Enhanced Sparsity-Aware RLS Algorithm for Efficient Estimation of Time-Varying Sparse System

The sparsity-aware recursive least squares (RLS) algorithms have been designed to impose norm
$(l_{0}$
or
$l_{1}$
-norm) constraint on RLS iteration to exploit sparsity contained in the target system. However, there is a lack of adaptability upon time variation of sparsity. In this brief, an enhanced sparsity-aware (ESa)-RLS algorithm is proposed to enable efficient estimation of the target system with time-varying sparsity. Under the framework of non-uniform norm constraint, the proposed ESa-RLS incorporates the tuning of sparsity constraint factor and forgetting factor to provide multiple aspects of adaptability for time-varying sparsity. The iterative optimization of the proposed algorithm is designed to minimize the sparsity-aware cost function, which consists of both variable sparse constraints and a variable forgetting factor. Simulation results demonstrate the superiority of the proposed algorithm in terms of sparse exploitation, system tracking capability, and steady-state misadjustment, with only a slight increase in computational complexity. The proposed algorithm is particularly suitable for systems with time-varying sparsity, such as underwater acoustic (UWA) channels with sparsity uncertainty.