Convergence and performance analysis of Godard family and multimodulus algorithms for blind equalization

We obtain the convergence of the Godard family [including the Sato and constant modulus (CM) algorithms] and the multimodulus algorithms (MMA) in a unified way. Our analysis also works for CMA fractionally spaced equalizer (FSE). Our assumptions are quite realistic: The channel input can be asymptotically stationary and ergodic, the channel impulse response is finite and can be stationary and ergodic (this models fading channels), and the equalizer length is finite. The noise is independent and identically distributed (i.i.d.). The channel input can be discrete or continuous. Our approach allows us to approximate the whole trajectory of the equalizer coefficients. This provides estimates of the rate of convergence, and the system performance (symbol error rate) can be evaluated under transience and steady state.

[1]  Zhi Ding,et al.  Local convergence of the Sato blind equalizer and generalizations under practical constraints , 1993, IEEE Trans. Inf. Theory.

[2]  Jitendra K. Tugnait,et al.  Comments on 'New criteria for blind deconvolution of nonminimum phase systems (channels)' , 1992, IEEE Trans. Inf. Theory.

[3]  Onkar Dabeer,et al.  Convergence analysis of the constant modulus algorithm , 2003, IEEE Trans. Inf. Theory.

[4]  Lang Tong,et al.  Blind identification and equalization based on second-order statistics: a time domain approach , 1994, IEEE Trans. Inf. Theory.

[5]  Ali H. Sayed,et al.  A feedback approach to the steady-state performance of fractionally spaced blind adaptive equalizers , 2000, IEEE Trans. Signal Process..

[6]  Philippe Loubaton,et al.  Prediction error methods for time-domain blind identification of multichannel FIR filters , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[7]  Roberto Cusani,et al.  Convergence analysis of the CMA blind equalizer , 1995, IEEE Trans. Commun..

[8]  Lee M. Garth,et al.  A dynamic convergence analysis of blind equalization algorithms , 2001, IEEE Trans. Commun..

[9]  Boris Buffoni,et al.  Analytic theory of global bifurcation , 2003 .

[10]  Guy A. Dumont,et al.  The multimodulus blind equalization algorithm , 1997, Proceedings of 13th International Conference on Digital Signal Processing.

[11]  D. Godard,et al.  Self-Recovering Equalization and Carrier Tracking in Two-Dimensional Data Communication Systems , 1980, IEEE Trans. Commun..

[12]  Zhi Ding,et al.  Blind Equalization and Identification , 2001 .

[13]  A. Benveniste,et al.  Robust identification of a nonminimum phase system: Blind adjustment of a linear equalizer in data communications , 1980 .

[14]  Phillip A. Regalia,et al.  Properties of some blind equalization criteria in noisy multiuser environments , 2001, IEEE Trans. Signal Process..

[15]  C. Richard Johnson,et al.  Bounds for the MSE performance of constant modulus estimators , 2000, IEEE Trans. Inf. Theory.

[16]  Ali H. Sayed,et al.  On the convergence of blind adaptive equalizers for constant modulus signals , 2000, IEEE Trans. Commun..

[17]  Zhi Ding,et al.  Ill-convergence of Godard blind equalizers in data communication systems , 1991, IEEE Trans. Commun..

[18]  P. Hartman.  Ordinary Differential Equations , 1965 .

[19]  Kenneth R. Laker,et al.  Convergence analysis of an algorithm for blind equalization , 1991, IEEE Trans. Commun..

[20]  William A. Sethares,et al.  Weak convergence and local stability properties of fixed step size recursive algorithms , 1993, IEEE Trans. Inf. Theory.

[21]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[22]  Eweda Eweda,et al.  Convergence analysis of self-adaptive equalizers , 1984, IEEE Trans. Inf. Theory.

[23]  W. Rudin.  Principles of mathematical analysis , 1964 .

[24]  Jian Yang,et al.  The multimodulus blind equalization and its generalized algorithms , 2002, IEEE J. Sel. Areas Commun..

[25]  Lang Tong,et al.  Relationships Between the Constant Modulus and Wiener Receivers , 1998, IEEE Trans. Inf. Theory.

[26]  Y. Sato,et al.  A Method of Self-Recovering Equalization for Multilevel Amplitude-Modulation Systems , 1975, IEEE Trans. Commun..

[27]  L. Tong,et al.  Multichannel blind identification: from subspace to maximum likelihood methods , 1998, Proc. IEEE.

[28]  Georgios B. Giannakis,et al.  Signal Processing Advances in Wireless and Mobile Communications, Volume 2: Trends in Single- and Multi-User Systems , 2000 .

[29]  G. David Forney,et al.  Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference , 1972, IEEE Trans. Inf. Theory.