Stability bounds on step-size for the 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. Only in the recent past has any work been done on deriving conditions for filter stability, convergence rate, and steady state error for the Partial Update LMS algorithm. In [5] approximate bounds were derived on the step size parameter which ensure stability in-the-mean of the alternating even/odd index coefficient updating strategy. Unfortunately, due to the restrictiveness of the assumptions, these bounds are unreliable when fast convergence (large ) is desired. In this paper, tighter bounds on are derived which guarantee convergence inthe-mean of the coefficient sequence for the case of wide sense stationary and cyclo-stationary signals.