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A Study of Channel Estimation for OFDM Systems and System Capacity for MIMO-OFDM Systems
Abstract of thesis entitled “A Study of Channel Estimation for OFDM Systems and System Capacity for MIMO-OFDM Systems” Submitted by Zhou Wen For the degree of Doctor of Philosophy at the university of Hong Kong in July 2010 This thesis concerns about two issues for the next generation of wireless communications, namely, the channel estimation for orthogonal frequency-division multiplexing (OFDM) systems and the multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) system capacity For channel estimation for OFDM systems over quasi-static fading channels having resolvable mulitipath number L, a novel fast linear minimum mean square error (LMMSE) channel estimation method is proposed and investigated The proposed algorithm deploys Fourier transform (FFT) and the computational complexity is therefore significantly reduced to O(Nplog2(Np)), as compared to that of O(Np3) for the conventional LMMSE method, where the notation O(·) is the Bachmann–Landau function and Np is the number of pilots for an OFDM symbol The normalized mean square errors (NMSE) are derived in closed-form expressions Numerical results show that the NMSE is marginally the same with that of the conventional LMMSE for signal to noise ratio (SNR) ranges from dB to 25 dB For channel estimation for OFDM systems over fast fading and dispersive channels, a novel channel estimation and data detection method is proposed to reduce the inter-carrier interference (ICI) A new pilot pattern composed of the comb-type and the grouped pilot pattern is proposed A closed-form expression for channel estimation mean square error (MSE) has been derived For SNR = 15 dB, normalized Doppler shift of 0.06, and L = 6, both computer simulation and numerical results have consistently shown that the ICI is reduced by 70.6% and 43.2%, respectively for channel estimation MSE and bit error rate (BER) The pilot number per OFDM symbol is also reduced significantly by 92.3%, as compared to the comb-type pilot pattern A closed-form mathematic expression has been proposed for the capacity of the closed-loop MIMO-OFDM systems with imperfect feedback channel The lower threshold of feedback SNR is derived For L = 6, numerical results show that the lower threshold of feedback SNR is proportional to antenna numbers N′ and system SNR The increasing rate of the feedback SNR threshold increases from 0.82 to 1.01 when N′ increases from to 16 The variance and mean of OFDM system capacity over Rayleigh channels and Ricean channels have been respectively investigated that the closed-form expression for the capacity variance has been proposed The resultant system capacity variances over the two channels are respectively evaluated by numerical method and also verified by computer simulation The joint probability density function (PDF) of two arbitrary correlated Ricean random variables has also been derived in an integral form Numerical results reveal that the variance of OFDM system is proportional to SNR and inversely proportional to L for the two channels respectively For the same two respective channels, the variance marginally increases with a linear rate of 0.166 bit2/dB and 0.125 bit2/dB, when L = and SNR ranges from dB to 15 dB The variance is reduced from 1.75 bit2 to 1.30 bit2 and from 1.48 bit2 to 1.26 bit2, when SNR = 10 dB and L ranges from to (Total words: 495) A Study of Channel Estimation for OFDM Systems and System Capacity for MIMO-OFDM Systems by Zhou Wen B Eng., M Eng., USTC, P R China A thesis submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy at the university of Hong Kong in July 2010 Declaration I declare that this thesis represents my own work, except where due acknowledgement is made, and that it has not been