Least squares approach to blind channel equalization

We present a least squares (LS) algorithm for blind channel equalization based on a reformulation of the Godard algorithm. A transformation for the equalizer parameters is considered to convert the nonlinear LS problem inherent in the Godard algorithm to a linear LS problem. Unlike the Godard (1980) algorithm, the proposed LS approach does not suffer from ill-convergence to closed-eye local minima. Methods for extracting the equalizer parameters from their transformed version are developed. Offline and recursive implementations of the LS algorithm are presented. The algorithm requires only a small number of channel output observations to estimate the equalizer parameters and is therefore fast vis-a-vis the Godard algorithm. The channel input correlation does not impose any restriction on the application of the algorithm, as long as a weak sufficient-excitation condition is satisfied. Simulation examples are presented to demonstrate the LS approach and to compare it with the Godard algorithm.