Blind channel identification and equalization using cyclostationary and/or higher order statistics

Channel equalization is an effective tool to eliminate intersymbol interferences caused by the linear distortion of unknown channels. Channel equalization requires that the channel transfer function be identified either implicitly or explicitly. This dissertation deals with blind channel identification and equalization using cyclostationary and/or higher order statistics.; In communication systems, channel output signal is cyclostationary instead of stationary. The dissertation first focuses on ARMA system identification based on second order cyclostationarity. A parametric and a nonparametric method are presented. The parametric method directly identifies the zeros and poles of ARMA channels with mixed phase. The nonparametric method estimates the channel phase based on the cyclic spectra alone. For specific, finite-dimensional ARMA channels, an improved method is given, which combines the parametric method with the nonparametric method. The channel (or system) can also be identified by higher order statistics. A new nonparametric method for linear system phase recovery from bispectrum is proposed. Most existing algorithms use only partial bispectrum phase information, which increases their sensitivity to noises and measurement errors. In contrast, the new nonparametric method uses all the available bispectrum phase information. The new method is also computationally simple.; Godard and Shalvi-Weinstein equalizers are two well-known blind equalizers which use the higher order statistics of the channel output. A one-to-one correspondence between the local minima of finite-length Shalvi-Weinstein and those of Godard equalizers is shown, hence establishing the equivalent relationship between the two algorithms. The convergence of finite-length Godard and Shalvi-Weinstein equalizers is analyzed and the potential stable equilibrium points are identified. The existence of undesirable stable equilibria for the finite-length Shalvi-Weinstein equalizer is demonstrated through a simple example. It is proved that the ultimate points of convergence for both finite-length equalizers depend on an initial kurtosis condition. It is also proved that when the length of the equalizer is long enough and the initial equalizer setting satisfies the kurtosis condition, the equalizer will converge to a stable equilibrium near a desired global minimum. When the kurtosis condition is not satisfied, generally the equalizer will take longer to converge to a desired equilibrium given sufficiently many parameters and adequate initialization. When Godard algorithm is implemented with a fractionally spaced equalizer (FSE), its average behavior changes. This in effect is a combined approach exploiting both cyclic and higher order statistics. It is shown that for channels satisfying some sufficient conditions, the Godard FSE always converges to a global minimum point.