previously included in a thesis, dissertation or report submitted t to this University or any other institution for a degree, diploma, or other qualifications Signature: _ Zhou Wen i Acknowledgements I would like to take this opportunity to express my gratitude to all the people who have ever helped me in the thesis writing and the course of the research My sincere and hearty thanks and appreciations go firstly to my supervisor, Dr W.H Lam, whose suggestions and encouragement have given me much insight into the research work It has been a great privilege and joy to study under his guidance and supervision His insightful observation and effective feedback inspired me during the research Furthermore, it is my honor to benefit from his personality and diligence, which I will treasure my whole life I also gratefully acknowledge Prof V.O.K Li, Prof G.L Li, Prof Y.C Wu, Prof S.C Chan, Prof T.S Ng and Prof Agnes S.L Lam for their interesting courses and helpful discussions I would like to thank the office staff and technical staff from the EEE department for their helpful administrative and facility supports Especially, Ms Julie Hung’s readiness to help students is very impressive I also appreciate the HKSAR government for the studentship support to the study in the University of Hong Kong I am extremely grateful to all my friends and classmates who have kindly provided me assistance and companionship in the process of preparing this thesis: Dr Zhi Zhang, Dr Zhiqiang Chen, Dr Mingxiang Xiao, Dr Fei Mai, Mr Xueyong Liu, Mr Xiaoguang Dai, Ms Ziyun Shao, Mr Ka-Chung Leung, Mr Peng Zhang, Dr Yanhui Geng, Ms Qiong Sun, Mr Haoling Xiahou, Mr Zhibo Ni, Mr Jun Zhang, Mr Xiaolei Sun, Mr Chengwen Xing They have made the life during the past four years an enjoyable and memorable experience Finally, I wish to express my hearty gratitude to my parents, for their encouragements and love in all my endeavors ii Contents Declarations i Acknowledgements ii Contents iii List of Figures vii Chapter 1: Introduction 1.1 Research motivation 1.2 Organization and contributions of the thesis Chapter 2: OFDM systems and MIMO systems 2.1 Wireless Channel 10 2.1.1 Large scale propagation 11 2.1.2 Small scale propagation 13 2.1.3 Typical wireless channel models 17 2.2 OFDM systems 20 2.2.1 Basic principles and characteristics for OFDM systems 21 2.2.2 Peak-to-Average (PAR) of OFDM systems 30 2.2.3 Channel estimation for OFDM systems 33 2.2.4 Synchronization of OFDM systems 38 2.2.5 Advantages and disadvantages of OFDM systems 39 2.3 MIMO systems 40 2.3.1 Basic MIMO system model 40 2.3.2 Functions of MIMO systems 42 2.3.3 Overview of Space Time codes 45 2.3.4 Capacity of MIMO systems 52 iii 2.4 MIMO-OFDM systems 54 2.5 Summary 56 Chapter 3: Channel estimation for OFDM systems over quasi-static fading channels 57 3.1 Introduction 58 3.2 System Model 61 3.3 The Proposed Fast LMMSE Algorithm 63 3.3.1 Properties of the channel correlation matrix in frequency domain 63 3.3.2 The proposed fast LMMSE channel estimation algorithm 65 3.3.3 Computational complexity comparison between the proposed method and the conventional LMMSE method 69 3.4 Analysis of the Mean Square Error (MSE) of the Proposed Fast LMMSE Algorithm 70 3.4.1 MSE analysis of the conventional LMMSE algorithm 71 3.4.2 MSE analysis for the proposed fast LMMSE algorithm 72 3.5 Numerical and Simulation Results 75 3.6 Conclusion 81 Chapter 4: Channel estimation and data detection for OFDM systems over fast fading channels 87 4.1 Introduction 88 4.2 System Model 91 4.3 The Proposed Channel Estimation and Data Detection 92 4.3.1 The proposed pilot pattern 92 iv 4.3.2 Channel Estimation and data detection for the first M1 OFDM symbols of each block 94 4.3.3 Channel estimation and data detection for the last M2 OFDM symbols of each block 95 4.3.4 Summary of the proposed channel estimation and