An affine combination of two adaptive filters for system identification with variable sparsity

Low complexity Normalized Least Mean Square (NLMS) adaptive algorithm is widely used in the adaptive system identification applications. To exploit the sparse impulse response of the system, different sparse penalties are introduced into the error function of the NLMS algorithm. Reweighted Zero Attracting-NLMS (RZA-NLMS) algorithm based on l1-norm relaxation offers improved performance in identifying the system with sparse echo path but when the system is non-sparse, NLMS algorithm dominates the sparse adaptive algorithm. In order to identify the system with varying sparseness, a new strategy is required. In this paper, we propose an affine combination of RZA-NLMS and NLMS filters used for system identification with variable sparsity. The robust performance of our proposed approach has been verified from the MATLAB simulations.