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

Correlatively Coded OFDM

A class of correlative codes is proposed to significantly improve the spectral performance of the rectangularly pulsed orthogonal frequency-division multiplexing (OFDM) signal with or without cyclic prefix or zero padding. It is analytically shown that the correlatively coded OFDM signal can achieve very high spectral efficiency while yielding an extremely small fractional out-of-band power

Correlatively Coded OFDM with Trellis Purging

在本篇論文中，我們將探討一新系統-分支消除相關性編碼正交分頻多工 (Correlatively Coded OFDM with Trellis Purging，簡稱 PCE-OFDM)系統之錯誤率與頻譜的效能。首先會說明相關性編碼正交分頻多工系統(Correlatively Coded OFDM，簡稱 CE-OFDM)編碼過程的籬笆 (Trellis)結構如何利用訊號標誌的集合分割（Signal label Set Partitioning）與消除分支的規則(Purging Rule)去得到所需的分支消除相關性編碼正交分頻多工系統的籬笆結構。接著利用籬笆結構所實現的編碼器，我們可以去探討分支消除相關性編碼正交分頻多工訊號的功率頻譜密度（Power Spectral Density）是否也擁有與相關性編碼正交分頻多工訊號一樣的快速衰減的邊葉。最後，經由模擬的方式探討未編碼、相關性編碼和分支消除相關性編碼正交分頻多工系統的錯誤率分別在可加成性高斯白雜訊通道與雙路徑衰減通道下的表現。In this thesis, we will discuss the error performance and power spectrum on the correlatively coded OFDM with trellis purging (PCE-OFDM). First, PCE-OFDM trellis assignment can be derived from correlatively coded OFDM (CE-OFDM ) trellis structure by using signal label set partitioning and purging rules. The power spectral density (PSD) of transmitted PCE-OFDM signal can then be analyzed after realizing the encoder for given PCE-OFDM trellis structure. Second, PCE-OFDM is shown to provide the same extremely small sidelobes as CE-OFDM. Eventually, we study the bit error rate (BER) characteristics among uncoded and CE-OFDM and PCE-OFDM on Additive white Gaussian noise (AWGN) and tow-ray fading channels.口試委員會審定書......................................................................................i 誌謝............................................................................................................ii 中文摘要.................................................................................................. iii 英文摘要...................................................................................................vi 第一章 緒論..........................................................................................1 第一節 相關性編碼正交分頻多工系統的介紹..................................1 第二節 動機..........................................................................................4 第二章 分支消除相關性編碼正交分頻多工系統.............................5 第一節 相關性編碼正交分頻多工系統訊號模型..............................5 第二節 分支消除相關性編碼正交分頻多工系統之由來................12 第三節 訊號標籤的集合分割方式....................................................17 第四節 消除分支的規則....................................................................20 第五節 兩組使用消除分支的例子....................................................25 第三章 分支消除相關性編碼正交分頻多工系統的實現方 式與頻譜探討........................................................................31 第一節 編碼器的實現........................................................................31 第二節 頻譜探討................................................................................37 第四章 分支消除相關性編碼正交分頻多工系統之效能擬...........43 第一節 高斯白雜訊通道下的模擬結果............................................43 第三節 雙路徑衰減通道下的模擬結果............................................45 第五章 結論............................................................................................58 參考文獻..................................................................................................6

