FrFT-OFDM系統的低復雜度峰均功率比抑制技術研究

趙 越 王 騰 陶 然 時鵬飛 蔣政國

?

FrFT-OFDM系統的低復雜度峰均功率比抑制技術研究

趙 越 王 騰 陶 然 時鵬飛 蔣政國

(北京理工大學信息與電子學院 北京 100081)

針對基于分數階Fourier變換的OFDM系統(簡稱FrFT-OFDM系統)的高峰均功率比(PAPR)問題，該文提出一種低復雜度的峰均比抑制算法。通過對隨機相位序列采用周期延拓至FrFT-OFDM符號長度，相位因子加權后與子載波調制前的數據相乘的方式，實現對高峰均比的有效抑制。該算法只需要一次逆離散分數階Fourier變換(IDFrFT)，所有備選信號直接通過時域chirp圓周移位的加權和得到。仿真結果表明，當備選信號個數相同時，該算法與選擇映射(SeLecting Mapping, SLM)算法的PAPR抑制性能相當，比部分傳輸序列(Partial Transmit Sequence, PTS)算法具有更好的PAPR抑制性能，同時，該算法較SLM和PTS算法的運算量降低。

正文頻分復用；分數階Fourier變換；峰均功率比；低復雜度

1 引言

由于在時頻雙彌散信道中，OFDM系統中子載波間的正交性容易受到破壞，從而形成嚴重的子載波間干擾。為了克服這一問題，文獻[1]提出了FrFT- OFDM系統，并得出在快速時變信道中FrFT- OFDM系統比傳統OFDM系統具有更好的傳輸性能；同時，FrFT的計算復雜度和FFT相近，容易實現，所以FrFT-OFDM系統具有很大的應用價值。

然而，作為多載波傳輸系統，FrFT-OFDM系統同樣存在高峰均功率比問題，這一問題直接影響系統的運行成本和效率，是該技術不可忽視的問題之一。文獻[2]對FrFT-OFDM系統的PAPR分布進行了理論推導與仿真驗證，并得出隨著子載波個數的增加，FrFT-OFDM系統的PAPR分布和傳統OFDM系統的PAPR分布趨于一致，即對應不同階次的FrFT-OFDM系統的PAPR分布趨于一致。目前，FrFT-OFDM系統的峰均比抑制算法僅僅是將傳統OFDM系統的算法直接應用到該系統中，傳統OFDM系統的峰均比抑制算法有：限幅法[3]、選擇映射法(SLM)[4]、部分傳輸序列法(PTS)[5]、有效星座擴展法(ACE)[6,7]、壓縮擴展法[8,9]、子載波預留法[10]等。文獻[11]將傳統的SLM法和PTS法分別應用于FrFT-OFDM系統，系統的峰均比特性有了明顯改善，但是這兩種算法存在計算復雜度大的問題。雖然文獻[12]針對傳統OFDM系統中PTS算法運算量大的問題提出了CSPS(Cyclically Shifted Phase Sequences)和OCSPS(Optimised CSPS)算法，但是由于分數階Fourier變換chirp周期性[13]的存在，該算法并不能直接應用到FrFT-OFDM系統。

基于以上問題，本文對CSPS和OCSPS算法進行了改進，提出一種適用于FrFT-OFDM系統的低復雜度的峰均比抑制算法，該算法基于分數階隨機相位序列和分數階圓周卷積定理，有效降低了算法運算復雜度。

2 FrFT-OFDM系統模型

FrFT-OFDM系統模型如圖1所示。FrFT- OFDM系統用chirp基代替正弦基作為子載波基信號，系統利用IDFrFT和DFrFT進行子載波的調制和解調，子載波調制信號表示為(這里將幅度進行了歸一化)[14]

圖1 FrFT-OFDM系統原理圖

3 低復雜度的峰均功率比抑制算法

3.1 設計分數階隨機相位序列

將式(2)和式(3)代入到式(4)中，得到

3.2 低復雜度峰均比抑制算法

圖2 算法原理圖

根據上面的描述，現對算法的步驟總結如下：

3.3 運算復雜度對比分析

表1 SLM, PTS和本文算法的運算復雜度

表2 具體參數下3種算法的運算復雜度

4 仿真驗證

圖3 時3種算法的PAPR抑制效果

5 結束語

[1] Massimiliano M. A Multi-carrier system based on the fractional Fourier transform for time-frequency-selective channels[J]., 2001, 49(6): 1011-1020.

[2] Ju Y, Barkat B, and Attallah S. Analysis of peak-to-average power ratio of a multicarrier system based on the fractional Fourier transform[C]. 2004 9th IEEE Singapore International Conference on Communication System, Singapore, 2004: 165-168.

[3] Wang Yong-chao and Luo Zhi-quan.Optimized iterative clipping and filtering for PAPR reduction of OFDM signals[J]., 2011, 59(1): 33-37.

