Stability analysis of the sequential partial update LMS algorithm

Partial updating of LMS filter coefficients is an effective method for reducing the computational load and the power consumption in adaptive filter implementations. The sequential partial update LMS algorithm is one popular algorithm in this category. A first-order stability analysis of this algorithm was performed (Douglas, 1997) on wide sense stationary signals under the restrictive assumption of small step size parameter μ. The necessary and sufficient condition derived on μ for convergence in the mean was identical to the one for guaranteeing stability in the mean of LMS. First-order sufficient conditions were derived (Godavarti et al., 1999) for stability without the aforementioned small μ assumption. The sufficient region of convergence derived was smaller than that of regular LMS. In this paper, we establish that for stationary signals the sequential algorithm converges in mean for the same values of the step size parameter μ for which the regular LMS does. In other words, we show that the conclusion drawn Douglas holds without the restrictive assumption of small μ. We also derive sufficient conditions for stability on μ for cycle-stationary signals