Adaptive regularization in frequency-domain NLMS filters

Regularization is an important part of adaptive filter design. Traditionally, the regularization parameter has been empirically selected, as there has not been a lot of work in the literature for determining an optimal method for finding its best value. In this work, we propose an adaptive method for finding the regularization parameter in the normalized least-mean-square (NLMS) algorithm. Furthermore, we apply this regularization approach in a frequency-domain version of the NLMS algorithm, in which a separate regularization parameter is computed for each frequency bin. Simulation results show that computing the regularization parameter for each frequency bin separately provided better performance for the filter, for the common case of colored noise excitation.