[4] Jeon Hyun-bae, No Jong-seon, and Shin Dong-joon. A low-complexity SLM scheme using additive mapping sequences for PAPR reduction of OFDM signals[J]., 2011, 57(4): 866-875.

[5] Ku Sheng-ju and Wang Chin-liang. A new side-information free PTS scheme for PAPR reduction in OFDM systems[C].2012 IEEE 8th International Conference on Wireless and Mobile Computing, Networking and Communications, Barcelona, 2012: 108-112.

[6] Niranjan M and Srikanth S. Adaptive active constellation extension for PAPR reduction in OFDM systems[C]. IEEE International Conference on Recent Trends in Information Technology, Chennai, Tamil Nadu, 2011: 1186-1189.

[7] Jeon Hyun-bae, No Jong-seon, and Shin Dong-joonA new PAPR reduction scheme using efficient peak cancellation for OFDM systems[J]., 2012, 58(4): 619-628.

[8] Wang Y, Wang L-H, Ge J-H,.. An efficient nonlinear companding transform for reducing PAPR of OFDM signals[J]., 2012, 58(4): 677-684.

[9] Wang Dong, Zou Nian-yu, Cui Gao-feng,.. Companding scheme for peak-to-average power ratio reduction in optical orthogonal frequency division multiplexing systems[J]., 2012, 19(6): 371-375.

[10] Park Kang-woo and Park In-cheol. Low-complexity tone reservation for PAPR reduction in OFDM communication systems[J]., 2012, 20(10): 1919-1923.

[11] Xie Dan, Yang Shou-yi, Qi Lin,.. PAPR reduction of FRFT-based MB-OFDM ultra wide band signals[C]. WiCOM’08, 4th International Conference on Wireless Communications, Networking and Mobile Computing, Dalian, 2008: 1-4.

[12] Lu G, Wu P, and Aronsson D. Peak-to-average power ratio reduction in OFDM using cyclically shifted phase sequences[J]., 2007, 1(6): 1146-1151.

[13] Tomaso E, Peter K, and Gianfranco C. Unified fractional Fourier transform and sampling theorem[J]., 1999, 47(12): 3419-3423.

[14] Chen En-qing, Tao Ran, and Meng Xiang-yi. The OFDM system based on the fractional Fourier transform[C]. 2006 International Conference on Innovative Computing, Information and Control, Beijing, 2006: 14-17.

[15] 陶然, 鄧兵, 王越. 分數階Fourier變換的原理與應用[M]. 北京: 清華大學出版社, 2009: 185-198.

Tao Ran, Deng Bing, Wang Yue. Fractional Fourier Transform and Its Applications[M]. Beijing: Tsinghua University Press, 2009: 185-198.

[16] Pei S C and Din J J. Closed-form discrete fractional and affine Fourier transform[J]., 2000, 48(5): 1338-1353.

趙 越： 女，1987年生，碩士生，研究方向為OFDM系統PAPR抑制、信道估計及均衡等關鍵技術的研究.

王 騰： 男，1988年生，博士生，研究方向為通信信號處理理論、擴頻通信抗干擾、寬帶與超寬帶信道估計及均衡等關鍵技術的研究.

陶 然： 男，1964年生，教授，博士生導師，研究方向為分數階傅里葉變換的理論與應用、雷達系統與技術、通信系統.

Peak to Average Power Ratio Reduction with Low Computational Complexity in FrFT-OFDM System

Zhao Yue Wang Teng Tao Ran Shi Peng-fei Jiang Zheng-guo

(,,100081,)

This paper proposes a low-complexity Peak to Average Power Ratio (PAPR) reduction method inOrthogonal Frequency Division Multiplexing (OFDM) system based on the Fractional Fourier Transform (FrFT). The method reduces PAPR effectively through periodic extension of random phase sequence to the length of FrFT-OFDM symbol,weighting it with phase factors and multiplying transmitted data vector.Only one Inverse Discrete Fractional Fourier Transform (IDFrFT) operation is performed in the proposed method, and the signal candidates can be calculated in time domain via weighted summation of the chirp circularly shifted FrFT-OFDM symbols. The simulation results show that, in the case that all the methods have 32 candidates, the proposed method hasalmost the same performance, when compared with the SeLecting Mapping (SLM) and performs even better than the Partial Transmit Sequence (PTS). More importantly, the proposed method has lower computational complexity compared with SLM and PTS.

Orthogonal Frequency Division Multiplexing (OFDM); Fractional Fourier Transform (FrFT); Peak to Average Power Ratio (PAPR); Low-complexity

TN914

A

1009-5896(2014)01-0246-04

10.3724/SP.J.1146.2013.00323

2013-03-15收到，2013-06-13改回

北京市自然科學基金(4112051)和教育部博士點基金優先發展領域(20121101130001)資助課題

趙越 zyozhm@163.com