正交分頻多工系統之低複雜度SLM及PTS峰值對平均功率比降低技術

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研究生：	古聖如 Ku, Sheng-Ju
論文名稱：	正交分頻多工系統之低複雜度SLM及PTS峰值對平均功率比降低技術 Low-Complexity SLM and PTS Schemes for PAPR Reduction in OFDM Systems
指導教授：	王晉良 Wang, Chin-Liang
口試委員:
學位類別：	博士 Doctor
系所名稱：	電機資訊學院 - 通訊工程研究所 Communications Engineering
論文出版年：	2009
畢業學年度：	97
語文別：	英文
論文頁數：	138
中文關鍵詞：	正交分頻多工、峰值對平均功率比、選擇映射方法、部分傳送續列方法、反快速傅立葉轉換、內插器
外文關鍵詞：	OFDM ( orthogonal frequency division multiplexing), PAPR (peak-to-average power ratio), SLM (selected mapping), PTS (partial transmit sequences), IFFT (inverse fast Fourier transform), interpolator
相關次數：	點閱：3 下載：0
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正交分頻多工(OFDM，orthogonal frequency division multiplexing)技術擁有高頻譜效能以及抵抗因多路徑所造成的衰減效應等特性，因此被廣泛的應用在許多高速的資料傳輸系統中。然而，OFDM系統具有高峰值對平均功率比(PAPR， peak-to-average power ratio)等缺點。當具有高PAPR的OFDM信號通過非線性元件時，經常造成信號失真等現象。
SLM (selected mapping) 與PTS (partial transmit sequences) 是兩種有效降低OFDM系統之PAPR的技術。在SLM 方法中，輸入資料區塊(input data block)被乘上不同的相位旋轉向量(phase rotation vectors)，然後經由反快速傅立葉轉換(IFFT，inverse fast Fourier transform)產生不同的候選OFDM信號(candidate OFDM signals)，再從中選出PAPR最小者傳送出去。在PTS 方法中，以子區塊分割法(SPM， subblock partition method)將輸入資料區塊平均分成數個子區塊，然後將每個子區塊的IFFT值做最佳化的組合，產生一個低PAPR的OFDM信號並傳送出去。雖然上述兩種方法都有很好的PAPR降低效能，然而在IFFT運算及/或最佳化的過程中需要高的運算複雜度。在本論文中，我們將提出數個方法用來解決SLM與PTS方法中高運算複雜度的問題。
首先，我們提出數個低複雜度的轉換矩陣(CMs，conversion matrices)用來降低SLM方法中的IFFT運算複雜度。對一個具有N個子載波(subcarriers)並採用L倍過取樣(oversampling)的OFDM系統而言，我們所提出的以轉換矩陣為基礎(CM-based)的方法只需要3LN個複數加法，就能利用一個LN點的IFFT輸出產生另一個LN點的IFFT輸出(即候選信號)。與傳統的SLM方法相比較，所提出的CM-based方法能以較低的運算複雜度達到極接近的位元錯誤率(BER，bit-error-rate)，而在降低PAPR的效能上只有少許的下降。其次，我們提出一個新的演算法來簡化PTS技術中的最佳化過程。在提出的PTS方法中，先產生一評估函數(cost function)用來選擇每個候選信號上適當的取樣點(samples)。在最佳化過程中，這些被選取的取樣點將被用來計算每一個候選信號上的峰值功率(peak power)。此新的PTS方法能以較低的運算複雜度，達到與傳統PTS方法幾乎一樣的PAPR降低效能。
我們也證明PTS方法是SLM方法的一個特例，其中相位旋轉向量(phase rotation vectors)裡的元素排列形式將由所採用的SPM來決定。特別是當PTS方法使用插入式(interleaved) SPM時，所相對的相位旋轉向量裡的元素具有週期性，此時可用低複雜度的CM-based方法將PTS方法以SLM的形式來實現。而當PTS方法使用毗連式(adjacent) SPM時，每個子區塊中的零元素(zero elements)將被連續的排列著。藉由此特性，我們提出一個機制及IFFT的架構來避免因零元素所造成的瑣細運算(trivial computations)，藉此降低當PTS方法使用adjacent SPM時所需的複雜度。
在現有的降低PAPR的方法中，為了能準確地估測出連續時間(continuous- time) OFDM信號的PAPR值，常採用四倍過取樣技術來取得離散時間(discrete-time) OFDM信號。然而，四倍過取樣技術會增加運算量及硬體的複雜度，特別是那些需要大量IFFT單元的方法尤甚。為了解決此問題，我們提出一個有效的方法來估測OFDM信號的PAPR值。此法先從過取樣因素(oversampling factor)小於四的原始離散時間OFDM信號中找出功率大於門檻值(threshold)的取樣點。再利用內插器(interpolator)對這些被選取的取樣點，找出四倍過取樣OFDM信號的峰值功率(peak power)。我們亦推導出訂定內插濾波器(interpolation filter)長度的準則，以及訂定在搜尋時域信號時之功率門檻值的準則。與一般採用四倍過取樣技術的方法相比，我們所提出的方法只需大約一半的運算複雜度就能達到非常接近的PAPR估測效能。此法可成功的與SLM技術相結合以降低OFDM系統的PAPR。

