On the performance of adaptive Gram-Schmidt algorithm for interference cancelling arrays

A detailed performance analysis of the least mean square (LMS) algorithm to update each stage of an adaptive Gram-Schmidt processor in interference cancelling adaptive arrays is presented. It is shown that although the number of adaptive weights in the processor is proportional to M². the total misadjustment contributed by weight jittering is proportional to only M, where M is the size of the processor. In absolute terms, the weight jittering noises do not accumulate as would be expected, but cancel one another out and decrease in magnitude as the optimal powers become smaller from one processing stage to the next. For optimal performance, the feedback factors used in the individual LMS loops should be normalized so that the amount of misadjustment contributed and the convergence time constant are the same for all processing stages. All the weights belonging to one processing stage must be adjusted in a synchronous manner with the same input vector. This synchronous updating requirement is essential for the cancellation of the jittering noises, although in situations where the weights are adaptively updated in a time-multiplexed manner, it may appear more efficient to update each weight based on the most current inputs