A fast exact least mean square adaptive algorithm

We present a general block formulation of the least mean square (LMS) algorithm for adaptive filtering. This formulation has an exact equivalence with the original LMS algorithm, hence retaining the same convergence properties, while allowing a reduction in arithmetic complexity, even for very small block lengths. Working with small block lengths is very interesting from an implementation point of view (large blocks result in large memory and large system delay) and, nevertheless, allows a significant reduction in the number of operations. Furthermore, trade-offs 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 (BLMS) appears as a special case, which explains its convergence behavior according to the type of input signal (correlated or uncorrelated).