data detection 98 4.4 Analysis of MSE of the proposed channel estimation method 99 4.4.1 MSE analysis of channel estimation for the first M1 OFDM symbols 100 4.4.2 MSE analysis of channel estimation for the last M2 OFDM symbols 103 4.4.3 MSE analysis of channel estimation for one OFDM block 105 4.5 Numerical and Simulation Results 106 4.6 Conclusion 112 Chapter 5: MIMO-OFDM system capacity with imperfect feedback channel 118 5.1 The open-loop and closed-loop capacity for MIMO Systems 119 5.1.1 MIMO system model 119 5.1.2 MIMO system capacity 120 5.1.3 Numerical Results and discussion 124 5.2 The closed-loop capacity with imperfect feedback channel for MIMO-OFDM systems 127 5.2.1 System Model 128 5.2.2 Closed-Loop Capacity and Feedback SNR for MIMO-OFDM Systems 130 5.2.3 Numerical Results 136 5.3 Summary 142 Chapter 6: Capacity of OFDM systems over time and frequency selective fading v channels 144 6.1 Introduction 145 6.2 OFDM System Model 147 6.3 OFDM System Capacity 148 6.3.1 OFDM system capacity over Rayleigh fading channels 148 6.3.2 OFDM system capacity over Ricean fading channels 153 6.4 Numerical and Simulation Results 157 6.5 Conclusion 161 Chapter 7: Conclusions and future works 167 7.1 Conclusions 167 7.2 Future works 169 APPENDIX A: The derivation of the rank of channel frequency autocorrelation matrix RHH in Chapter 170 APPENDIX B: The derivation of equation (3-20) in Chapter 171 APPENDIX C: The derivation of the joint PDF of two arbitrary correlated Ricean random variables 173 Appendix D: List of Abbreviations 176 REFERENCES 179 Publications 191 vi KL Karhunen-Loeve LMMSE linear minimum mean square error LOS line of sight signal LS least square LST Layered Space Time LSTC Layered Space Time Code LTE 3GPP Long Term Evolution MIMO multiple-input multiple-output MIMO-OFDM multiple-input multiple-output orthogonal division multiplexing MISO multiple input single output ML maximum likelihood MMSE minimum mean square error MST most significant taps NLOS non line of sight NMSE normalized mean square errors OFDM Orthogonal Frequency Division Multiplexing OFDMA Orthogonal Frequency Division Multiple Access PSD power spectrum density RV random variable SIC successive interference cancellation 177 frequency SINR signal to interference and noise ratio SNR signal to noise 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pages, 2009 [2] W Zhou and W H Lam, “Channel Estimation and Data Detection for OFDM systems over Fast Fading and Dispersive Channels ” , IEEE Transactions on Vehicular Technology, vol 59, no 3, pp 1381-1392, 2010 [3] W Zhou, X Y Liu, and W H Lam, “Capacity of OFDM systems over time and frequency selective fading channels”, submitted to IEEE Transactions on Vehicular Technology [4] W Zhou, W H Lam, “MIMO-OFDM system Capacity with imperfect feedback channel”, submitted to IET Communications Conference papers: [1] W Zhou and W H Lam, “A novel method of Doppler shift estimation for OFDM systems”, IEEE Military Communication Conference (MILCOM 2008), pp 1-7, San Deigo, USA, November 2008 [2] W Zhou and W H Lam, “Channel Estimation and Data Detection for OFDM systems over Fast Fading Channels”, IEEE International Symposium on Personal, Indoor and Mobile Communications (PIMRC 2009), pp 3109-3113, Tokyo, Japan, September 2009 191 ... that is system capacity In Chapter 5, the MIMO -OFDM system capacity with imperfect feedback channel is investigated In Chapter 6, the capacity variances for OFDM systems over Rayleigh and Ricean... 6) Chapter 2: OFDM systems and MIMO systems Since the thesis studies the channel estimation for OFDM systems and system capacity for MIMO -OFDM systems, this chapter briefly introduces the background... for OFDM systems 21 2.2.2 Peak-to-Average (PAR) of OFDM systems 30 2.2.3 Channel estimation for OFDM systems 33 2.2.4 Synchronization of OFDM systems 38 2.2.5 Advantages