Carrier Synchronization of OFDM Systems over Dispersive Multipath Fading Channels

近年來，網際網路上影像、語音及數據通訊的驚人成長及同樣快速拓展的行動電話服務證明了行動多媒體的高度期待性。全球各地正研發能創造全球資訊聚落的無線寬頻多媒體通訊系統。目前的通訊系統主要是為某項特定應用而設計，例如語音、行動電話或無線網路。下一代無線寬頻多媒體通訊系統除將整合數種功能應用外，也被期待能提供使用者超過50 Mbps的高速傳輸。想提供如此速率並且對無線通道干擾具足夠的強健性必須慎選適當的調變技術。目前最有希望的技術就是正交分頻多工，因其對多路徑衰減通道及脈衝雜訊具抵抗力。儘管它如此優越，仍有一項最嚴重弱點，即對於同步錯誤之敏感度，尤其由震盪器的不穩定性及都卜勒偏移所造成的頻率偏移和相位雜訊。此弱點很明顯地是實現正交分頻多工系統的主要障礙。因此，載波同步具有基本的重要性。為了達到快速並強健的同步，資料輔助方法一般比盲蔽方法具吸引力。因此，本論文的目標在研究發展有效且適合運作於分散性多路徑衰減通道的資料輔助載波同步演算法。 在本論文中，我們首先研究資料傳遞訊號的統計特性。將資料傳遞訊號塑模為高斯隨機程序，我們根據最大概似準則將循環前綴和領航訊號合併考慮以推導一系列頻率偏移估測器。同時，我們分析演算法的均方誤差並以模擬驗證，而複雜度簡化的議題也有所討論。接下來，我們專注於解析頻率選擇性慢速瑞雷衰減通道的頻率混淆。我們研究並提出時域和頻域的兩種方法，並且利用關於通道脈衝響應的事前統計資訊來消除通道選擇性對於估測性能的影響。我們所提出方法的特徵是僅需要一個前置導航訊號並且可以估測整個信號傳輸頻寬的頻率混淆偏移。與一般訊號偵測的直覺相異，我們發現越大的通道選擇性並不會對我們所提出演算法的估測性能造成衰減，相反地由於使通道統計特性更加顯著的緣故而造成效能增益，這個特性展現了我們所提出方法的優異性與實用性。 除此之外，我們研究溫納相位雜訊的統計特性並且推導由相位雜訊所造成之載波間干擾的二階統計量。我們使用這個統計量、領航訊號以及嘗試性決策，並且根據最大概似準則來發展一個共相位誤差估測器。透過模擬，我們發現這個估測方法較傳統的方法優異。接著，我們研究兩種穩態相位雜訊模型並且分別推導由這兩種相位雜訊所造成之載波間干擾的二階統計量。同樣地，我們利用這些統計量、領航訊號以及嘗試性決策，根據最大概似準則來發展一個共相位誤差估測器。這個估測方法除了相較於傳統做法可以得到效能增益外，當接收端的相位雜訊統計模型與實際情況有所偏差時，效能仍可強健地維持。 更進一步，我們考慮在正交分頻多重接取上行鏈路中的多重相位雜訊估測問題。透過推導一個統合的矩陣訊號模型，我們分別根據最小平方準則以及最大概似準則提出兩種相位雜訊估測演算法。數值結果顯示我們提出的演算法可以廣泛地應用到各種程度的相位雜訊並且實作出來。最後，本論文以未來研究方向及結論作結尾。In recent years, the spectacular growth of video, voice and data communication over the Internet and the equally rapid pervasion of mobile telephony justify the great expectations for mobile multimedia. Research and development are taking place all over the world to define the next generation wireless broadband multimedia communications system that may create the global information village. While present communications systems are primarily designed for one specific application, such as speech on mobile telephony or high-rate data in wireless local area network (WLAN), the next generation wireless broadband multimedia communications system will integrate various functions and applications, besides, it is expected to provide its users with high speed transmissions over 50 Mbps. Supporting such large data rates with sufficient robustness to radio channel impairments requires careful choosing of modulation technique. The most promising choice seems to be orthogonal frequency division multiplexing (OFDM) by its immunity to multipath fading and impulse noise [1]. Despite its superiority, the principal weakness of OFDM is its sensitivity to synchronization errors, especially carrier frequency offset and phase noise caused by oscillator instability and/or Doppler shifts. This vulnerability is obviously the main obstacle to the implementation of a practical OFDM communications system. Thus, the task of carrier synchronization is of fundamental importance. To enable fast and robust synchronization, data-aided approaches are in general more attractive than blind approaches. Consequently, the goal of this dissertation is to study and develop effective data-aided carrier synchronization algorithms suitable for operation in dispersive multipath environment. In this dissertation, we first investigate the statistical property of data-conveying OFDM signals. Treating the data signal as an Gaussian random process, we show that cyclic-prefix and pilot signals can be combined to yield a class of frequency offset estimators based on maximum likelihood criterion. The mean square error of the proposed estimators are analyzed to justify simulation. The issue of complexity reduction are also addressed. Next, we concentrate on the frequency ambiguity resolution over frequency selective slowly Rayleigh fading channels. Approaches in time and frequency domain are studied and proposed respectively. The prior information of the statistic of the channel impulse response is exploited to eliminate the effect of channel selectivity on the estimation performance. The distinguishing features of our proposed methods are that only one preamble is required and the range of carrier frequency offset which can be handled is the overall transmission spectrum. Different from the intuition in signal detection, we find that higher channel selectivity does not degrade the estimation performance of our proposed methods but improve it by making the statistical characteristics of the channel more remarkable which demonstrates the superiority and practicability of our proposed methods. In addition, the statistical property of Wiener phase noise is investigated and the second order statistics of the ICI introduced by phase noise is