若干种盲信道辨识与均衡算法的研究
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摘要
盲信道辨识与均衡是通信信号处理中的核心技术之一，本文的内容围绕着它
的算法实现来展开。首先阐述了这一问题的理论基础，接着详细地讨论了有关非
最小相位系统的盲反卷积的准则设计问题，然后又深入地研究了基于二阶统计量
的盲信道辨识与均衡的子空间方法以及时域方法，并作了大量细致的仿真实验工
作。最后利用通信信号超采样后所具有的循环平稳性，给出了一种新的基于二阶
统计量的算法来完成对非最小相位系统的辨识和估计。传统的盲均衡方法只利用
一到二个特征矩阵，而此方法利用了一组特征矩阵所包含的信息来进行估计，使
估计性能得到了提高。与基于二阶统计量的非递推盲均衡算法相比，这种方法给
出求所定义的代价函数的最优解的有效递推算法，可以逐个地得到所有特征矢量，
最终得到了解析解。仿真实验表明，该算法在低信噪比的环境下仍然可以有效地
完成估计，克服了传统的盲均衡算法所具有的抗噪声性差的缺点。另外，虽然采
用了多个特征矩阵，但是其运算复杂度仍然比较小。
Blind identification and equalization is the pivotal technology in communication
signal precessing, the main work of this dissertation is on this topic. At the first, the
theoretic basis is expatiated. Then we detailedly discuss how to design a criteria for
blind deconvolution of nonminimum phase systems. And then we study the subspace
methods and the time domain approach for blind identification and equalization, which
are based on second-order statistics. In the research, lots of work of simulation is
concerned. At the last, a new recursive algorithm for blind identification and
equalization is proposed. The algorithm exploits the cyclostationarity of oversampled
communication signals to achieve identification and equalization of possibly
nonminimum phase channels. Compared with other blind equalization algorithms which
only exploit one or two eigenmatrix, this algorithm utilizes a set of eigenmatrices, so
that the performance is improved. By solving the cost function to obtain the best
solution, the recursive algorithm is given which can obtain all the eigenvectors one by
one. Further, the analytic solution is provided. Simulations show that algorithm here is
effective even under the condition of low signal-to-noise ratio (SNR) which can
overcome the shortcomings of conventional algorithms. In addition, our algorithm has
low complexity of computation.
的算法实现来展开。首先阐述了这一问题的理论基础，接着详细地讨论了有关非
最小相位系统的盲反卷积的准则设计问题，然后又深入地研究了基于二阶统计量
的盲信道辨识与均衡的子空间方法以及时域方法，并作了大量细致的仿真实验工
作。最后利用通信信号超采样后所具有的循环平稳性，给出了一种新的基于二阶
统计量的算法来完成对非最小相位系统的辨识和估计。传统的盲均衡方法只利用
一到二个特征矩阵，而此方法利用了一组特征矩阵所包含的信息来进行估计，使
估计性能得到了提高。与基于二阶统计量的非递推盲均衡算法相比，这种方法给
出求所定义的代价函数的最优解的有效递推算法，可以逐个地得到所有特征矢量，
最终得到了解析解。仿真实验表明，该算法在低信噪比的环境下仍然可以有效地
完成估计，克服了传统的盲均衡算法所具有的抗噪声性差的缺点。另外，虽然采
用了多个特征矩阵，但是其运算复杂度仍然比较小。
Blind identification and equalization is the pivotal technology in communication
signal precessing, the main work of this dissertation is on this topic. At the first, the
theoretic basis is expatiated. Then we detailedly discuss how to design a criteria for
blind deconvolution of nonminimum phase systems. And then we study the subspace
methods and the time domain approach for blind identification and equalization, which
are based on second-order statistics. In the research, lots of work of simulation is
concerned. At the last, a new recursive algorithm for blind identification and
equalization is proposed. The algorithm exploits the cyclostationarity of oversampled
communication signals to achieve identification and equalization of possibly
nonminimum phase channels. Compared with other blind equalization algorithms which
only exploit one or two eigenmatrix, this algorithm utilizes a set of eigenmatrices, so
that the performance is improved. By solving the cost function to obtain the best
solution, the recursive algorithm is given which can obtain all the eigenvectors one by
one. Further, the analytic solution is provided. Simulations show that algorithm here is
effective even under the condition of low signal-to-noise ratio (SNR) which can
overcome the shortcomings of conventional algorithms. In addition, our algorithm has
low complexity of computation.
