# An affine combination of two LMS adaptive filters - Transient mean-square analysis

Bershad, Neil J. and Bermudez, José Carlos Moreira and Tourneret, Jean-Yves An affine combination of two LMS adaptive filters - Transient mean-square analysis. (2008) IEEE Transactions on Signal Processing, 5 (5). 1853-1864. ISSN 1053-587X

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Official URL: http://dx.doi.org/10.1109/TSP.2007.911486

## Abstract

This paper studies the statistical behavior of an affine combination of the outputs of two LMS adaptive filters that simultaneously adapt using the same white Gaussian inputs. The purpose of the combination is to obtain an LMS adaptive filter with fast convergence and small steady-state mean-square deviation (MSD). The linear combination studied is a generalization of the convex combination, in which the combination factor $\lambda(n)$ is restricted to the interval $(0,1)$. The viewpoint is taken that each of the two filters produces dependent estimates of the unknown channel. Thus, there exists a sequence of optimal affine combining coefficients which minimizes the MSE. First, the optimal unrealizable affine combiner is studied and provides the best possible performance for this class. Then two new schemes are proposed for practical applications. The mean-square performances are analyzed and validated by Monte Carlo simulations. With proper design, the two practical schemes yield an overall MSD that is usually less than the MSD's of either filter.

Item Type: Article The original publication is available on http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78 International peer-reviewed journal Adaptive filtering Other partners > University of California - UCIrvine (USA)Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)Other partners > Universidade Federal de Santa Catarina - UFSC (BRAZIL) Institut de Recherche en Informatique de Toulouse - IRIT (Toulouse, France) - Signal et Communication - SC download Jean-yves TOURNERET 13 May 2008 08:17

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