Convergence Performance Improvement of Affine Projection Adaptive Algorithm for Sparse Linear System Modeling with Correlated Input Signals

One of the most important challenges for the adaptive filtering is the slow convergence rate of adaptive algorithm against highly correlated input signals. The affine projection adaptive algorithm (APA) is an extension of the well-known normalized least mean square (NLMS) algorithm which achieves a higher convergence rate in both full-band and sub-band structures. In this paper, to further improve the convergence rate of the algorithm against high-correlation input signals in the application of sparse linear system modeling, a sub-band APA is proposed in which the number of projection vectors is determined as a function of the estimated sub-band mean square error (MSE). In addition, variable sub-band step-sizes are proposed as a function of filter weights and the estimated MSE such that at the initial convergence stage, bigger weights make an increased contribution to the adaptation process while during convergence, the contributions approach the same amount. The proposed idea improves the convergence rate and lowers the steady-state MSE. Simulation results for the sparse linear system modeling and for the application of acoustic echo cancellation, verify the superiority of the proposed algorithm in the convergence performance and estimation accuracy of the acoustic path coefficients over its counterparts.