Proportionate adaptive algorithms for network echo cancellation

By analyzing the coefficient adaptation process of the steepest descent algorithm, the condition under which the fastest overall convergence will be achieved is obtained and the way to calculate optimal step-size control factors to satisfy that condition is formulated. Motivated by the results and using the stochastic approximation paradigm, the μ-law PNLMS (MPNLMS) algorithm is proposed to keep, in contrast to the proportionate normalized least-mean-square (PNLMS) algorithm, the fast initial convergence during the whole adaptation process in the case of sparse echo path identification. Modifications of the MPNLMS algorithm are proposed to lower the computational complexity.