LAUSR

For adaptive echo cancellation in hands-free communication systems, a family of bias-compensated sparsity-aware normalized least mean M-estimate (NLMM) algorithms is proposed that are robust to both impulsive noise and noisy inputs. First, we define a new cost function that integrates the M-estimate function of the a posteriori error, the Riemannian distance between the current and previous weight vectors, and the $L_{0}$ norm of the weighted current weight vector. By minimizing the defined cost function, we develop the sparsity-aware NLMM algorithms to achieve robustness against the impulsive noise. Then, an improved cost function is developed and proved to be unbiased in the presence of input noise. This leads to the development of the bias-compensated sparsity-aware NLMM algorithms that can deal with noisy inputs. The stability and computational complexity of the proposed algorithms are analyzed as well. Experimental results for system identification and adaptive echo cancellation demonstrate that the proposed algorithms outperform the existing ones in terms of convergence rate and steady-state misalignment.