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By L. Morales

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5) i  That is to say, getting  is equivalent to getting the MSE. A first-order random-walk model is widely used to get the tracking performance in nonstationary environments [11], [12], which assumes that w o ,i appearing in (3) undergoes random variations of the form w o ,i  1  w o , i  qi , (6) where qi is  M  1  column vector and denotes some random perturbation. , zero-mean, with  M  M  covariance matrix E qiqH  Q , which is independent of the regressor sequences u i  and weight-error i i.

2 Steady-State Performance Analyses of Adaptive Filters Bin Lin and Rongxi He College of Information Science and Technology, Dalian Maritime University, Dalian, China 1. Introduction Adaptive filters have become a vital part of many modern communication and control systems, which can be used in system identification, adaptive equalization, echo cancellation, beamforming, and so on [l]. The least mean squares (LMS) algorithm, which is the most popular adaptive filtering algorithm, has enjoyed enormous popularity due to its simplicity and robustness [2] [3].

The least mean squares (LMS) algorithm, which is the most popular adaptive filtering algorithm, has enjoyed enormous popularity due to its simplicity and robustness [2] [3]. Over the years several variants of LMS have been proposed to overcome some limitations of LMS algorithm by modifying the error estimation function from linearity to nonlinearity. Sign-error LMS algorithm is presented by its computational simplicity [4], least-mean fourth (LMF) algorithm is proposed for applications in which the plant noise has a probability density function with short tail [5], and the LMMN algorithm achieves a better steady state performance than the LMS algorithm and better stability properties than the LMF algorithm by adjusting its mixing parameter [6], [7].

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