FrFT-OFDM系統(tǒng)的低復(fù)雜度峰均功率比抑制技術(shù)研究

趙 越 王 騰 陶 然 時(shí)鵬飛 蔣政國(guó)

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FrFT-OFDM系統(tǒng)的低復(fù)雜度峰均功率比抑制技術(shù)研究

趙 越 王 騰 陶 然 時(shí)鵬飛 蔣政國(guó)

(北京理工大學(xué)信息與電子學(xué)院 北京 100081)

針對(duì)基于分?jǐn)?shù)階Fourier變換的OFDM系統(tǒng)(簡(jiǎn)稱FrFT-OFDM系統(tǒng))的高峰均功率比(PAPR)問題，該文提出一種低復(fù)雜度的峰均比抑制算法。通過對(duì)隨機(jī)相位序列采用周期延拓至FrFT-OFDM符號(hào)長(zhǎng)度，相位因子加權(quán)后與子載波調(diào)制前的數(shù)據(jù)相乘的方式，實(shí)現(xiàn)對(duì)高峰均比的有效抑制。該算法只需要一次逆離散分?jǐn)?shù)階Fourier變換(IDFrFT)，所有備選信號(hào)直接通過時(shí)域chirp圓周移位的加權(quán)和得到。仿真結(jié)果表明，當(dāng)備選信號(hào)個(gè)數(shù)相同時(shí)，該算法與選擇映射(SeLecting Mapping, SLM)算法的PAPR抑制性能相當(dāng)，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(shí)，該算法較SLM和PTS算法的運(yùn)算量降低。

正文頻分復(fù)用；分?jǐn)?shù)階Fourier變換；峰均功率比；低復(fù)雜度

1 引言

由于在時(shí)頻雙彌散信道中，OFDM系統(tǒng)中子載波間的正交性容易受到破壞，從而形成嚴(yán)重的子載波間干擾。為了克服這一問題，文獻(xiàn)[1]提出了FrFT- OFDM系統(tǒng)，并得出在快速時(shí)變信道中FrFT- OFDM系統(tǒng)比傳統(tǒng)OFDM系統(tǒng)具有更好的傳輸性能；同時(shí)，F(xiàn)rFT的計(jì)算復(fù)雜度和FFT相近，容易實(shí)現(xiàn)，所以FrFT-OFDM系統(tǒng)具有很大的應(yīng)用價(jià)值。

然而，作為多載波傳輸系統(tǒng)，F(xiàn)rFT-OFDM系統(tǒng)同樣存在高峰均功率比問題，這一問題直接影響系統(tǒng)的運(yùn)行成本和效率，是該技術(shù)不可忽視的問題之一。文獻(xiàn)[2]對(duì)FrFT-OFDM系統(tǒng)的PAPR分布進(jìn)行了理論推導(dǎo)與仿真驗(yàn)證，并得出隨著子載波個(gè)數(shù)的增加，F(xiàn)rFT-OFDM系統(tǒng)的PAPR分布和傳統(tǒng)OFDM系統(tǒng)的PAPR分布趨于一致，即對(duì)應(yīng)不同階次的FrFT-OFDM系統(tǒng)的PAPR分布趨于一致。目前，F(xiàn)rFT-OFDM系統(tǒng)的峰均比抑制算法僅僅是將傳統(tǒng)OFDM系統(tǒng)的算法直接應(yīng)用到該系統(tǒng)中，傳統(tǒng)OFDM系統(tǒng)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(kuò)展法(ACE)[6,7]、壓縮擴(kuò)展法[8,9]、子載波預(yù)留法[10]等。文獻(xiàn)[11]將傳統(tǒng)的SLM法和PTS法分別應(yīng)用于FrFT-OFDM系統(tǒng)，系統(tǒng)的峰均比特性有了明顯改善，但是這兩種算法存在計(jì)算復(fù)雜度大的問題。雖然文獻(xiàn)[12]針對(duì)傳統(tǒng)OFDM系統(tǒng)中PTS算法運(yùn)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?jǐn)?shù)階Fourier變換chirp周期性[13]的存在，該算法并不能直接應(yīng)用到FrFT-OFDM系統(tǒng)。

基于以上問題，本文對(duì)CSPS和OCSPS算法進(jìn)行了改進(jìn)，提出一種適用于FrFT-OFDM系統(tǒng)的低復(fù)雜度的峰均比抑制算法，該算法基于分?jǐn)?shù)階隨機(jī)相位序列和分?jǐn)?shù)階圓周卷積定理，有效降低了算法運(yùn)算復(fù)雜度。

2 FrFT-OFDM系統(tǒng)模型

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

圖1 FrFT-OFDM系統(tǒng)原理圖

3 低復(fù)雜度的峰均功率比抑制算法

3.1 設(shè)計(jì)分?jǐn)?shù)階隨機(jī)相位序列

將式(2)和式(3)代入到式(4)中，得到

3.2 低復(fù)雜度峰均比抑制算法

圖2 算法原理圖

根據(jù)上面的描述，現(xiàn)對(duì)算法的步驟總結(jié)如下：

3.3 運(yùn)算復(fù)雜度對(duì)比分析

表1 SLM, PTS和本文算法的運(yùn)算復(fù)雜度

表2 具體參數(shù)下3種算法的運(yùn)算復(fù)雜度

4 仿真驗(yàn)證

圖3 時(shí)3種算法的PAPR抑制效果

5 結(jié)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?jǐn)?shù)階Fourier變換的原理與應(yīng)用[M]. 北京: 清華大學(xué)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?yàn)镺FDM系統(tǒng)PAPR抑制、信道估計(jì)及均衡等關(guān)鍵技術(shù)的研究.

王 騰： 男，1988年生，博士生，研究方向?yàn)橥ㄐ判盘?hào)處理理論、擴(kuò)頻通信抗干擾、寬帶與超寬帶信道估計(jì)及均衡等關(guān)鍵技術(shù)的研究.

陶 然： 男，1964年生，教授，博士生導(dǎo)師，研究方向?yàn)榉謹(jǐn)?shù)階傅里葉變換的理論與應(yīng)用、雷達(dá)系統(tǒng)與技術(shù)、通信系統(tǒng).

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(xué)基金(4112051)和教育部博士點(diǎn)基金優(yōu)先發(fā)展領(lǐng)域(20121101130001)資助課題

趙越 zyozhm@163.com