Stochastic partial update LMS algorithm for adaptive arrays

Partial updating of LMS filter coefficients is an effective method for reducing the computational load and the power consumption in adaptive filter implementations. Several algorithms have been proposed in the literature based on partial updating. Unfortunately, it has been observed that these algorithms do not have good convergence properties in practice. In particular, there generally exist signals for which these algorithms stagnate or diverge. We propose a new algorithm, called the stochastic partial update LMS (SPU-LMS) algorithm which attempts to remedy some of the drawbacks of existing algorithms. The SPU-LMS algorithm differs from the existing algorithms in that the subsets to be updated are chosen in a random manner at each iteration. We derive conditions for filter stability, convergence rate, and steady state error for the proposed algorithm under an independent snapshots assumption in the context of adaptive beamforming for antenna arrays. We verify the analysis via computer simulations and illustrate the advantages of the new algorithm through examples