A novel sparse system estimation method based on least squares, ℓ1-norm minimization and shrinkage

In this article, a novel low-complexity block-processing sparse system estimation method, based on least squares (LS), ℓ₁-norm minimization and support shrinkage, is proposed. The proposed method can be seen as a counterpart for the Least Absolute Shrinkage and Selection Operator (LASSO), in the sense that the proposed method aims to find the vector that minimizes its ℓ₁-norm subject to a maximum arbitrary value J_max for the LS cost function. Thus, it is suitable to be used when there is no a priori knowledge of the maximum ℓ₁-norm value of the system impulse response. In addition, making J_max directly proportional to the minimum LS cost function grants the proposed method low sensitivity to wide ranges of signal to noise-plus-interference ratio. Simulation results show that the proposed method has better convergence performance than the ordinary Full-support Least Squares (LS), the Recursive Least Squares with ℓ₁-norm regularization (ℓ₁-RLS), the Relaxations and the Basis Pursuit Denoising (BPDN) estimation methods.