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Abstract We propose two sparsity-aware normalized subband adaptive filter (NSAF) algorithms by using the gradient descent method to minimize a combination of the original NSAF cost function and the l 1 -norm penalty function on the filter coefficients. This l 1 -norm penalty exploits the sparsity of a system in the coefficients update formulation, thus improving the performance when identifying sparse systems. Compared with prior work, the proposed algorithms have lower computational complexity with comparable performance. We study and devise statistical models for these sparsity-aware NSAF algorithms in the mean square sense involving their transient and steady-state behaviors. This study relies on the vectorization argument and the paraunitary assumption imposed on the analysis filter banks, and thus does not restrict the input signal to being Gaussian or having another distribution. In addition, we propose to adjust adaptively the intensity parameter of the sparsity attraction term. Finally, simulation results in sparse system identification demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

Abstract A bias-compensated constrained least mean square (BC-CLMS) adaptive filter algorithm for noisy input is proposed. To derive the proposed algorithm, we present a novel cost function whose gradient vector is unbiased. Thereby, the proposed algorithm can mitigate the effect of input noise and obtain an unbiased estimation. Then, the detail performance analysis of the proposed algorithm is also provided. Finally, simulations are carried out to illustrate the advantage of the proposed algorithm. In addition, the correctness of performance analysis is also verified by simulations. [ABSTRACT FROM AUTHOR]