Distortion-Constraint-Based Group Sparse Channel Estimation Under $\alpha$ -Stable Noise

The ever-increasing requirements of wireless communications have inspired the search for a better method to tackle the problem of group sparse channel estimation in practical applications. Sparsity with group structure is encountered in numerous applications, but efforts to devise group sparse adaptive methods remain scarce, especially under impulse noise with symmetric alpha stable (<inline-formula> <tex-math notation="LaTeX">$S\alpha S$ </tex-math></inline-formula>) statistics. In this paper, we propose an improved adaptive algorithm using the distortion constraints based group sparse recursive least square (DC-GRLS) to exploit channel group sparsity and obtain robust performance under the background of <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> stable noise. We introduce distortion constraints combined with the mixed norms (<inline-formula> <tex-math notation="LaTeX">$l_{p,q}$ </tex-math></inline-formula> norm), to obtain the relative balance between correctiveness and conservativeness. The MATLAB simulation results reveal that the improved algorithm can improve robustness under <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> stable noise when compared with the <inline-formula> <tex-math notation="LaTeX">$l_{p,q}$ </tex-math></inline-formula> group algorithms and it can effectively predict the channel impulse response for a group sparse structure.