Intercarrier Interference of Correlatively Coded OFDM

本篇論文所要探討的主題是相關性編碼正交分頻多工（Correlatively Coded Orthogonal Frequency Division Multiplexing，簡稱 CE-OFDM）訊號之次載波間的相互干擾（Inter-carrier Interference，簡稱 ICI）。首先，吾人先對 CE-OFDM 訊號帶有保護區間（Guard Interval）為循環字首（Cyclic Prefix）及全為零的傳輸資料（Zero Padding）分別建立所屬之 ICI 問題數學模型。其次，則使用所定義之兩個指標：平均載波干擾比（Average Carrier to Interference Ratio）及最小載波干擾比（Minimum Carrier to Interference Ratio）著眼於正規化頻率偏移量（Normalized Frequency Offset）的比值，個別衡量以上所述兩種訊號在接收端遭受頻率偏差所導致的 ICI 影響程度。接下來，吾人對CE-OFDM 訊號及未編碼之OFDM 訊號採用訊號共軛法（Data-Conjugate Method）消除因為頻率偏差所致之ICI。最後，吾人會組成訊號之參數對已編碼及未編碼之訊號做效能方面之比較。This thesis presents the investigation of inter-carrier interference (ICI) in correlatively coded orthogonal frequency-division multiplexing (OFDM) communication system. First of all, we establish the mathematical model of the ICI problem individually for CP-OFDM and ZP-OFDM, which are the correlatively coded OFDM signals with cyclic prefix and with zero padding, respectively. Then we will take the average and minimum carrier-to-interference radio (CIR) respect to normalized frequency offset as two major indicators when measuring the ICI problem. Secondly, the data-conjugate method of ICI self-cancellation is studied to reduce ICI effectively and the system performance of the data-conjugate method is compared with the normal OFDM. Finally, we will make a comparison between the systems which we have discussed above in different system parameters in the conclusion chapter.Contents Contents I List of Figures III List of Tables VI 1 Introduction 1 2 Introduction to CE-OFDM 4 2.1 CE-OFDM Signals [1] . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 PSD of CE-OFDM Signals [1] . . . . . . . . . . . . . . . . . . . . . 6 3 ICI of CE-OFDM 14 3.1 Introduction to ICI . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2 ICI Analysis of CE-CP-OFDM Signals . . . . . . . . . . . . . . . . 15 3.2.1 Analysis and Comparison of Average CIR . . . . . . . . . . 16 3.2.2 Analysis and Comparison of Minimum CIR . . . . . . . . . 23 3.3 ICI Analysis of CE-ZP-OFDM Signals . . . . . . . . . . . . . . . . 26 3.3.1 Analysis and Comparison of Average CIR . . . . . . . . . . 27 3.3.2 Analysis and Comparison of Minimum CIR . . . . . . . . . 30 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4 ICI of CE-OFDM with Data-Conjugate Method 35 4.1 Introduction to DCM [3] . . . . . . . . . . . . . . . . . . . . . . . . 36 4.2 ICI Analysis of CP-OFDM Signals with DCM . . . . . . . . . . . . 37 4.2.1 Analysis and Comparison of Average CIR . . . . . . . . . . 38 4.2.2 Analysis and Comparison of Minimum CIR . . . . . . . . . 45 4.3 ICI Analysis of ZP-OFDM Signals with DCM . . . . . . . . . . . . 48 4.3.1 Analysis and Comparison of Average CIR . . . . . . . . . . 49 4.3.2 Analysis and Comparison of Minimum CIR . . . . . . . . . 53 4.4 PSD of CE-OFDM signals with DCM . . . . . . . . . . . . . . . . . 55 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5 Conclusion 64 A 65 Bibliography 67 List of Figures 2.1 Block diagram of CE-OFDM system [1] . . . . . . . . . . . . . . . . 5 2.2 Illustration of CE-OFDM symbol with guard interval . . . . . . . . 6 2.3 Power spectral density of CE-CP-OFDM signals . . . . . . . . . . . 8 2.4 Power spectral density of CE-ZP-OFDM signals . . . . . . . . . . . 8 2.5 Equivalent lowpass PSD comparison between CE-CP-OFDM, CE- ZP-OFDM and Uncoded OFDM . . . . . . . . . . . . . . . . . . . . 9 2.6 illustration of two adjacent subcarriers of coded OFDM . . . . . . . 10 3.1 E®ect of frequency o®set . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Block diagram of the CE-OFDM system for ICI analysis . . . . . . 16 3.3 Average CIR comparison between Uncoded OFDM and CE-CP- OFDM (N = 64; Tg = T=8) . . . . . . . . . . . . . . . . . . . . . . . 