ADMM-based l1 - l1 optimization algorithm for robust sparse channel estimation in OFDM systems

In this paper, an l(1) - l(1) optimization algorithm based on the alternating direction method of multipliers (ADMM) is proposed for robust sparse channel estimation in OFDM systems. Particularly, this algorithm considers the sparsity of the channel impulse response (CIR) often encountered in multipath channels. Further, to improve the performance of the proposed algorithm in the presence of impulsive noise, the residual error is modeled using an l(1)-norm loss function which is derived from describing the underlying contamination as additive random samples obeying to a Laplacian distribution. Furthermore, the solution of the proposed algorithm is obtained by reformulating the unconstrained l(1) - l(1) minimization as a constrained optimization problem. To reduce the complexity of this constrained formulation, a proximal linearization is included into the augmented Lagrangian which facilitates the iterative computation of the CIR update. In addition, in order to stably estimate the channel coefficients, a heuristic rule for updating the penalty parameter is proposed. Extensive numerical simulations are shown for evaluating the behavior of the proposed method in the presence of impulsive noise, where the proposed approach outperforms other linear and robust approaches under multiple performance criteria. (C) 2019 Elsevier B.V. All rights reserved.