Transcription of THE LEAST-MEAN-SQUARE (LMS) ALGORITHM
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THE LEAST-MEAN-SQUARE (LMS) ALGORITHM
3. THE LEAST-MEAN-SQUARE (LMS). ALGORITHM . INTRODUCTION. The LEAST-MEAN-SQUARE (LMS) is a search ALGORITHM in which a simplification of the gradient vector computation is made possible by appropriately modifying the objective function [1]-[2]. The LMS. ALGORITHM , as well as others related to it, is widely used in various applications of adaptive filtering due to its computational simplicity [3]-[7]. The convergence characteristics of the LMS ALGORITHM are examined in order to establish a range for the convergence factor that will guarantee stability. The convergence speed of the LMS is shown to be dependent on the eigenvalue spread of the input signal correlation matrix [2]-[6]. In this chapter, several properties of the LMS ALGORITHM are discussed including the misadjustment in stationary and nonstationary environments [2]-[9] and tracking performance [10]-[12]. The analysis results are verified by a large number of simulation examples.
78 Chapter 3 The Least-Mean-Square (LMS) Algorithm If good estimates of matrix R, denoted by Rˆ(k), and of vector p, denoted by ˆp(k), are available, a steepest-descent-based algorithm can be used to search the Wiener solution of equation (3.1) as
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