20 3.4 Average CIR comparison between CE-CP-OFDM with di®erent N (L = 1; Tg = T=8) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.5 Average CIR comparison between Uncoded OFDM and CE-CP- OFDM (L = 1;N = 64) . . . . . . . . . . . . . . . . . . . . . . . . 22 3.6 Minimum CIR comparison between Uncoded OFDM and CE-CP- OFDM (N = 64; Tg = T=8) . . . . . . . . . . . . . . . . . . . . . . . 24 3.7 Minimum CIR comparison between CE-CP-OFDM with di®erent N (L = 1; Tg = T=8) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.8 Minimum CIR comparison between Uncoded OFDM and CE-CP- OFDM (L = 1;N = 64) . . . . . . . . . . . . . . . . . . . . . . . . 26 3.9 Average CIR comparison between Uncoded OFDM and CE-ZP- OFDM (N = 64) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.10 Average CIR comparison between CE-ZP-OFDM with di®erent N (L = 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.11 Minimum CIR comparison between Uncoded OFDM and CE-ZP- OFDM (N = 64) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.12 Minimum CIR comparison between CE-ZP-OFDM with di®erent N (L = 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.1 Block diagram of the OFDM system using the DCM. [3] . . . . . . 36 4.2 Block diagram of the CE-OFDM system using the DCM for ICI analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.3 Average CIR comparison between Uncoded OFDM and CE-CP- OFDM (N = 64; Tg = T=8; with DCM) . . . . . . . . . . . . . . . . 43 4.4 Average CIR comparison between CE-CP-OFDM with di®erent N (L = 1; Tg = T=8; with DCM) . . . . . . . . . . . . . . . . . . . . . 44 4.5 Average CIR comparison between Uncoded OFDM and CE-CP- OFDM (L = 1;N = 64; with DCM) . . . . . . . . . . . . . . . . . . 45 4.6 Minimum CIR comparison between Uncoded OFDM and CE-CP- OFDM (N = 64; Tg = T=8; with DCM) . . . . . . . . . . . . . . . . 46 4.7 Minimum CIR comparison between CE-CP-OFDM with di®erent N (L = 1; Tg = T=8; with DCM) . . . . . . . . . . . . . . . . . . . . . 47 4.8 Minimum CIR comparison between Uncoded OFDM and CE-CP- OFDM (L = 1;N = 64; with DCM) . . . . . . . . . . . . . . . . . . 48 4.9 Average CIR comparison between Uncoded OFDM and CE-ZP- OFDM (N = 64; with DCM) . . . . . . . . . . . . . . . . . . . . . 52 4.10 Average CIR comparison between CE-ZP-OFDM with di®erent N (L = 1; with DCM) . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.11 Minimum CIR comparison between Uncoded OFDM and CE-ZP- OFDM (N = 64; with DCM) . . . . . . . . . . . . . . . . . . . . . 54 4.12 Minimum CIR comparison between CE-ZP-OFDM with di®erent N (L = 1; with DCM) . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.13 Power spectral density of CE-CP-OFDM signals with DCM (L=1) . 57 4.14 Power spectral density of CE-CP-OFDM signals with DCM (L=2) . 57 4.15 Power spectral density of CE-CP-OFDM signals with DCM (L=3) . 58 4.16 Power spectral density of CE-ZP-OFDM signals with DCM (L=1) . 59 4.17 Power spectral density of CE-ZP-OFDM signals with DCM (L=2) . 60 4.18 Power spectral density of CE-ZP-OFDM signals with DCM (L=3) . 60 4.19 Fractional out-of-band power characteristics of CE-CP-OFDM with DCM and CE-ZP-OFDM with DCM (N=64, L=1) . . . . . . . . . 61 List of Tables 3.1 The correlation between system parameters and average or mini- mum CIR of CE-CP-OFDM . . . . . . . . . . . . . . . . . . . . . . 33 3.2 The correlation between system parameters and average or mini- mum CIR of CE-ZP-OFDM . . . . . . . . . . . . . . . . . . . . . . 34 4.1 The correlation between system parameters and average or mini- mum CIR of CE-CP-OFDM with DCM . . . . . . . . . . . . . . . . 62 4.2 The correlation between system parameters and average or mini- mum CIR of CE-ZP-OFDM with DCM . . . . . . . . . . . . . . . . 6

