摘 要： DWT比DFT在子信道间有更高的频谱约束力，可以去除COFDM（编码正交频分复用）系统中必须的CP（循环前缀），从而提高带宽利用率。对不同小波下CWOFDM（编码小波正交频分复用）系统在无线信道下的传输性能进行仿真。结果表明，CWOFDM系统抗噪声和多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" 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title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落" title="多径衰落">多径衰落性能优于COFDM，而且小波的滤波器长度和分解层数都会影响CWOFDM系统抗噪声和多径衰落的性能。
　　关键词： 编码正交频分复用； 离散小波变换； 编码小波正交频分复用； 小波分解层数

　　在4G通信系统中，OFDM已经被证明是一种处理高速数据流的有效方法，每一个COFDM帧之前增加的循环前缀可以避免多径衰落信道带来的ISI（符号间干扰）和ICI（码间干扰），但这样将大大降低带宽利用率。为了提高带宽利用率，一方面将OFDM系统做得越来越复杂，将高效的纠错码与OFDM系统相结合，构成更高性能的COFDM系统^[1]；另一方面寻找新的变换替代傅里叶变换，其中用离散小波变换去替代傅里叶变换是最受关注的。这是因为OFDM系统频谱旁瓣较大，而小波变换则能克服这一问题，因此可以在OFDM系统中不加循环前缀的情况下，避免ISI和ICI^[2]。由于OFDM系统中循环前缀长度一般为FFT长度的1/4，因此，去除循环前缀的WOFDM系统比OFDM系统可提高近20%的带宽利用率。同时，WOFDM（小波正交频分复用）在复杂信道环境中尤其是电力线通信中的优势，使人们有理由相信CWOFDM在4G通信中具有重要地位^[3,4]。目前，对于CWOFDM的研究更多地关注高效的纠错码，参考文献[5]对比了不同正交基的OFDM系统在频率选择性信道中的性能优劣，但没有对小波进行比较选取。参考文献[6-8]分别从Turbo码、LDPC码和MLC码角度去分析CWOFDM在AWGN和瑞利衰落信道中的性能，但是这几种不同的信道编码方案中所采用的都只是Haar小波，没有分析比较其他小波。因此本文对采用不同小波的CWOFDM系统在多种信道中的传输性能进行研究。
1 编码小波正交频分复用系统
　　图1给出了CWOFDM的系统框图。

　　本文对不同小波下的CWOFDM系统进行了对比研究，得出以下结论： CWOFDM系统抗多径干扰误码率低于COFDM系统；不同族小波由于其特性不同，应用在CWOFDM系统中的性能也是不同的；CWOFDM系统抗高斯白噪声和多径衰落的误码率随着小波滤波器长度的增加而降低，除了bior族小波；采用QPSK调制方式，不同分解层数的小波下的CWOFDM系统抗噪声性能随着分解层数的增大而增强，与抗多径衰落性能相反；相同滤波器长度的CWOFDM系统抗噪声性能中，bior族小波性能稍差，但其抗多径衰落性能与其他小波一致。

参考文献
[1]  FERNANDO W A C, RAJATHEVA R M A P, AHMED K M. Performance of coded OFDM with higher modulation  schemes. In Proc. ICCT 1998, 2(10):5.
[2]  OZTURK, KUCAR E, HACIOGLU O. Performance analysis of CDMA signals using orthogonal wavelets as chip wave-forms in multipath fading and noisy channels. In Proc.SIU  2004, Aydm, Turkey, April 2004:712-715.

[3]  KEITA I, DAISUKE U, SATOSHI D. Performance evaluation of wavelet OFDM using ASCET. In Proc. ISPLC′07, Pisa, Italy, March 2007:246-251.
[4] ZHANG You Bing, CHENG Shi Jie. Automation of electric power systems, Sep 10, 2003,27(17):31-34.
[5]  ZHAO Feng, ZHANG Hai Xia, YUAN Dong Feng.Performance of COFDM with different orthogonal bases on AWGN and frequency selective channel.Proceedings of the IEEE 6th Circuits and Systems Symposium on Emerging Technologies,2004(2):473-475.
[6]  ZHANG Hai Xia, ZHAO Feng, YUAN Dong Feng, et al.Performance of turbo code an WOFDM system on rayleigh fading channels. In Proc. PIMRC 2003(2):1570-1573.
[7]  ZHANG Hai Xia, YUAN Dong Feng, JIANG Ming Yan, et al. Performance comparison of WOFDM with different coding schemes. In Proc. RAWCON′03, Boston, USA, Aug 2003:59-62.
[8]  ZHANG Hai Xia,YUAN Dong Feng,GAO Xing Ying,et al.Performance of coded WOFDM systems with MLC/MSD on  AWGN and Rayleigh fading channels. In Proc. ISSPIT 2003, Darmstadt, Germany, Dec 2003:447-450.