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

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... y. 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. Appendix B, section B.1, complements this chapter by analyzing the finite-wordlength effects in LMS algorithms. The LMS algorithm is by far the most widely used algorithm in adaptive filtering for several reasons. The main features that attracted the use of the LMS algorithm are low computational complexity, proof of convergence in stationary environment, unbiased convergence in the mean to the Wiener solution, and stable behavior when implemented with finite-precision arithmetic. The convergence analysis of the LMS presented here utilizes the independence assumption. P.S.R. Diniz, Adaptive Filtering,