Undermodeled equalization: Extrema of the Godard/Shalvi-Weinstein criterion

The more promising results to date in blind equalization are restricted to so-called sufficient-order settings, in which all configurations in the combined (channel-equalizer cascade) impulse response space are attainable for some setting of the equalizer coefficients. Here we address issues related to equalizer undermodelling, in which only a proper subset within the combined impulse response space is attainable by adjusting the equalizer coefficients. We derive an analytic characterization of stationary points for the Godard and Shalvi-Weinstein criteria in undermodeled cases, an establish relations to the convergence of super-exponential algorithms in undermodeled cases.