Spectrally efficient FDM communication signals and transceivers: design, mathematical modelling and system optimization

This thesis addresses theoretical, mathematical modelling and design issues of Spectrally Efficient FDM (SEFDM) systems. SEFDM systems propose bandwidth savings when compared to Orthogonal FDM (OFDM) systems by multiplexing multiple non-orthogonal overlapping carriers. Nevertheless, the deliberate collapse of orthogonality poses significant challenges on the SEFDM system in terms of performance and complexity, both issues are addressed in this work. This thesis first investigates the mathematical properties of the SEFDM system and reveals the links between the system conditioning and its main parameters through closed form formulas derived for the Intercarrier Interference (ICI) and the system generating matrices. A rigorous and efficient mathematical framework, to represent non-orthogonal signals using Inverse Discrete Fourier Transform (IDFT) blocks, is proposed. This is subsequently used to design simple SEFDM transmitters and to realize a new Matched Filter (MF) based demodulator using the Discrete Fourier Transforms (DFT), thereby substantially simplifying the transmitter and demodulator design and localizing complexity at detection stage with no premium at performance. Operation is confirmed through the derivation and numerical verification of optimal detectors in the form of Maximum Likelihood (ML) and Sphere Decoder (SD). Moreover, two new linear detectors that address the ill conditioning of the system are proposed: the first based on the Truncated Singular Value Decomposition (TSVD) and the second accounts for selected ICI terms and termed Selective Equalization (SelE). Numerical investigations show that both detectors substantially outperform existing linear detection techniques. Furthermore, the use of the Fixed Complexity Sphere Decoder (FSD) is proposed to further improve performance and avoid the variable complexity of the SD. Ultimately, a newly designed combined FSD-TSVD detector is proposed and shown to provide near optimal error performance for bandwidth savings of 20% with reduced and fixed complexity. The thesis also addresses some practical considerations of the SEFDM systems. In particular, mathematical and numerical investigations have shown that the SEFDM signal is prone to high Peak to Average Power Ratio (PAPR) that can lead to significant performance degradations. Investigations of PAPR control lead to the proposal of a new technique, termed SLiding Window (SLW), utilizing the SEFDM signal structure which shows superior efficacy in PAPR control over conventional techniques with lower complexity. The thesis also addresses the performance of the SEFDM system in multipath fading channels confirming favourable performance and practicability of implementation. In particular, a new Partial Channel Estimator (PCE) that provides better estimation accuracy is proposed. Furthermore, several low complexity linear and iterative joint channel equalizers and symbol detectors are investigated in fading channels conditions with the FSD-TSVD joint equalization and detection with PCE obtained channel estimate facilitating near optimum error performance, close to that of OFDM for bandwidth savings of 25%. Finally, investigations of the precoding of the SEFDM signal demonstrate a potential for complexity reduction and performance improvement. Overall, this thesis provides the theoretical basis from which practical designs are derived to pave the way to the first practical realization of SEFDM systems

