. 2.4 Cycic Prefix Reconstruction Usuay, for OFDM or SC-FDE systems, a CP is added to the beginning of each transmission bock to prohibit IBI as we as transform the inear convoution between channe and transmitted data bock into a circuar convoution, thus simpify channe equaization task. The CP is a repetition of the ast data symbos in a bock and for sufficient IBI canceation, the ength of CP shoud be arger or equa to N h 1. When CP is not avaiabe, the received signa is contaminated by IBI as shown in (2.2). In order to recover the contaminated sampes, two steps, caed IBI-canceation and CPR must be taken [67, 68]. We adopted the IBI-canceation and CPR agorithm proposed in [68] in our system, and here we briefy describe it for competeness of the dissertation. An iterative IBI-canceation and CPR is impemented jointy with IFDE. For the first iteration where j = 1, the IBI-canceation and CPR is performed as N h 1 N h 1 y n (1) (i) = r n (i) h (i)ŝ <n >N (i 1) + h (i)ŝ (0) <n > N (i), 0 n < N h 1. =n+1 =n+1 r n (i) N h 1 n < N (2.3) where {ŝ n (i 1)} are the fina estimates of previous-bock symbos, and {ŝ (0) <n > N (i)} can be ineary estimated from {y (0) n (i)}, which is obtained from a inear combination between r(i) and r(i + 1) as: 25