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A joint-optimization method is proposed for enhancing the behavior of the l 1 -norm- and sum-log norm-penalized NLMS algorithms to meet the requirements of sparse adaptive channel estimations. The improved channel estimation algorithms are realized by using a state stable model to implement a joint-optimization problem to give a proper trade-off between the convergence and the channel estimation behavior. The joint-optimization problem is to optimize the step size and regularization parameters for minimizing the estimation bias of the channel. Numerical results achieved from a broadband sparse channel estimation are given to indicate the good behavior of the developed joint-optimized NLMS algorithms by comparison with the previously proposed l 1 -norm- and sum-log norm-penalized NLMS and least mean square (LMS) algorithms.

Norm Penalized Joint-Optimization NLMS Algorithms for Broadband Sparse Adaptive Channel Estimation