Performance Analysis of Transceiver Impairments in OFDM Systems

針對正交分頻多工(orthogonal frequency division multiplexing, OFDM) 系統中的頻率偏移，本論文首先根據週期性的訓練訊號，提出一種延伸的最佳線性非偏移估計子(extended best linear unbiased estimator, EBLUE)。該延伸的最佳線性非偏移估計子不僅具有一般性的架構，也具有彈性，使其適用於不同的複雜度限制，易於以軟/硬體實現。本論文亦提供了該延伸的最佳線性非偏移估計子的效能分析及設計策略，以實現效能與複雜度間的最加權衡。此外，本論文也提供了該延伸的最佳線性非偏移估計子的效能分析及權重的封閉型解，提高了該延伸的最佳線性非偏移估計子的實用價值。 另一方面，本論文將非時變最大似然通道估計子(time-invariant maximum likelihood channel estimator, TI-MLCE)延伸至時變通道，並以具有一般性的設定來分析該非時變最大似然通道估計子，使分析的結果可應用於各種特例。 電腦模擬則用來驗證分析結果的正確性以及與其他方法相比較，比較結果證明本論文所提供的方法具有較佳的效能、較低的複雜度及較少的設計參數，易於以軟/硬體實現。 由於傳收機減損(包含有頻率偏移、相位雜訊及雙選擇性通道)會產生載波間干擾(inter-carrier interference, ICI)，傳收機減損成為決定正交分頻多工系統效能的重要因素。這些傳收機減損已為研究學者所熟知，並個別地被研究及探討。 然而，這些傳收機減損通常同時出現，從接收機設計及系統評估的角度來看，應該同時被考量。因此，本論文將同時分析這些傳收機減損，分析的結果可退化成僅考慮任一種傳收機減損組合的特例。根據分析的結果，本論文提出一種以區段接區段時域內插(segment-by-segment time-domain interpolation, STI)做為輔助的改善方法，該區段接區段時域內插具有一般性的架構，根據內插方法及系統需求，其權重可任意的被設定，故具有相當大的彈性。 最後，我們以較一般性的設定來推導訊號對干擾及雜訊比(signal-to-interference-plus-noise ratio, SINR)，並用其來評估接收機的效能。分析結果及模擬結果間的一致性驗證了分析的有效性，模擬結果也證實了所提出的接收機的效能遠優於僅使用非時變最大似然通道估計子的接收機的效能。The thesis presents an extended best linear unbiased estimator (EBLUE) based on a periodic training sequence, to estimate a frequency offset in orthogonal frequency division multiplexing (OFDM) systems. The structure of the EBLUE is general and flexible so that it adapts to different complexity constraints. The features of generality and flexibility are attractive for practical implementation. Performance analysis and design strategy of the EBLUE are provided to realize the best tradeoff between performance and complexity. Moreover, closed-form results of both weight and performance make the EBLUE even more attractive for practical implementation. Time-invariant maximum likelihood channel estimator (TI-MLCE) originally designed for time-invariant channels is extended to OFDM systems in time-varying channels. The analysis of the extended TI-MLCE is performed under a general setup, and results degenerate to special cases. Simulation is then used to verify the accuracy of analysis, and the performance of the extended TI-MLCE is compared with that of other proposals. It is demonstrated that the extended TI-MLCE has better performance, lower complexity and fewer design parameters. Thus, the extended TI-MLCE is practical for implementation. The effect of transceiver impairments (including frequency offset, phase noise and doubly-selective channel) is a key factor in determining the performance of an OFDM system. These impairments are well known and have been investigated separately in the past. However, these impairments usually arise concurrently and should be jointly considered from the perspectives of both receiver design and system evaluation. Impacts of these impairments on the OFDM system are jointly analyzed in the research, and the analysis result degenerates to the special cases where only a subset of the impairments is present. A mitigation method aided by segment-by-segment time-domain interpolation (STI) is then proposed following the analysis. The STI is general, and weights for realizing the STI can be specified according to the interpolation method and system requirements. Signal-to-interference-plus-noise ratio (SINR) is treated as a performance measure for evaluating the receiver using the TI-MLCE with the STI, and is derived under a general setting. Consistency between our analysis and simulations verifies the validity of our derivation. Significant improvement over the receiver using only the TI-MLCE is demonstrated in the simulation results.1 Introduction 1 1.1 Wireless Communications . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Bandwidth Efficiency of a Wireless Link . . . . . . . . . . . . . . . . . . 2 1.3 Receiver Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 Orthogonal Frequency Division Multiplexing . . . . . . . . . . . . . . . 3 1.5 Motivation of the Research . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.6 Overview of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Improved Frequency Offset Estimation in OFDM Systems Using Periodic Training Sequence 9 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Single-Distance Estimator and Its Performance . . . . . . . . . . . . . . 11 2.2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.2 Single-Distance Estimator . . . . . . . . . . . . . . . . . . . . . 