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 ${\ell }_1$-regularized proportionate recursive least-squares algorithm (DR-${\ell }_1$-PRLS) for sparse adaptive equalization. The proposed method incorporates a data reuse (DR) mechanism into the ${\ell }_1$-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 ${\ell }_1$ 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, ${\ell }_1$-PRLS, and DR-PRLS algorithms. Simulation results show that, under sparse underwater acoustic channel conditions, DR-${\ell }_1$-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.

Accurate estimation of sparse underwater acoustic channels is challenging because of multipath delay spread, correlated inputs, and impulsive non-Gaussian noise. Existing KRSL-based algorithms still suffer from limited convergence speed and tracking capability in time-varying sparse scenarios. This paper proposes a VFF-PRKRSL algorithm, which jointly introduces an error-driven variable forgetting factor and a proportionate gain matrix into the recursive KRSL framework to achieve adaptive historical-information weighting and enhanced updating of dominant taps. Simulation results show that for Bellhop-generated underwater acoustic channels with sparsity levels of 0.125 and 0.4688, the proposed algorithm achieves NMSD values of $-38.4763$ dB and $-37.9417$ dB at the 2000th iteration, improving upon PRKRSL by approximately 5.31 dB and 5.29 dB, respectively. Under Cauchy noise, it reaches an NMSD of $-46.3042$ dB, about 5.95 dB better than PRKRSL. Ablation results indicate that the variable forgetting factor is the main source of the performance gain and is complementary to the proportionate update mechanism. These results demonstrate that VFF-PRKRSL outperforms existing methods in convergence speed, steady-state accuracy, and robustness against impulsive noise.