引文
[1] G. H. Gloub, Matrix Computations. Baltimore and London: The Johns Hopkins
University Press, 1996
[2] 张贤达,保铮. 通信信号处理. 北京: 国防工业出版社, 2000
[3] 程云鹏. 矩阵论. 西安: 西北工业大学出版社, 1999
[4] Y. Sato, “A mothod of self-recovering equalization for multilevel amplitude-mo-
dulation,”IEEE Trans. Commun, vol. COM-23, pp. 679-682, June 1975.
[5] D. N. Godard, “Self-recovering equlazation and carrier tracking in two-dimensi-
onal data communication systems,”IEEE Trans. Commun, vol. COM-28, pp.
1867-1875, Nov. 1980.
[6] A. Benveniste, M. Goursat, and G. Ruget, “Robust identification of non-minimi-
m phase system: Blind adjustment of a linear equalizer in data communication,”
IEEE Trans. Automat. Contr., vol.25, pp. 385-399, June. 1980.
[7] O. Shalvi and E. Weinstein, “New criteria for blind deconvolution of nonminim-
um phase systems,”IEEE Trans. Inform. Theory, vol. 36, pp. 312-321, Mar. 1990.
[8] A. Benveniste and M. Goursat, “Blind equalizaters,”IEEE Trans. Commun, vol.
COM-32,pp. 871-883, Aug. 1984.
[9] G. Giannakis,Y. lnouye, and J, Mendal.”Cumulant-based identifation of multich-
annel moving averge models,”IEEE Trans. Automat. Contr., vol. 34, pp. 783-787,
Apr. 1989.
[10] G. Giannakis and J. Mendal, “Identification of non-minimum phase systems
using higer-order statistics,”IEEE Trans. Acaust. Speech, Signal Proseecing, vol.
37, pp. 360-377, Feb. 1991.
[11] J. Mendal, “Tutorial on higher-order statistics (spectra) in signal processing and
system theory:Theoretical results and some applications,”Proc. IEEE, vol. 79, pp.
278-305, Mar. 1991.
[12] C. Nikias, “Blind deconvolution using higher-order statistics,”Proc. 2nd Int.
Conf. Higher-Order Stat. Elsevier. 1992, pp. 49-56.
[13] L. Tong, G. Xu, and T. Kailath, “Blind identification and equalization based on
second-order statistics: a time domain approach,”IEEE Trans. Inform. Theory,
vol. 40, pp. 340-350, Mar. 1994.
[14] E. Moulines, P. Duhamel, J. F. Cardoso, S. Mayrargue, “Subspace methods for
the blind identification of multichannel FIR filters,” IEEE Trans. Signal
Processing, vol. 43, pp. 516-525, Feb. 1995.
参考文献 55
[15] D. L. Donoho, "On minimum entropy deconvolution," in Applied Time Series
Analysis II, ed. D.F. Findlay, Academic Press, New York, 1981.
[16] G. Xu, et al., "A least-squares approach to blind channel identification," IEEE
Trans. Signal Processing, Vol. 43, pp. 2982-2993, De. 1995.
[17] D. T. M. Slock, “Blind fractionally-spaced equalization, perfect-reconstruction
filter banks and multichannel linear prediction,”in Proc. Int. Conf. Acoust., Speeh,
Signal Process., vol. IV, Adelaide, Australia, 1994, pp. 585-588.
[18] X. Li and H. Fan, “Direct estimation of blind zero-forcing euqlizers based on
second-order statistics,”IEEE Trans. Signal Precessing, vol.48, pp. 2211-2218,
Apr. 2000.
[19] C. B. Papadias and D. T. M. Slock, “Fractionally spaced equalization of linear
polyphase channels and related blind techniques based on multichannel linear
prediction,”IEEE Trans. Signal Precessing, vol.47, pp. 641-654, Mar. 1999.
[20] G. B. Giannakis and S. D. Halford, “Blind fractionally spaced equalization of
noisy FIR channels:Direct and adaptive solutions,” IEEE Trans. Signal
Precessing, vol. 45, pp. 2277-2292, Sept. 1997.
