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A variable-parameter normalized mixed-norm (VPNMN) adaptive algorithm

EURASIP JOURNAL ON ADVANCES IN SIGNAL PROCESSING 2012年第1期2012卷 1页

作者： Zerguine, Azzedine King Fahd Univ Petr & Minerals Dept Elect Engn Dhahran 31261 Saudi Arabia

Since both the least mean-square (LMS) and least mean-fourth (LMF) algorithms suffer individually from the problem of eigenvalue spread, so will the mixed-norm LMS-LMF algorithm. Therefore, to overcome this problem for the mixed-norm LMS-LMF, we are adopting here the same technique of normalization (normalizing with the power of the input) that was successfully used with the LMS and LMF separately. Consequently a new normalized variable-parameter mixed-norm (VPNMN) adaptive algorithm is proposed in this study. This algorithm is derived by exploiting a time-varying mixing parameter in the traditional mixed-norm LMS-LMF weight update equation. The time-varying mixing parameter is adjusted according to a well-known technique used in the adaptation of the step-size parameter of the LMS algorithm. In order to study the theoretical aspects of the proposed VPNMN adaptive algorithm, our study also addresses its convergence analysis, and assesses its performance using the concept of energy conservation. Extensive simulation results corroborate our theoretical findings and show that a substantial improvement, in both convergence time and steady-state error, can be obtained with the proposed algorithm. Finally, the VPNMN algorithm proved its usefulness in a noise cancellation application where it showed its superiority over the normalized least-mean square algorithm.

关键词： LMS algorithm NLMS algorithm LMF algorithm mixed-norm algorithms normalized mixed-norm algorithms

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Variable weight mixed-norm adaptive algorithm

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2002年第6期21卷 547-566页

作者： Zerguine, A King Fahd Univ Petr & Minerals Dept Elect Engn Dhahran 31261 Saudi Arabia

In this work, the convergence analysis of the variable weight mixed-norm least-mean squares (LMS)-least mean-fourth (LMF) adaptive algorithm is derived. The proposed algorithm minimizes an objective function defined as a weighted sum of the LMS and LMF cost functions, where the weighting factor is time varying and adapts itself to allow the algorithm to keep track of the variations in the environment. As a by-product of this novel approach, new necessary and sufficient conditions for the LMF algorithm have been derived. Furthermore, a more general expression for the excess steady-state error for the LMF algorithm has been derived.

关键词： adaptive algorithms LMS and LMF algorithms mixed-norm algorithms

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