Adaptive Filtering pp 71-131 | Cite as

# The Least-Mean-Square (LMS) Algorithm

## Abstract

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 of 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], tracking performance, and finite wordlength effects [10]–[12].

## Keywords

Quantization Error Adaptive Filter Filter Coefficient Convergence Factor Convergence Path## Preview

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