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+ mu X(k)(D-k - X(k)(T)W(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.