Mean-square analysis of the multiple-error and block LMS adaptive algorithms

Stochastic-gradient adaptive algorithms for block-based or frequency-domain single channel filters and for true multichannel filters share a common multiple-error LMS algorithm update, given by W _k+1=W_k+μX_k(D_k-X_k ^TW_k). We examine the mean-square performance of the multiple-error LMS adaptive algorithm for correlated Gaussian input data channels and arbitrary i.i.d. input data channels. Using our analysis, we show that the multiple-error LMS algorithm performs uniformly worse than the single-channel LMS algorithm for a given amount of data consumed. We also derive simple step size bounds to guarantee mean-square convergence of the multiple-error and block LMS adaptive algorithms. Simulations of both the block LMS adaptive algorithm and the multichannel filtered-X LMS adaptive algorithm corroborate our theoretical results