Normalized recursive least moduli algorithm with normalization by q-norm of filter input

This paper proposes normalized recursive least moduli (NRLM) algorithm for complex-domain adaptive filters in which the normalizing factor is q-norm of filter input. Stochastic models are given for two types of impulse noise found in adaptive filtering systems: one in observation noise and another at filter input. We first review q-norm and normalized least mean modulus (NLMM) algorithm, and then derive the NRLM algorithm. Analysis of the NRLM algorithm is developed to calculate theoretical convergence. Through experiment, we find that the filter convergence behavior does not critically depend on the value of q. This suggests use of infinity-norm which is easiest to compute. It is also demonstrated that the NRLM algorithm is effective in improving the filter convergence speed, while it enhances the robustness of the NLMM algorithm against both types of impulse noise. Validity of the analysis is confirmed by good agreement observed between simulations and theory.