Abstract

This paper deals with efficient algorithms in the sense of minimization of the computational complexity for least-squares (LS) adaptive filters with finite memory. These filters obtain the current estimate of the desired response using only a fixed finite number of past data. First, two new fast recursive least-squares algorithms with computational complexities <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">14m</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">15m</tex> multiplications and divisions per recursion (MADPR), respectively, are introduced ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</tex> is the filter order). Then a new estimation-error-oriented recursive modified Gram-Schmidt (RMGS) scheme with a complexity of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2m^{2} + 10m</tex> MADPR is given. Finally, the learning characteristics of these algorithms are discussed and some simulation results are included.

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