Improved affine projection algorithms with selective projection order for channel identification

One of the most significant challenges in adaptive filters is the slow convergence speed of the adaptive algorithm when dealing with highly correlated input signals. The adaptive affine projection algorithm (APA) which is a generalized version of the well-known normalized least mean square algorithm, improves convergence speed against correlated input signals, but with a high steady-state weight error and considerable computational complexity. In this paper, to enhance the convergence performance of APA and reduce its complexity, a selective projection order APA and its proportionate variant are proposed. In these algorithms, the projection order varies during convergence. Initially, a high projection order is employed in adaptation, gradually decreasing as the mean-square deviation (MSD) of the weight error decreases. This adaptive approach maintains a high initial convergence speed while reducingss the steady-state error. Moreover, the computational complexity decreases during convergence. Additionally, we propose a combination of proportionate and non-proportionate adaptive algorithms, leveraging the variation of MSD during convergence. Simulation results in identification of sparse/dispersive channels confirm the improved convergence performance of the proposed algorithms compared to competing adaptive algorithms.