Orthogonal frequency division multiplexing (OFDM) is an attractive technique for high-speed data transmission because it has high spectral efficiency and is robust against multipath fading. One main drawback of OFDM systems is the high peak-to-average power ratio (PAPR) at the transmitter’s output. When a high-PAPR OFDM signal passes through a nonlinear device, it may cause in-band distortion and undesired spectral spreading.
Selected mapping (SLM) and partial transmit sequence (PTS) schemes are two efficient techniques for reducing the PAPR of OFDM systems. In SLM, the input data block is multiplied by a set of pre-determined phase rotation factors and then passed through a bank of inverse fast Fourier transform (IFFT) units to generate candidate OFDM signals, where the one with the lowest PAPR is selected for transmission. In PTS, the input data block is partitioned into a number of disjoint subblocks using a subblock partition method (SPM), and then the IFFTs of all the subblocks are optimally combined to form a low-PAPR OFDM signal for transmission. Although these two approaches have good PAPR reduction performance, the IFFT computation and/or the optimization process may involve high computational complexity. In this dissertation, we present several methods to alleviate these problems.
We first develop a new set of low-complexity conversion matrices (CMs) to simplify the IFFT computation required for the SLM scheme. For an N-subcarrier OFDM system using L times oversampling, the proposed CM-based method uses an LN-point IFFT to generate other LN-point IFFTs (i.e., candidate signals) for the SLM scheme with only 3LN complex additions for each of them. As compared to the conventional SLM scheme, the proposed CM-based method achieves close bit-error-rate (BER) performance with much lower computational complexity but slightly worse PAPR reduction. We then develop a new algorithm to simplify the optimization process of the PTS technique. The proposed PTS scheme uses a cost function to select appropriate samples of each candidate signal for peak power calculation during the optimization process. It achieves almost the same PAPR reduction performance as the conventional PTS scheme, but has much lower computational complexity.
We also show that the PTS scheme is a kind of SLM in which the elements of each phase rotation vector are arranged in a pattern determined by the SPM used. Specifically, the elements in the corresponding phase rotation vector are periodic when the PTS scheme uses the interleaved SPM. In this case, the PTS scheme can be realized as SLM by using the proposed low-complexity CM-based method. For the PTS using the adjacent SPM, each subblock of data consists of successive zero elements. Based on this special feature, we develop a mechanism along with an IFFT architecture to avoid trivial computations caused by those zero elements, which can reduce the complexity of the PTS scheme using the adjacent SPM.
The existing PAPR reduction methods usually use four times oversampling for the discrete-time OFDM signal to approximate the PAPR of the continuous-time OFDM signal. However, the four times oversampling process increases the computational complexity, especially for those schemes with a large number of IFFT units. To overcome this problem, we propose an efficient method for PAPR estimation of OFDM signals. The proposed method uses an interpolator to find the peak of the four times oversampled OFDM signal around some searched samples of the original discrete-time OFDM signal using oversampling with a factor smaller than four. We also derive some criteria to determine the interpolation filter length and the threshold of sample power for the search process. As compared to the method with four times oversampling, the proposed scheme achieves close PAPR estimation performance with only about half of the computational complexity. It is verified that the proposed PAPR estimation method can successfully be combined with the SLM technique for PAPR reduction.

