Effect of delay on the performance of the leaky LMS adaptive algorithm

The effect of incorporating a nonzero delay in the update of the leaky LMS (LLMS) algorithm on the overall performance is studied. The stability bound on the step size is obtained for the leaky delayed LMS (LDLMS) to ensure error convergence; bounds for LMS, DLMS, and LLMS can then be obtained as special cases. It is shown that leakage improves the performance of the DLMS by allowing for a larger bound on the step size, this making up for the reduction resulting from nonzero delay in updating the coefficients. Theoretical bounds are verified by simulations. Examples of the improved performance of LDLMS are also provided. The performance of the LDLMS is shown to reduce the detrimental effect of the delay on tracking nonstationarities.<>