[21] L. Tong, G. Xu, and T. Kailath, “Blind identification and equalization of multipat-
h channels,”proc. Int. Conf. Commun., June 1992. pp. 1513-1527.
[22] H. Luo and R. Liu, “Blind equlizers for multipath channels with best equalization
delay,”in Proc. ICASSP, Phoenic, AZ, Mar. 1999.
[23] Y. Li and Z. Ding, “Global convergence of fractionally spaced Godard (CMA)
adaptive equalizers,”IEEE Trans. Signal Precessing, vol.44, pp. 818-826, Apr.
1996.
[24] J. K. Tugnait and B. Huang, “Second-order statistics-based blind equalization of
IIR single-input multiple-output channels with common zeros,”IEEE Trans.
Signal Precessing, vol.47, pp. 147-157, Sept. 1999.
[25] G. J. Foschini, “Equalization without altering or detecting data,”Bell Syst. Tech. J,
vol. 64, no. 8, pp. 1885-1911, Oct. 1985.
[26] E. Bai and M. Fu, “Blind system identification and channel equalization of IIR
systems without statistical information,”IEEE Trans. Signal Precessing, vol.47,
pp. 1910-1921, Jul. 1999.
[27] 冯大政, 保铮, 张贤达. 信号盲分离问题多阶段分解算法. 自然科学进展,
2002, 12(3)：324-328.
[28] 刘琚, 何振亚. 盲源分离和盲反卷积. 电子学报, 2002, 30(4)：570-576.
[29] S. Haykin, Adaptive Filter Theory, Third Edition, Prentice-Hall, 1996.
56 若干种盲信道辨识与均衡算法的研究
[30] S. Haykin, Adaptive Blind Deconvolution, Prentice-Hall, Englewood Cliffs,
1994.
[31] A. Touzni, "A globally convergent approach for blind MIMO adaptive deconvol-
ution," IEEE Trans. Signal Processing, Vol.49, No. 6, pp.1166-1177, 2001.
[32] R.A. Axford, Jr., et al. "Effects on PN sequences on the misconvergence of the
constant modulus algorithm," IEEE Trans. Signal Processing, Vol.46, pp. 519-523,
Feb. 1998.
[33] A. J. Van der Veen, and A. Paulraj, "An analyyticl constant modulus algorithm,"
IEEE Trans. Signal Processing, Vol.44, pp.1136-1155, 1998.
[34] O. Shalvi, and E. Weistein, "Super-exponential methods for blind deconvolution,"
IEEE Trans. Information Theory, Vol. IT-39, pp.504-519, 1993.
[35] J.K. Tugnait, "Estimation of linear parametric models using inverse filter criteria
and higher-order statistics," IEEE Trans. Signal Processing, Vol.41, No. 11,
pp.3196-3199, 1993.
[36] J.K. Tugnait, "Identification and deconvolution of multichannel linear non-Gaus-
sian processes using higher order statistics and inverse filter criteria," IEEE Trans.
Signal Processing, Vol.45, No. 3, pp.658-672, 1997.
[37] C.Y. Chi and M.C. Wu, "Inverse filter criteria for blind deconvolution and equal-
ization using two cumulants," Signal Processing, Vol.43, pp.55-63, Apr. 1995.
[38] C-Y. Chi, and C-H. Chen, Cumulani-based inverse filter criteria for MIMO blind
deconvolution: Properties, algorithms, and allication to DS/CDMA systems in
multipath," IEEE Trans. Signal Processing, Vol.49, No. 7, pp.1282-1299, 2001.
[39] K. Abed-Meraim, et al., "Prediction error method for second-order blind identify-
cation," IEEE Trans. Signal Processing, Vol.45, pp. 694-705, March 1997.
[40] Y. Hua, "Fast maximum likelihood for blind identification of multiple FIR
channels," IEEE Trans. Signal Processing, Vol.44, pp. 661-672, March 1996.
[41] J. L. Bapat, "Partially blind estimation: ML-based approaches and Cramer-Rao
bound," Signal Processing, Vol.71, pp.265-277, 1998
[42] H. A. Cirpan. And M. K. Tsatsanis, "Stochastic maximum likelihood methods for
semi-blind channel equalization," IEEE Trans. Signal Processing Lett., Vol.5, No.
6, pp.21-24, 1998.
