Normalized Recursive Least Moduli algorithm with p-modulus of error and q-norm of filter input

This paper proposes a new adaptation algorithm named Normalized Recursive Least Moduli (NRLM) algorithm which employs “p-modulus” of error and “q-norm” of filter input. p-modulus and q-norm are generalization of the modulus and norm used in complex-domain adaptive filters. The NRLM algorithm with p-modulus and q-norm makes adaptive filters fast convergent and robust against two types of impulse noise: one is found in observation noise and another at filter input. We develop theoretical analysis of the algorithm for calculating filter convergence. Through experiment with simulations and theoretical calculations, effectiveness of the proposed algorithm is demonstrated. We also find that the filter convergence does not critically depend on the value of p or q, allowing use of p = q = infinity that makes it easiest to calculate the p-modulus and q-norm. The theoretical convergence is in good agreement with the simulation results which validates the analysis.