12 2.2.3 Performance Analysis of SDE . . . . . . . . . . . . . . . . . . . 13 2.3 Enhanced Frequency Offset Estimator . . . . . . . . . . . . . . . . . . . 15 2.4 Design Strategy and Complexity . . . . . . . . . . . . . . . . . . . . . . 17 2.4.1 Design Strategy Under the Complexity Constraint . . . . . . . . . 17 2.4.2 Complexity Calculation . . . . . . . . . . . . . . . . . . . . . . 18 2.5 Numerical and Simulation Results . . . . . . . . . . . . . . . . . . . . . 19 2.5.1 Performance Comparison Under The Same Complexity . . . . . . 20 2.5.2 Performance Comparison Under The Same FFT Size . . . . . . . 20 2.5.3 Performance Comparison Under The Time-Varying Multipath Chan- nel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.6 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3 An Effective Channel Estimator for OFDM Systems in Time-Variant Chan- nels 31 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.3 Time-Invariant-Maximum Likelihood Channel Estimator . . . . . . . . . 33 3.3.1 TI-MLCE for Pilot-Based Transmission . . . . . . . . . . . . . . 33 3.3.2 Performance Analysis with Respect to havg . . . . . . . . . . . . 34 3.3.3 Performance Analysis with Respect to hn . . . . . . . . . . . . . 37 3.4 Segment-by-Segment Time-Domain Piece-Wise Linear Interpolation . . . 38 3.4.1 STI for Time-Variant Channels . . . . . . . . . . . . . . . . . . . 38 3.4.2 Performance Analysis of TI-MLCE with STI . . . . . . . . . . . 39 3.5 Analysis and Simulation Results . . . . . . . . . . . . . . . . . . . . . . 39 3.5.1 Analysis and Simulation Results of TI-MLCE . . . . . . . . . . . 40 3.5.2 Analysis and Simulation Results of TI-MLCE with STI . . . . . . 41 3.5.3 Comparison of Performance and Complexity . . . . . . . . . . . 43 3.6 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4 Unified Analysis of ICI-Cancelled OFDM Systems in Doubly-Selective Channels 47 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.2.1 Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.2.2 Frequency-Domain Signal Model . . . . . . . . . . . . . . . . . 51 4.3 Phase Noise Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.3.1 Stationary Phase Noise . . . . . . . . . . . . . . . . . . . . . . . 52 4.3.2 Wiener Phase Noise . . . . . . . . . . . . . . . . . . . . . . . . 53 4.4 Time-Invariant-Maximum Likelihood Channel Estimator . . . . . . . . . 53 4.4.1 TI-MLCE for Pilot-Based Transmission . . . . . . . . . . . . . . 53 4.4.2 Unified Analysis of Time-Domain Performance of TI-MLCE regarding cavg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.4.3 Unified Analysis of Frequency-Domain Performance of TI-MLCE regarding Cavg(k) . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.5 Estimation of Complete Impairments . . . . . . . . . . . . . . . . . . . . 60 4.5.1 Performance of TI-MLCE Regarding cn . . . . . . . . . . . . . . 60 4.5.2 Proposed Segment-by-Segment Time-Domain Interpolation . . . 61 4.5.3 Unified Analysis of Time-Domain Performance of STI . . . . . . 62 4.5.4 Unified Analysis of Frequency-Domain Performance of STI . . . 62 4.5.5 Implementation of STI . . . . . . . . . . . . . . . . . . . . . . . 64 4.6 Analysis and Simulation Results . . . . . . . . . . . . . . . . . . . . . . 64 4.6.1 Analysis and Simulation Results of TI-MLCE . . . . . . . . . . . 66 4.6.2 Analysis and Simulation Results of STI . . . . . . . . . . . . . . 67 4.7 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.8 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.8.1 Derivation of σ2t ,ipi . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.8.2 Derivation of σ2t ,idi . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.8.3 Derivation of σ2a vg(n) . . . . . . . . . . . . . . . . . . . . . . . . 75 4.8.4 Derivation of σ2t ,sti(mJ + s) . . . . . . . . . . . . . . . . . . . . . 76 5 SINR of ICI-Cancelled OFDM Systems in Doubly-Selective Channels 79 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.3 SINR Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.3.1 SINR with TI-MLCE Estimated CTI . . . . . . . . . . . . . . . . 81 5.3.2 SINR with STI Estimated CTI . . . . . . . . . . . . . . . . . . . 83 5.4 Analysis and Simulation Results of SINR . . . . . . . . . . . . . . . . . 85 5.5 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.6 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 6 Conclusion and FutureWorks 89 Bibliography 9