Analysis of the multiple-error and block least-mean-square adaptive algorithms

In some block-based and frequency-domain filtering tasks and in multichannel filtering applications, a multiple-error LMS adaptive algorithm, given by W_k+1=W_k+μX_k(D _k-X_k^TW_k), is employed, In this paper, 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. We provide a new mean-square analysis of this algorithm that accounts for the correlations between successive data vectors in the data matrix X_k. Using our analysis, we show that for both correlated and i.i.d. input data channels, 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 for our correlated data model. Simulations of both the block LMS adaptive algorithm and the multichannel filtered-X LMS adaptive algorithm corroborate our theoretical results