Improving convergence of the MPNLMS algorithm for echo cancellation

Recently, μ-law proportionate normalized least mean-square algorithm (MPNLMS) has been proposed. This algorithm exploits an approximation of the optimal proportionate step size to keep the fast initial convergence speed during the whole adaptation process until the adaptive filter reaches its steady state. However, the convergence performance of MPNLMS demonstrates slow convergence speed when the excitation signal is colored. The affine projection algorithm (APA) achieves a fast convergence speed for correlated input signals by updating the weight vector based on several previous input vectors. In this paper, generalization of the reliable method from the affine projection algorithm to a MPNLMS algorithm is presented. The proposed algorithm is evaluated using impulse responses with various degrees of sparseness. Simulations show good results in terms of speed of convergence and final mean-squared error.