An enhanced IAF-MPNLMS algorithm for sparse system identification

For a highly sparse impulse response the modified proportionate normalized least-mean-square (MPNLMS) algorithm converges slowly during the update of small coefficients, because the proportionality of these coefficients is ignored in the learning process of the algorithm. An individual-activation factor (IAF)-MPNLMS algorithm resolves this problem by assigning individual activation factors for the coefficients. However, it suffers from slow convergence if the input signal is highly correlated. In Enhanced (E)IAF-PNLMS algorithm, a new gain distribution strategy for the coefficients that have already almost converged is introduced. In this paper, a square-root(non-linear) activation factor is suggested for the IAF-MPNLMS algorithm and subsequently, gain redistribution strategy following the procedure given in the EIAF-PNLMS algorithm is adopted in updating the tap coefficients. The proposed algorithm converges faster than EIAF-PNLMS as well as with the other well-known MPNLMS and IAF-MPNLMS algorithms for identification of sparse system when input signal becomes highly correlated. We conclude numerical experiments to illustrate the performance of the proposed (EIAF-MPNLMS) algorithm. Simulation results exhibit that the EIAF-MPNLMS algorithm achieves faster convergence, outperforming the EIAF-PNLMS and other existing PNLMS type algorithms.