A DR-ℓ₁-PRLS Approach to Adaptive Equalization in Single-Carrier UWA Communication

In single-carrier underwater acoustic (UWA) communication systems, sparse multipath channels and long delay spreads pose significant challenges to adaptive equalization, often leading to limited steady-state accuracy and degraded detection performance. To address this issue, this paper proposes a data reuse-based ℓ1-regularized proportionate recursive least-squares algorithm (DR-ℓ1-PRLS) for sparse adaptive equalization. The proposed method incorporates a data reuse (DR) mechanism into the ℓ1-PRLS framework, enabling multiple equivalent uses of each received-reference sample pair without increasing pilot overhead. Meanwhile, by combining the proportionate update strategy with the ℓ1 sparsity constraint, the structural information of sparse channels can be more fully exploited, thereby improving parameter estimation accuracy. Numerical simulations are conducted to evaluate the proposed method in terms of convergence behavior, tracking capability, computational complexity, and bit error rate (BER), and comparisons are made with LMS, RLS, PRLS, ℓ1-PRLS, and DR-PRLS algorithms. Simulation results show that, under sparse underwater acoustic channel conditions, DR-ℓ1-PRLS achieves lower steady-state error and better BER performance while maintaining good tracking capability, thereby demonstrating its effectiveness and robustness for sparse adaptive equalization in single-carrier underwater acoustic communications.