A Novel Modified Improved Propotionnate Fast NLMS Algorithm for Acoustic Echo Cancellation

The Modified Improved Proportionate Normalized Least Mean Square (m-IPNLMS) algorithm enhanced the performance of the original IPNLMS algorithm by establishing a relationship between an important parameter known as the proportional term and the sparseness measure built on the $\boldsymbol{\ell}_2$ and $\boldsymbol{\ell}_1$ norms. To further improve the performance of the m-IPNLMS algorithm, we propose first, to extend the Fast NLMS concept to the m-IPNLMS algorithm and then, by using the sparseness measure based on the $\boldsymbol{\ell}_1, \boldsymbol{\ell}_2$ and $\boldsymbol{\ell}_\infty$ norms, which provide adequate representations of both dispersive and sparse impulse responses, we also replace the quadratic output filtering error with a recursive estimation version. The proposed algorithm, called Novel-Modified IPNLMS (Novel-m-IPNLMS) algorithm is superior in terms of convergence speed, tracking ability and steady-state mean square error (MSE) for sparse and dispersive systems. Simulation results are presented to validate the effectiveness of the suggested algorithm.