Proportionate kernel risk sensitive loss adaptive filtering algorithms and their performance analysis for sparse system identification under non-Gaussian noise

In practical communication systems, achieving accurate channel estimation under sparse non-Gaussian noise channel environments is a prerequisite for ensuring reliable signal transmission. However, most existing methods focus on system identification under Gaussian noise environments. Although the Kernel Risk-Sensitive Loss (KRSL) algorithm exhibits excellent steady-state performance in non-Gaussian impulsive noise, it fails to fully utilize prior channel information. To address this issue, we propose the proportionate KRSL (PKRSL) algorithm. This algorithm improves the recursive version of the KRSL algorithm by introducing a proportionate matrix. Concurrently, we develop the zero-attracting (ZA), reweighted zero-attracting (RZA), and l0-norm variants with proportionate matrix, named as the convex regularized PKRSL (CR-PKRSL) algorithm. While preserving robustness against non-Gaussian noise, the proposed algorithms enable more efficient integration of prior channel sparsity information and make better use of limited training sequences. This not only significantly accelerates the convergence speed but also reduces the estimation error of the algorithms. Theoretical analysis of the PKRSL algorithm is conducted from the perspective of first-order and second-order statistical characteristics of steady-state, and the selection ranges for the step size and convex penalty strength are provided. The results demonstrate that under sparse channel conditions and in a non-Gaussian noise environment, both the PKRSL and CR-PKRSL algorithms exhibit greater robustness and faster convergence speed compared with traditional algorithms. Finally, experimental validations confirm the consistency between the theoretically derived steady-state deviation and the simulation results, thus verifying the correctness of the theoretical analysis.