Stochastic Analysis of LMS Algorithm with Delayed Block Coefficient Adaptation

TL;DR

This paper introduces a stochastic analysis of the delayed block LMS algorithm, examining how pipelining delays and block sizes affect convergence, accuracy, and speed in high sample-rate adaptive filtering.

Contribution

It provides a novel joint analysis of pipelining and block processing effects on the LMS algorithm's performance, including bounds and accuracy estimates.

Findings

Large delay and small block size slow convergence for constant speed-up.

Small delay and large block size achieve faster convergence with similar steady-state MSE.

Monte Carlo simulations confirm the accuracy of the theoretical estimates.

Abstract

In high sample-rate applications of the least-mean-square (LMS) adaptive filtering algorithm, pipelining or/and block processing is required. As opposed to earlier work, pipelining and block processing are jointly considered to obtain what we refer to as the delayed block LMS (DBLMS) algorithm. Different stochastic analyses for the steady and transient states to estimate the step-size bound, adaptation accuracy, and adaptation speed based on the recursive relation of delayed block excess mean square error (MSE) are presented. The effect of different amounts of pipelining delays and block sizes on the adaptation accuracy and speed of the adaptive filter with different filter lengths and speed-ups are studied. It is concluded that for a constant speed-up, a large delay and small block size lead to a slower convergence rate compared to a small delay and large block size with almost the same steady-state MSE. Monte Carlo simulations indicate a good agreement with the proposed estimates for Gaussian inputs.