Methods for PAPR and Spectral Improvement of Correlatively Coded OFDM Systems

[[abstract]]相關性編碼夠改善正交分頻多工(OFDM)的頻譜效能。高峰均功率比(PAPR)值是OFDM中一個嚴重的缺點，然而，相關性編碼OFDM訊號PAPR值比起一般OFDM訊號還要高。 本論文提出了兩種降低相關性編碼OFDM訊號PAPR值的方法，第一種方法是將相關性編碼OFDM中的前置編碼矩陣利用奇異值分解，以重新組合構成一個新的前置編碼矩陣，由此達成同時改善頻頻譜效能與降低PAPR值。第二種方法，利用低自相關特性的振幅恆定零自相關(CAZAC)序列，將相關性編碼OFDM訊號的星座點擴展，以降低頻率訊號彼此的相關性，因而達到降低PAPR值的效果。 模擬的結果證明，第一種方法，改善頻譜效能的同時將PAPR值降低3dB。第二種方法，PAPR值比起一般的OFDM還要好，也不會導致頻譜效能降低。[[abstract]]A class of correlative codes is proposed to significantly improve the spectral performance of the rectangularly pulsed orthogonal frequency-division multiplexing (OFDM) signal High PAPR is one of the most serious drawbacks of OFDM However correlatively coded OFDM has much larger PAPR than general OFDM In this thesis proposed two method to reduce the PAPR in correlatively coded OFDM signals The first method it use singular value decomposition (SVD) precoding matrix of correlative codes OFDM and then recombine a new precoding matrix thus at the same time to improve the spectral performance and reduce PAPR value The second method it use the low autocorrelation characteristics of CAZAC sequence expands the correlatively coded OFDM signal constellation points and decreases relevance between the frequency symbols in order to reduce PAPR value of the correlative codes OFDM signal Simulation results show that the first method at the same time improve the spectral performance and reduction PAPR value 3dB The second method PAPR value is even better than the general OFDM and it not cause decrease spectral performanc

Precoding Techniques for Concurrently Improving PAPR and Spectrum Performance of OFDM Signals

