A fast exact least mean square adaptive algorithm

A general block formulation of the least-mean-square (LMS) algorithm for adaptive filtering is presented. This formulation has an exact equivalence with the original LMS algorithm; hence it retains its convergence properties, while allowing a reduction in arithmetic complexity, even for very small block lengths. Working with small block lengths is interesting from an implementation point of view (large blocks result in large memory and large system delay) and allows a significant reduction in the number of operations. Tradeoffs between a number of operations and a convergence rate are obtainable by applying certain approximations to a matrix involved in the algorithm. Hence, the usual block LMS appears as a special case, which explains its convergence behavior according to the type of input signal (correlated or uncorrelated)