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

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.