[43] V. Buchoux, et al., "On the performance of semi-blind subspace-based channel
estimation," IEEE Trans. Signal Processing, Vol.48, No. 6, pp.1750-1759, 2000.
University Press, 1996
[2] 张贤达,保铮. 通信信号处理. 北京: 国防工业出版社, 2000
[3] 程云鹏. 矩阵论. 西安: 西北工业大学出版社, 1999
[4] Y. Sato, “A mothod of self-recovering equalization for multilevel amplitude-mo-
dulation,”IEEE Trans. Commun, vol. COM-23, pp. 679-682, June 1975.
[5] D. N. Godard, “Self-recovering equlazation and carrier tracking in two-dimensi-
onal data communication systems,”IEEE Trans. Commun, vol. COM-28, pp.
1867-1875, Nov. 1980.
[6] A. Benveniste, M. Goursat, and G. Ruget, “Robust identification of non-minimi-
m phase system: Blind adjustment of a linear equalizer in data communication,”
IEEE Trans. Automat. Contr., vol.25, pp. 385-399, June. 1980.
[7] O. Shalvi and E. Weinstein, “New criteria for blind deconvolution of nonminim-
um phase systems,”IEEE Trans. Inform. Theory, vol. 36, pp. 312-321, Mar. 1990.
[8] A. Benveniste and M. Goursat, “Blind equalizaters,”IEEE Trans. Commun, vol.
COM-32,pp. 871-883, Aug. 1984.
[9] G. Giannakis,Y. lnouye, and J, Mendal.”Cumulant-based identifation of multich-
annel moving averge models,”IEEE Trans. Automat. Contr., vol. 34, pp. 783-787,
Apr. 1989.
[10] G. Giannakis and J. Mendal, “Identification of non-minimum phase systems
using higer-order statistics,”IEEE Trans. Acaust. Speech, Signal Proseecing, vol.
37, pp. 360-377, Feb. 1991.
[11] J. Mendal, “Tutorial on higher-order statistics (spectra) in signal processing and
system theory:Theoretical results and some applications,”Proc. IEEE, vol. 79, pp.
278-305, Mar. 1991.
[12] C. Nikias, “Blind deconvolution using higher-order statistics,”Proc. 2nd Int.
Conf. Higher-Order Stat. Elsevier. 1992, pp. 49-56.
[13] L. Tong, G. Xu, and T. Kailath, “Blind identification and equalization based on
second-order statistics: a time domain approach,”IEEE Trans. Inform. Theory,
vol. 40, pp. 340-350, Mar. 1994.
[14] E. Moulines, P. Duhamel, J. F. Cardoso, S. Mayrargue, “Subspace methods for
the blind identification of multichannel FIR filters,” IEEE Trans. Signal
Processing, vol. 43, pp. 516-525, Feb. 1995.
参考文献 55
[15] D. L. Donoho, "On minimum entropy deconvolution," in Applied Time Series
Analysis II, ed. D.F. Findlay, Academic Press, New York, 1981.
[16] G. Xu, et al., "A least-squares approach to blind channel identification," IEEE
Trans. Signal Processing, Vol. 43, pp. 2982-2993, De. 1995.
[17] D. T. M. Slock, “Blind fractionally-spaced equalization, perfect-reconstruction
filter banks and multichannel linear prediction,”in Proc. Int. Conf. Acoust., Speeh,
Signal Process., vol. IV, Adelaide, Australia, 1994, pp. 585-588.
[18] X. Li and H. Fan, “Direct estimation of blind zero-forcing euqlizers based on
second-order statistics,”IEEE Trans. Signal Precessing, vol.48, pp. 2211-2218,
Apr. 2000.
[19] C. B. Papadias and D. T. M. Slock, “Fractionally spaced equalization of linear
polyphase channels and related blind techniques based on multichannel linear
prediction,”IEEE Trans. Signal Precessing, vol.47, pp. 641-654, Mar. 1999.
[20] G. B. Giannakis and S. D. Halford, “Blind fractionally spaced equalization of
noisy FIR channels:Direct and adaptive solutions,” IEEE Trans. Signal
Precessing, vol. 45, pp. 2277-2292, Sept. 1997.
[21] L. Tong, G. Xu, and T. Kailath, “Blind identification and equalization of multipat-
h channels,”proc. Int. Conf. Commun., June 1992. pp. 1513-1527.
