Tracking of time-varying channels using two-step LMS-type adaptive algorithm

This paper presents a modified version of the two-step least-mean-square (LMS)-type adaptive algorithm motivated by the work of Gazor. We describe the nonstationary adaptation characteristics of this modified two-step LMS (MG-LMS) algorithm for the system identification problem. It ensures stable behavior during convergence as well as improved tracking performance in the smoothly time-varying environments. The estimated weight increment vector is used for the prediction of weight vector for the next iteration. The proposed modification includes the use of a control parameter to scale the estimated weight increment vector in addition to a smoothing parameter used in the two-step LMS (G-LMS) algorithm, which controls the initial oscillatory behavior of the algorithm. The analysis focuses on the effects of these parameters on the lag-misadjustment in the tracking process. The mathematical analysis for a nonstationary case, where the plant coefficients are assumed to follow a first-order Markov process, shows that the MG-LMS algorithm contributes less lag-misadjustment than the conventional LMS and G-LMS algorithms. Further, the stability criterion imposes upper bound on the value of the control parameter. These derived analytical results are verified and demonstrated with simulation examples, which clearly show that the lag-misadjustment reduces with increasing values of the smoothing and control parameters under permissible limits