Abstract    i
Contents    iii
List of Figures    vii
List of Tables    xi
Chapter 1 OFDM Principles    1
1 Introduction    1
2 OFDM Basics    1
3 Operations of OFDM Systems    4
4 Outline of the Dissertation    4
Chapter 2 The Peak-to-Average Power Ratio Problem in OFDM Systems    9
1 Introduction    9
2 Definition of PAPR    9
3 Distribution of PAPR    10
4 Effect of Nonlinear Devices    11
4.1 Model of Nonlinear Devices    12
4.2 Out-of-Band Radiation    13
4.3 In-Band Distortion    14
5 Overview of PAPR Reduction Methods    14
6 Summary    16
Chapter 3 New Conversion Matrices for SLM-Based PAPR Reduction Schemes    23
1 Introduction    23
2 The Conventional SLM Technique    24
3 The SLM Methods Using Low-Complexity Conversion Matrices    26
4 Proposed Phase Rotation Vectors and Conversion Matrices for the IFFT Computation    27
5 Simulation Results    29
6 Summary    31
Chapter 4 A New Reduced-Complexity PTS Scheme    39
1 Introduction    39
2 The Conventional PTS Technique    40
3 Subblock Partition Methods for PTS    41
4 Existing Methods for the Complexity Reduction of PTS    42
4.1 Reducing the Number of Candidate Signals    42
4.2 Reducing the Number of Samples Used to Calculate the Peak Power    43
5 A New PTS Scheme    44
5.1 A New Criterion for the Peak Position Prediction in a Candidate Signal    44
5.2 Selection of the Threshold □T for      46
6 Computational Complexity of PTS Schemes    47
6.1 Probability Distribution of      47
6.2 Comparisons of Computational Complexity    49
7 Comparison of PAPR Reduction Performance    50
8 Summary    51
Chapter 5 Relation Between SLM and PTS Schemes    59
1 Background    59
1.1 The Conventional SLM Technique    59
1.2 The Conventional PTS Technique    60
2 Phase Rotation Vectors   of Different SPMs    61
3 Redundant Candidate Signals of the Interleaved SPM    63
4 Implementation of the PTS Scheme Using the Interleaved SPM    66
5 Comparison of Computational Complexity    68
6 Simulation Results    69
7 Summary    69
Chapter 6 Complexity Reduction of IFFT for PTS    77
1 Introduction    77
2 PTS Scheme by Using the Adjacent SPM    78
3 Examples for Subblocks Partitioned Using the Adjacent SPM    81
4 Implementation of IFFT for the PTS Scheme Using the Adjacent SPM    82
5 Computational Complexity Analysis    84
6 Summary    85
Chapter 7 Low-Complexity PAPR Estimation Schemes    93
1 Introduction    93
2 Background    94
2.1 PAPR Principles    94
2.2 Oversampling Techniques    96
3 Proposed PAPR Estimation Methods and the Modified SLM Schemes    97
3.1 Proposed “Search-and-Partial-Interpolation” (SPI) Scheme    97
3.2 The SPI Scheme Combined with the SLM Technique    100
4 Criteria for Determination of I and □    100
4.1 Determination of I1 and I2    100
4.2 Determination of □1 and □2    101
4.3 Simulation Results    102
5 Complexity Analysis    103
5.1 IFFT Computation    103
5.2 SPI-1 and SPI-2 Schemes    103
5.3 MSLM-1 and MSLM-2 Schemes    105
6 Comparisons of PAPR Reduction Performance    105
7 Summary    106
Chapter 8 Conclusions    113
Appendix A Proof of Theorem 3.1    117
Appendix B Derivation of Equation (4.12)    121
Appendix C Computational Complexity of IFFT    123
Bibliography    127
Publications List    137

                                

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