Robust sparse channel estimation and equalization in impulsive noise using linear programming

In this paper, an algorithm for sparse channel estimation, called ℓ1-regularized least-absolutes (ℓ1-LA), and an algorithm for equalization, called linear least-absolutes (LLA), in non-Gaussian impulsive noise are proposed. The proposed approaches are based on the minimization of the absolute error function, rather than the squared error function. By replacing the standard modulus with the ℓ1-modulus of complex numbers, the resulting optimization problem can be efficiently solved through linear programming. The selection of an appropriate regularization parameter is also addressed. Numerical results demonstrate that the proposed algorithms, compared with the classical methods, are more robust to impulsive noise and have a superior accuracy.