[[abstract]]多重輸入/多重輸出正交多重載波(MIMO-OFDM)系統已經被視為提供多媒體、視訊、資料、語音、與高速網際網路接取等高品質服務 4G寬頻無線通訊與室內網路系統的主角。然而 OFDM 的主要缺點就是具有較高的峰均功率比值(PAPR)；當大量的同相位子載波加在一起時，OFDM 訊號就會造成很大的波封浮動，而具有很大波封浮動的 MIMO-正交多載波訊號會產生高峰均功率比 (PAPR)值。本研究專題將專注在對 OFDM 系統發展各種不同的前置編碼矩陣技術以及相關調整演算法來同時達成降減 OFDM訊號的 PAPR值以及改善 OFDM頻帶外圍功率頻譜密度的效能為目標。由於前置編碼技術具有控制區塊資料之間的相關性又不會破壞子載波之間正交性的優點，因此極適合依據不同的需求發展演算法來調整矩陣特性。對於計畫的執行，我們首先考量選擇相關編碼序列與固定振幅零自相關 (Constant Amplitude Zero Auto Correlation，CAZAC)序列兩種技術做為起點，相關編碼序列技術能夠改善 OFDM 訊號頻帶外圍的頻譜效能，但是造成訊號 PAPR值比一般 OFDM訊號的 PAPR值還要高。依據序列我們建構相對應的 OFDM 系統前置編碼矩陣，然後根據各種降減 OFDM 訊號PAPR 值的方法與理論分別發展最小-最大-調整演算法(Min-Max-Adaptation Algorithm)與組合演算法(Combined Algorithm)來修改前置編碼矩陣特性，使得前置編碼系統可以同時達到改善 OFDM訊號頻帶外圍的頻譜效能以及降減 PAPR值。 另一個方法是從既有的 OFDM訊號 PAPR值降減技術出發，降減 OFDM訊號 PAPR值的技術很多，主要可分為頻率領域技術與時間訊號技術兩類，頻率領域技術降減 PAPR 值是藉由增加反離散傅立葉轉換(Inverse Discrete Fourier Transform, IDFT)的輸入資料交相關性，降低 IDFT 輸出訊號的峰值，或是增加 IDFT 輸出訊號的平均值等。時間訊號技術降減 PAPR值是直接在訊號放大之前將它失真，降低發射機輸出訊號的峰值，或是藉由加入額外的訊號來增加訊號的平均值等等。基於我們的研究主題，我們選擇脈波整形訊號法、單式矩陣轉換法、與最佳前端濾波器與後端濾波器等三種方法，這些方法能有效率地區降低 OFDM 訊號的 PAPR 值但是會升高頻繁帶外圍的功率譜密度值。針對每種方法我們建立相對應的 OFDM 系統前置編碼矩陣，然後根據各種改善正交分頻多工訊號頻譜效能的理論來發展分解調整演算法(Decomposition-adaptation Algorithms)以修改 PAPR降減前置編碼矩陣特性，讓前置編碼系統可以同時達到 PAPR值降減以及頻帶外圍的功率譜密度改善的效能。。我們將撰寫 MATLAB 與 C/C++程式對本計畫案中的每種機制進行 Monte-Carlo 效能模擬，將分析模擬結果和其他方法所獲得的結果做比較。最後我們將對本研究的成果撰寫數篇學術論文發表，提供學界與業界參考，做為本計畫的總結。[[abstract]]The multi-input multi-output orthogonal frequency-division multiplexing (MIMO-OFDM) system is a potential candidate for 4G broadband wireless communication and indoor networks for high quality services in multimedia, video, data, voice, and high-speed internet access. However, one major drawback of OFDM is its high peak-to-average power ratio (PAPR). As a large number of subcarriers are added with the same phase, OFDM signals will have a large envelope fluctuation such that the MIMO-OFDM signals incur a large envelope fluctuation would have a high PAPR value. In this research project, we focus on the precoding techniques and related adaptation algorithms for concurrently improving out-of-band power spectral density and PAPR reduction performance of the OFDM signals. Since the precoding technique has the convenience advantage in controlling and adapting the correlation between the OFDM block samples without destroying the orthogonal property between the subcarriers, it was suitable for developing various algorithms to adjust the matrix for different requirements. To reach the goal, we first take the techniques like correlatively coded sequences and constant amplitude zero auto correlation sequences (CAZAC) for spectrum improvement of OFDM signals as the starting point. In generally, a correlative code sequence significantly improves the spectral performance of OFDM signals but results in much larger PAPR values than general OFDM signals. A procedure to construct the corresponding precoding matrix is developed. Then the Min-max-adaptation Algorithm and Combined Algorithm will be developed respectively for adjusting the precoding matrix for PAPR reduction and hence we obtain the precoding matrix able to simultaneously improve out-of-band spectrum and PAPR reduction performance of OFDM signals. On the other hand, we take the PAPR reduction techniques as the starting point. Many methods have been proposed to reduce the PAPR values. These techniques can be divided into two categories: frequency domain techniques and signal time domain techniques. Frequency domain techniques reduce PAPR by increasing the cross-correlation of the input data of the inverse discrete Fourier transform (IDFT), decreasing the peak values of output signal of IDFT, or increasing the average value of the output signals. Time domain techniques reduce PAPR directly by distorting the signal prior to amplification, decreasing the peak values of output signal of transmitter, or increasing the average power of the signals by adding extra signals. The methods of pulse shaping, unitary matrix transform, and optimum front-and-post-end filters for reducing the PAPR values of OFDM signals were selected for our purposes. The corresponding precoding matrix for each method is established. These methods can significantly reduce PAPR values of OFDM signals, however, accompanied by much higher out-of-band power spectral density. We then develop the Decomposition-adaptation Algorithms for adjusting the precoding matrix for PAPR reduction such that power spectral density and PAPR reduction performance of OFDM signals can be improved concurrently. Monte-Carlo simulations programmed in Matlab and C/C++ will be executed for various schemes proposed in this project. Simulations results will be analyzed and compared with those from other methods. Finally, the achievements obtained in this research will be presented in several articles as the conclusion of this research.[[note]]MOST103-2221-E327-01