Advanced Study on Spectrally Precoded OFDM and OFDMA

因可提供f−2L−2 速度衰減之頻譜旁波並具有頻譜緊密度，頻域預編碼式正交分頻多工及多重存取系統是有效率的方波成形正交分頻多重存取系統。已存的頻域預編碼是針對類比方波成形正交分頻多工以及多重存取系統設計，因為此系統有無限的頻寬，故無法於離散傅立葉架構系統中實現。因此，這些頻域預編碼需要修正才可以適用在離散傅立葉架構之正交分頻多工及多重存取系統。離散系統中，訊號波形是由離散傅立葉架構數位化合成並且提供相對應之類比多載波波形的具體化離散估測值。此外，藉由使用比1/Td更小的頻域間隔，同條路徑不同子載波間的正交性因此而破壞離但也導致一個比1/Td頻域間隔正交分頻多工波形更緊密的頻譜。這啟發了此篇報告來設計使用比1/Td頻域間隔更小的非正交分頻多工訊號。一個普遍性的條件和符合此條件的頻域預編碼因此被提出來保證過取樣離散傅立葉架構之正交與非正交分頻多工及多重存取系統的頻譜旁波擁有f−2L−2速度衰減。在理論上可以看出，這些適用於離散傅立葉架構的預編碼可以經由適當轉換適用於類比架構的預編碼而得到，並且提供相同的頻譜表現以及峰均值比特性。 相關性編碼在文獻中被使用於正交分頻多工系統以分別提供進一步的頻譜旁波抑制而產生非常緊密的頻譜或增強載波互相干擾自我消除而產生頻域不同步的強健對抗性。然而，這些良好的特性在相關性預編碼波型中通常會與峰均值比有所取捨。在此論文中，我們設計出新的相關性預編碼來大幅的降低峰均值比同時保留這些上述提到的良好信號特性。Abstract i Contents iii List of Figures vii List of Tables x Notations xi 1 Introduction 1 1.1 Review of Spectrally Precoded OFDM and OFDMA Systems . . . . . . . . . 1 1.2 Review of Nonorthogonal OFDM Systems . . . . . . . . . . . . . . . . . . . 3 1.3 Review of Correlatively Precoded OFDM Systems . . . . . . . . . . . . . . 5 1.4 Thesis Motivation, Overview, and Contributions . . . . . . . . . . . . . . . . 7 2 Spectrally Precoded DFT-based OFDM and OFDMAWith Oversampling 10 2.1 SP-OFDMA and SP-OFDM Signal Models . . . . . . . . . . . . . . . . . . 10 2.1.1 Analog Multicarrier Waveform Representation . . . . . . . . . . . . 12 2.1.2 Oversampled DFT-Based Waveform Representation . . . . . . . . . 14 2.2 Fast Sidelobe Decaying Constraint and Codes . . . . . . . . . . . . . . . . . 18 2.3 Spectral and PAPR Performance Results . . . . . . . . . . . . . . . . . . . . 22 iii 2.3.1 Spectral Performance of Oversampled DFT-based SP-OFDMA and SP-OFDM using Ganalog . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3.2 Spectral Performance of Oversampled DFT-based SP-OFDMA and SP-OFDM using Gdft . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.3.3 PAPR Performance Comparison Among DFT-based and AnalogMulticarrier IOFDMA Waveforms . . . . . . . . . . . . . . . . . . . . . 33 2.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3 Spectrally Precoded DFT-based Nonorthogonal OFDMWith Oversampling 38 3.1 SP-NOFDM Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.1.1 Analog Multicarrier Waveform Representation . . . . . . . . . . . . 39 3.1.2 Oversampled DFT-Based Waveform Representation . . . . . . . . . 41 3.2 Fast Sidelobe Decaying Constraint and Codes . . . . . . . . . . . . . . . . . 45 3.3 Spectral and PAPR Performance Results . . . . . . . . . . . . . . . . . . . . 49 3.3.1 Spectral Performance of Oversampled DFT-based SP-NOFDMusing Ganalog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.3.2 Spectral Performance of Oversampled DFT-based SP-NOFDMusing Gdft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.3.3 PAPR Performance Comparison Among DFT-based and AnalogMulticarrier NOFDM Waveforms . . . . . . . . . . . . . . . . . . . . . 52 3.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4 Correlatively Precoded OFDMWith Reduced PAPR 56 4.1 System Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.2 Correlative Precoder Design . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.2.1 A Form of Correlative Precoders With Low PAPR . . . . . . . . . . 60 iv 4.2.2 Reduced-PAPR Correlative Precoder Design for Spectral Sidelobe Suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.2.3 Reduced-PAPR Correlative Precoder Design for ICI Self-Cancellation 64 4.2.4 Correlative Precoder Design for Joint Sidelobe Suppression and ICI Self-Cancellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.2.5 Reduced-PAPR Correlative Precoder Design for Joint Sidelobe Suppression and ICI Self- Cancellation . . . . . . . . . . . . . . . . . . 67 4.3 Spectral, PAPR, and CIR Performance Results . . . . . . . . . . . . . . . . . 68 4.3.1 Reduced-PAPR Correlative Precoder Design for Spectral Sidelobe Suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.3.2 Reduced-PAPR Correlative Precoder Design for ICI Self-Cancellation 71 4.3.3 Correlative Precoder Design for Joint Sidelobe Suppression and ICI Self-Cancellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.3.4 Reduced-PAPR Correlative Precoder Design for Joint Sidelobe Suppression and ICI Self- Cancell ation . . . . . . . . . . . . . . . . . . 73 4.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5 Conclusion 77 Bibliography 79 Appendix A: Derivation of (2.9) 85 Appendix B: Derivation of (2.23) 87 Appendix C: Derivation of (2.26) and (2.27) 88 Appendix D: Derivation of (2.28) 90 v Appendix E: Derivations of (4.19) and (4.20) 92 Appendix F: Derivation of E[|y(l) n |4] 94 Appendix G: Derivations of (4.21) and (4.22) 95 Appendix H: Proof That X0 Has Column Rank 2L 96 List of Publications 9