A noise-resilient affine projection algorithm and its convergence analysis

Recently a new normalized least mean square algorithm has been proposed by minimizing the summation of the squared Euclidean norms of the changes between the weight vectors to be updated and the past weight vector. The resultant algorithm exhibits noise resilience in that they prevent the adaptive filter from fluctuating around an optimal solution, but its convergence behavior has not been studied in detail. Thus, we first apply the constrained criterion to an affine projection algorithm (APA) for identifying a highly noisy system by reusing weight vectors. Since the performance of the APA declines under low signal-to-noise ratio (SNR) conditions, this approach is more effective for decreasing the steady-state mean-square deviation (MSD). Then, we analyze the convergence behavior of the proposed APA theoretically using energy conservation arguments. The experimental results show that the proposed theoretical results agree well with the simulation results.