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In all presented analyses of the normalized subband adaptive filter (NSAF) algorithm, there is a common assumption that the length of the adaptive filter is equal to that of the unknown system. In many practices, however, the adaptive filter usually works in an under-modeling situation. Namely, the length of the adaptive filter is less than that of the unknown system. Therefore, for this case, the existing analysis results for the NSAF algorithm are not applicable. In this paper, we analyze the performance of the deficient length NSAF algorithm based on some reasonable assumptions and approximations. More precisely, the expressions that characterize the transient-state and steady-state mean-square behavior of the algorithm are presented. Simulation results in various scenarios support our theoretical expressions. In addition, based on our analyses, a variable step size NSAF algorithm suitable for the under-modeling case is developed, which improves the performance. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose a new time-varying step-size for the affine projection (AP) algorithm based on the minimization of the mean-square error (MSE) at each time instant. The step-size is dependent on accessible quantities and, therefore, does not need approximation. In addition, we show how the new step-size control equations can be incorporated into the fast AP (FAP) algorithm leading to a reduced complexity implementation of the proposed algorithm. The algorithm improved performance characteristics are verified by simulation experiments. [Copyright &y& Elsevier]