A New Variable Step Size Control Method for the Transform Domain LMS Adaptive Algorithm

Abstract

This paper develops a new adaptive step size control method for the transform domain least mean-square (TDLMS) adaptive algorithm. The time-varying step size is an efficient approximation of an optimal step size based on a proposed cost function, therefore leading to significant improvements in the performance characteristics of the TDLMS algorithm. Mean-square analysis is provided, and an expression for the steadystate excess mean-squared error (MSE) is derived. Simulation experiments confirm the algorithm's enhanced convergence properties and verify the theoretical steady-state MSE results.

An LMS adaptive algorithm with a new step-size control equation

“…(13) as follows [17]: where 0ogo1, which controls the quality of estimations. A sufficient condition for mean coefficient vector convergence of the proposed algorithm is given by [9,10] 0oE mðnÞ…”

“…Here, it is extended to the LMS algorithm, and the resulting algorithm performance is examined against some popular VSSLMS algorithms. Similar to the TDLMS case [17], it will be shown that the proposed algorithm possesses several advantages that make it favorable in practical applications compared with other existing VSSLMS algorithms. The algorithm uses one parameter to control its step-size equations, where the parameter value can be used to provide a good estimation of the algorithm steady state misadjustment.…”

“…This approach was first applied in [17] to the Transform Domain LMS (TDLMS) algorithm. Here, it is extended to the LMS algorithm, and the resulting algorithm performance is examined against some popular VSSLMS algorithms.…”

A new switch-mode noise-constrained transform domain NLMS adaptive filtering algorithm

“…In conventional TDNLMS algorithms, the step-size is fixed and therefore the convergence speed is limited by the desired misadjustment. This has motivated considerable interest in designing reliable and efficient variable stepsize (VSS) algorithms to overcome this drawback [6][7][8][9][10][11]. These algorithms aim to employ large step-size to speed up the convergence rate initially and gradually decrease the step-size in order to achieve a low excess mean square error (EMSE).…”

“…This is often accomplished by varying the stepsize values based on a certain measure of convergence status [7][8][9][10][11]. In [6], the modified VSS TDNLMS (MVSS-TDNLMS) algorithm varies the step-size by estimating the noise power.…”