A study of echo in VoIP systems and synchronous convergence of the μ-law PNLMS algorithm

A recent algorithm, the mu-law PNMLS, introduces a stepsize proportionate to the mu-law of the estimated tap coefficient to cancel sparse echo in telephony over packet-switch networks. It is derived by optimizing the following criterion: fastest convergence is obtained when all coefficients reach the vicinity of their target value at the same time. We present a study of synchronous convergence as introduced in this algorithm. Simulations for a 2-tap adaptive filter illustrate the optimality of mu-law PNLMS. We then compare the performances of this algorithm on multiple echo paths. This comparison shows some restrictions in the applicability of the optimality criterion and highlights possible improvements in robustness for this algorithm.