derived. This statistics are used to generate a common phase error estimator based on maximum likelihood criterion by using the pilot symbols and tentative decisions. The estimation scheme is shown to outperform conventional approaches as justified by simulations. To proceed, the statistical property of two stationary phase noise model is investigated and the second order statistics of the ICI introduced by phase noise are derived respectively. This statistics are used to generate a common phase error estimator based on maximum likelihood criterion by combining the pilot symbols and tentative decisions. The estimation scheme is shown to provide performance gain to the conventional approaches and is quite robust against possible model mismatch. Furthermore, the multiple phase noise estimation problem is considered in uplink OFDMA systems. By deriving the unified matrix-form signal models, two multiple phase noise estimation algorithms based on least-square and maximum likelihood criterion are proposed respectively. Numerical results demonstrate that the proposed algorithms has a wide range of applicable phase noise level and practically implemented. Finally, the directions of future researches and conclusions of this dissertation are provided.Contents Abstract i Contents iv List of Tables x List of Figures xi 1 Introduction 1 1.1 Orthogonal Frequency Division Multiplexing . . . . . . . . . . . . . . . . 1 1.1.1 History and Evolution . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Carrier Synchronization of OFDM Systems . . . . . . . . . . . . . . . . . 4 1.2.1 Carrier Frequency Offset . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.2 Carrier Phase Noise . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Topics to be Addressed in this Dissertation . . . . . . . . . . . . . . . . . 7 1.3.1 Data-Aided Maximum Likelihood Frequency Synchronization for OFDM Systems over AWGN Channel . . . . . . . . . . . . . . . . 7 1.3.2 Data-Aided Frequency Ambiguity Resolution for OFDM Systems by Channel Statistics over Frequency Selective Slowly Rayleigh Fading Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 iv 1.3.3 Estimation of Wiener Phase Noise by the Autocorrelation of the ICI Weighting Function in OFDM Systems . . . . . . . . . . . . . 8 1.3.4 Estimation of Stationary Phase Noise by the Autocorrelation of the ICI Weighting Function in OFDM Systems . . . . . . . . . . . 9 1.3.5 Multiuser Estimation of Wiener Phase Noise for Uplink OFDMA Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4 Organization of this Dissertation . . . . . . . . . . . . . . . . . . . . . . 10 2 Data-AidedMaximum Likelihood Frequency Synchronization for OFDM Systems over AWGN Channel 11 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Generalized Data-Aided OFDM Signal Model . . . . . . . . . . . . . . . 13 2.3 DA-ML Frequency Estimation: Integer Part . . . . . . . . . . . . . . . . 15 2.3.1 Stochastic Characteristics of r(k) . . . . . . . . . . . . . . . . . . 16 2.3.1.1 Conditional Complex Gaussian PDF of r(k) . . . . . . . 16 2.3.1.2 Conditional Joint Complex Gaussian PDF of the Cyclic Prefix Pair: r(k) and r(k + N) . . . . . . . . . . . . . . 17 2.3.2 Time Domain Approach with Cyclic Prefix . . . . . . . . . . . . . 19 2.3.3 Time Domain Approach without Cyclic Prefix . . . . . . . . . . . 20 2.3.4 Frequency Domain Approach . . . . . . . . . . . . . . . . . . . . 21 2.4 ML-DA Frequency Acquisition Using Preamble . . . . . . . . . . . . . . 22 2.4.1 Mixed Preamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4.2 Pure Preamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.4.3 Acquisition Range . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.5 ML-DA Fine Frequency Estimation . . . . . . . . . . . . . . . . . . . . . 25 2.5.1 Method of Linear Interpolation . . . . . . . . . . . . . . . . . . . 27 2.6 Mathematical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 v 2.6.1 Conditional Mean Square Error . . . . . . . . . . . . . . . . . . . 30 2.6.2 Probability Distribution of |ǫ,SNR(f) . . . . . . . . . . . . . . . . 31 2.6.3 The Indenpendency between |φ,η(ǫ0), |φ,η(ǫ1), · · · , |φ,η(ǫN−1) 32 2.6.4 A Compact Form of (η) . . . . . . . . . . . . . . . . . . . . . . 35 2.7 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.8 Issue About Complexity Reduction . . . . . . . . . . . . . . . . . . . . . 37 2.8.1 Direct Implementation . . . . . . . . . . . . . . . . . . . . . . . . 40 2.8.2 Decimation Based Approach . . . . . . . . . . . . . . . . . . . . . 