Gain allocation in proportionate-type NLMS algorithms for fast decay of output error at all times

In this paper, we propose three new proportionate-type NLMS algorithms: the water filling algorithm, the feasible water filling algorithm, and the adaptive μ-law proportionate NLMS (MPNLMS) algorithm. The water filling algorithm attempts to choose the optimal gains at each time step. The optimal gains are found by minimizing the mean square error (MSE) at each time with respect to the gains, given the previous mean square weight deviations. While this algorithm offers superior convergence times, it is not feasible. The second algorithm is a feasible version of the water filling algorithm. The adaptive MPNLMS (AMPNLMS) algorithm is a modification of the MPNLMS algorithm. In the MPNLMS algorithm, the parameter μ of the μ-law compression is constant. In the AMPNLMS algorithm the parameter μ is allowed to vary with time. This modification allows the algorithm more flexibility when attempting to minimize the MSE. Compared with several feasible algorithms, the AMPNLMS algorithm has the fastest MSE decay for almost all times.