[22] H. Luo and R. Liu, “Blind equlizers for multipath channels with best equalization
delay,”in Proc. ICASSP, Phoenic, AZ, Mar. 1999.
[23] Y. Li and Z. Ding, “Global convergence of fractionally spaced Godard (CMA)
adaptive equalizers,”IEEE Trans. Signal Precessing, vol.44, pp. 818-826, Apr.
1996.
[24] J. K. Tugnait and B. Huang, “Second-order statistics-based blind equalization of
IIR single-input multiple-output channels with common zeros,”IEEE Trans.
Signal Precessing, vol.47, pp. 147-157, Sept. 1999.
[25] G. J. Foschini, “Equalization without altering or detecting data,”Bell Syst. Tech. J,
vol. 64, no. 8, pp. 1885-1911, Oct. 1985.
[26] E. Bai and M. Fu, “Blind system identification and channel equalization of IIR
systems without statistical information,”IEEE Trans. Signal Precessing, vol.47,
pp. 1910-1921, Jul. 1999.
[27] 冯大政, 保铮, 张贤达. 信号盲分离问题多阶段分解算法. 自然科学进展,
2002, 12(3)：324-328.
[28] 刘琚, 何振亚. 盲源分离和盲反卷积. 电子学报, 2002, 30(4)：570-576.
[29] S. Haykin, Adaptive Filter Theory, Third Edition, Prentice-Hall, 1996.
56 若干种盲信道辨识与均衡算法的研究
[30] S. Haykin, Adaptive Blind Deconvolution, Prentice-Hall, Englewood Cliffs,
1994.
[31] A. Touzni, "A globally convergent approach for blind MIMO adaptive deconvol-
ution," IEEE Trans. Signal Processing, Vol.49, No. 6, pp.1166-1177, 2001.
[32] R.A. Axford, Jr., et al. "Effects on PN sequences on the misconvergence of the
constant modulus algorithm," IEEE Trans. Signal Processing, Vol.46, pp. 519-523,
Feb. 1998.
[33] A. J. Van der Veen, and A. Paulraj, "An analyyticl constant modulus algorithm,"
IEEE Trans. Signal Processing, Vol.44, pp.1136-1155, 1998.
[34] O. Shalvi, and E. Weistein, "Super-exponential methods for blind deconvolution,"
IEEE Trans. Information Theory, Vol. IT-39, pp.504-519, 1993.
[35] J.K. Tugnait, "Estimation of linear parametric models using inverse filter criteria
and higher-order statistics," IEEE Trans. Signal Processing, Vol.41, No. 11,
pp.3196-3199, 1993.
[36] J.K. Tugnait, "Identification and deconvolution of multichannel linear non-Gaus-
sian processes using higher order statistics and inverse filter criteria," IEEE Trans.
Signal Processing, Vol.45, No. 3, pp.658-672, 1997.
[37] C.Y. Chi and M.C. Wu, "Inverse filter criteria for blind deconvolution and equal-
ization using two cumulants," Signal Processing, Vol.43, pp.55-63, Apr. 1995.
[38] C-Y. Chi, and C-H. Chen, Cumulani-based inverse filter criteria for MIMO blind
deconvolution: Properties, algorithms, and allication to DS/CDMA systems in
multipath," IEEE Trans. Signal Processing, Vol.49, No. 7, pp.1282-1299, 2001.
[39] K. Abed-Meraim, et al., "Prediction error method for second-order blind identify-
cation," IEEE Trans. Signal Processing, Vol.45, pp. 694-705, March 1997.
[40] Y. Hua, "Fast maximum likelihood for blind identification of multiple FIR
channels," IEEE Trans. Signal Processing, Vol.44, pp. 661-672, March 1996.
[41] J. L. Bapat, "Partially blind estimation: ML-based approaches and Cramer-Rao
bound," Signal Processing, Vol.71, pp.265-277, 1998
[42] H. A. Cirpan. And M. K. Tsatsanis, "Stochastic maximum likelihood methods for
semi-blind channel equalization," IEEE Trans. Signal Processing Lett., Vol.5, No.
6, pp.21-24, 1998.
[43] V. Buchoux, et al., "On the performance of semi-blind subspace-based channel
estimation," IEEE Trans. Signal Processing, Vol.48, No. 6, pp.1750-1759, 2000.
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