42 2.8.3 Look-Up Table Based Approach . . . . . . . . . . . . . . . . . . . 43 2.8.4 FFT Based Approach . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.8.5 Overall Complexity: A Comparison . . . . . . . . . . . . . . . . . 46 2.9 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Appendix 2A Derivation of Cx2 49 Appendix 2B Derivation of (x − ˜μ2)H C−1 ˜x2 (x − ˜μ2) 52 Appendix 2C Derivation of l cp(ǫ) 53 Appendix 2D Derivation of l f (ǫ) 54 3 Data-Aided Frequency Ambiguity Resolution for OFDM Systems by Channel Statistics over Frequency Selective Slowly Rayleigh Fading Channels 55 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.2 Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.3 Maximum Likelihood Estimator . . . . . . . . . . . . . . . . . . . . . . . 59 3.3.1 Frequency Domain Approach . . . . . . . . . . . . . . . . . . . . 59 3.3.2 Time Domain Approach . . . . . . . . . . . . . . . . . . . . . . . 61 3.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 vi 3.4.1 Comparison of Optimum and Sub-optimum Approaches . . . . . . 64 3.4.2 Effects of the Employed Modulation Scheme . . . . . . . . . . . . 66 3.4.3 Effect of Different Channel Condition . . . . . . . . . . . . . . . . 67 3.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Appendix 3A Derivation of E[A(m,H)2] 68 4 Estimation of Wiener Phase Noise by the Autocorrelation of the ICI Weighting Function in OFDM Systems 71 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.2.1 Phase Noise Corrupted OFDM Signal Model . . . . . . . . . . . . 73 4.2.2 Phase Noise Model . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.3 The Autocorrelation Function of the ICI Weighting Function . . . . . . . 76 4.4 Pilot-Aided Decision-Directed CPE Estimation . . . . . . . . . . . . . . . 78 4.4.1 Statistical Characteristics of the Sufficient Statistics . . . . . . . . 78 4.4.1.1 The Mean of ICI . . . . . . . . . . . . . . . . . . . . . . 80 4.4.1.2 The Second Order Statistics of ICI . . . . . . . . . . . . 80 4.4.2 Maximum Likelihood CPE Estimator . . . . . . . . . . . . . . . . 84 4.5 Performance Analysis on the Effect of ICI . . . . . . . . . . . . . . . . . 85 4.6 Performance Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.7 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Appendix 4A Proof of Proposition 4.1 90 5 Estimation of Stationary Phase Noise by the Autocorrelation of the ICI Weighting Function in OFDM Systems 93 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.2 Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 vii 5.3 Phase Noise Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.4 Data-Aided Decision-Directed CPE Estimation . . . . . . . . . . . . . . 98 5.5 Statistical Characteristics of the Sufficient Statistics . . . . . . . . . . . . 99 5.5.0.1 The Mean of the ICI . . . . . . . . . . . . . . . . . . . . 100 5.5.0.2 The Second Order Statistics of the ICI . . . . . . . . . . 100 5.6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.7 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6 Multiuser Estimation ofWiener Phase Noise for Uplink OFDMA Com- munications 107 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.2 Signal Model for Uplink OFDMA Transmissions with Phase Noise . . . . 109 6.2.1 Basic Uplink OFDMA Signal Model . . . . . . . . . . . . . . . . . 109 6.2.2 Uplink OFDMA Signal Model in Matrix Form . . . . . . . . . . . 112 6.3 Phase Noise Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 6.4 Multiuser CPE Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 115 6.4.1 Pilot-Aided CPE Estimation: Least-Square Approach . . . . . . . 115 6.4.2 Pilot-Aided Decision-Directed CPE Estimation: Maximum Likelihood Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 6.4.2.1 Maximum Likelihood CPE Estimator . . . . . . . . . . . 116 6.4.2.2 Statistical Characteristics of the ICI . . . . . . . . . . . 117 6.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 6.5.1 System Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 118 6.5.2 The Effect of the Number of Active Users . . . . . . . . . . . . . 119 6.5.3 The Effect of the Number of Pilot Symbols . . . . . . . . . . . . . 119 6.5.4 The Effect of Phase Noise Level . . . . . . . . . . . . . . . . . . . 120 6.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 viii 7 Conclusions 124 7.1 Contributions of this Dissertation . . . . . . . . . . . . . . . . . . . . . . 124 7.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 i