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 Jmax 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 Jmax 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.