Dual parameters optimization lp-LMS for estimating underwater acoustic channel with uncertain sparsity

The sparse norm constraint (l0,l1,l2 and lp) least mean square algorithm (LMS) is established technique for modeling sparse systems. However, when applied in target systems with uncertain sparsity, such as temporal-spatial-varying sparse underwater acoustic (UWA) channel, the parameters tuning (the step-size and parameter p) of lp-LMS faces significant challenges. In this paper, with the purpose to simplify the complicated dual-parameter selection problem via gradient strategy, a dual parameters optimization lp-LMS (DPO-lp-LMS) algorithm is derived by iteratively adjusting the step-size and the parameters p in parallel along the descent gradient. Convergence analysis of the proposed algorithm is given. A numerical simulation under varying sparsity systems exhibits that the proposed algorithm outperforms the lp-LMS algorithms driven by the existing optimization approaches in convergence speed and steady-state error. Meanwhile, a field shallow water experiment of UWA communication demonstrated that the proposed algorithm achieves superior performance under the framework of direct adaptation turbo equalization (DA-TEQ).