Properties of some blind equalization criteria in noisy multiuser environments

Blind equalization in noisy multiuser channels has met with increasing atte ntion with the advent of multiaccess digital communication systems. We exam ine blind equalizer performance in cases where perfect equalization proves unattainable due to noise and interference from concurrent users. In partic ular, we obtain a characterization of stationary points and extrema for a f amily of blind criteria in "undermodeled" cases, which assimilates the infl uence of differing source statistics and background noise correlation prope rties; relations to mean-square equalization measures are then obtained as a byprocuct. By re-examining a gradient search procedure, we obtain domains of attraction of each extremum in a special "sufficient order" setting. We also derive a global step-size bound for undermodeled cases, which ensures convergence of a gradient search procedure to an extremum of a blind cost function. We likewise confirm that the super-exponential algorithm results from an optimal choice of this step-size parameter.