A fast exact least mean square adaptive algorithm

A general block-formulation is presented for the LMS (least-mean-square) algorithm for adaptive filtering. This formulation has an exact equivalence with the initial LMS, hence retaining the same convergence properties while allowing a reduction in the arithmetic complexity, even for very small block lengths. Furthermore, tradeoffs between number of operations and convergence rate are obtainable by applying certain approximations to a matrix involved in the algorithm. The usual block LMS (BLMS) hence appears as one of the possible approximations, which explains some of its properties