Convergence and Performance Issues for Autocorrelation Based Adaptive Channel Shortening

We derive bounds on the signal to interference ratio performance of several blind channel shortening designs based on autocorrelation minimization. We focus in particular on the performance of these designs in oversampled communications systems with multiple receive antennas. The utility of the bounds is demonstrated by proving inherent performance problems with certain classes of designs that previous low dimensional plots of the cost functions were not able to predict. We conclude the paper by providing a convergence result for adaptive versions of these blind designs which can be coupled with the performance results to determine performance of the adaptive designs.