A GCD Method for Blind Channel Identification,

Abstract Using the second-order statistics (SOS) for the estimation of impulse responses of multiple FIR channels driven by an unknown input has become a topic of great interest since Tong-Xu-Kailath proposed a SOS-based matrix pair (MP) method in 1991. The MP method exploits a pair of covariance matrices of the channel output vectors to identify the channel impulse responses. In this paper, we show that one of the two covariance matrices contains all the information about the channel impulse responses, and this information can be retrieved by a simple application of a notion called the greatest common divisor (GCD). The GCD method is shown to be much more robust to noise than the MP method.

[1]  M. Rosenblatt,et al.  Deconvolution and Estimation of Transfer Function Phase and Coefficients for NonGaussian Linear Processes. , 1982 .

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

[3]  Jitendra K. Tugnait,et al.  Identification of non-minimum phase linear stochastic systems , 1986, Autom..

[4]  William A. Gardner,et al.  Cyclostationarity in communications and signal processing , 1994 .

[5]  Yingbo Hua,et al.  A subspace method for the computation of the GCD of polynomials , 1997, Autom..

[6]  Jitendra K. Tugnait,et al.  Identification of linear stochastic systems via second- and fourth-order cumulant matching , 1987, IEEE Trans. Inf. Theory.

[7]  John G. Proakis,et al.  A 'quantized' channel approach to blind equalization , 1992, [Conference Record] SUPERCOMM/ICC '92 Discovering a New World of Communications.

[8]  Hui Liu,et al.  A deterministic approach to blind symbol estimation , 1994, Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers.

[9]  Philippe Loubaton,et al.  A subspace algorithm for certain blind identification problems , 1997, IEEE Trans. Inf. Theory.

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

[11]  Jerry M. Mendel,et al.  Identification of nonminimum phase systems using higher order statistics , 1989, IEEE Trans. Acoust. Speech Signal Process..

[12]  Benjamin Friedlander,et al.  Asymptotically optimal estimation of MA and ARMA parameters of non-Gaussian processes from high-order moments , 1990 .

[13]  T. Kailath,et al.  A least-squares approach to blind channel identification , 1995, IEEE Trans. Signal Process..

[14]  J. Treichler,et al.  A new approach to multipath correction of constant modulus signals , 1983 .

[15]  Yingbo Hua,et al.  Previously Published Works Uc Riverside Title: Fast Maximum Likelihood for Blind Identification of Multiple Fir Channels Fast Maximum Likelihood for Blind Identification of Multiple Fir Channels , 2022 .

[16]  A. Benveniste,et al.  Blind Equalizers , 1984, IEEE Trans. Commun..

[17]  J. Mendel,et al.  ARMA parameter estimation using only output cumulants , 1988, Fourth Annual ASSP Workshop on Spectrum Estimation and Modeling.

[18]  Lang Tong,et al.  Blind channel identification based on second-order statistics: a frequency-domain approach , 1995, IEEE Trans. Inf. Theory.

[19]  Dirk T. M. Slock,et al.  Blind fractionally-spaced equalization, perfect-reconstruction filter banks and multichannel linear prediction , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

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

[21]  G. Giannakis,et al.  Linear cyclic correlation approaches for blind identification of FIR channels , 1994, Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers.

[22]  Hui Liu,et al.  Recent developments in blind channel equalization: From cyclostationarity to subspaces , 1996, Signal Process..

[23]  John J. Shynk,et al.  Bayesian/decision-feedback algorithm for blind adaptive equalization , 1992 .

[24]  Eric Moulines,et al.  Subspace methods for the blind identification of multichannel FIR filters , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[25]  Ehud Weinstein,et al.  New criteria for blind deconvolution of nonminimum phase systems (channels) , 1990, IEEE Trans. Inf. Theory.

[26]  D. Donoho.  ON MINIMUM ENTROPY DECONVOLUTION , 1981 .

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

[28]  Zhi Ding,et al.  Blind adaptive equalizers for quadrature amplitude modulated communication systems based on convex cost functions , 1992 .

[29]  Ananthram Swami,et al.  On estimating noncausal nonminimum phase ARMA models of non-Gaussian processes , 1990, IEEE Trans. Acoust. Speech Signal Process..

[30]  G. J. Foschini,et al.  Equalizing without altering or detecting data , 1985, AT&T Technical Journal.

[31]  Giancarlo Prati,et al.  Blind Equalization and Carrier Recovery Using a "Stop-and-Go" Decision-Directed Algorithm , 1987, IEEE Trans. Commun..

[32]  Chrysostomos L. Nikias,et al.  ARMA bispectrum approach to nonminimum phase system identification , 1988, IEEE Trans. Acoust. Speech Signal Process..