## 1 Introduction  
In recent years, the expanding scope of marine exploration and the burgeoning Internet of Underwater Things (IoUT) in maritime domains have increased the demand for high-data-rate and reliable wireless communication links [1; 2]. Underwater Acoustic (UWA) transmission, leveraging sound waves for their lower attenuation and longer propagation range compared to alternative carriers like electromagnetic and optical waves, is still the most practical solution in ocean environments [3]. However, the development of high-performance Underwater Acoustic Communication (UAC) systems is fundamentally constrained by the intrinsic properties of the UWA channel and the availability of accurate Channel State Information (CSI) [4]. Channel estimation remains a critical challenge in UAC systems. This is compounded by the dynamic and diverse nature of ocean environments and the high dimensionality of the estimation problem due to the large delay and Doppler spreads, along with the need to minimize the number of pilot or training symbols to reduce overhead [5; 6; 7]. Extensive research has been conducted on acquiring channel information for various modulation schemes through different methods. Compared to conventional methods such as Least Squares (LS) [8] and Minimum Mean Squared Error (MMSE) [9], it is widely recognized that Compressed Sensing (CS)-based algorithms offer a more efficient solution for accurate channel estimation with low overhead [10; 11; 12; 13; 14]. UWA channels often exhibit sparsity in both delay and Doppler domains when the transmission bandwidth is sufficiently wide to ensure that multipath arrivals are resolvable [10; 11; 12]. Iterative greedy algorithms represented by Orthogonal Matching Pursuit (OMP) are the most popular CS-based methods used in practice due to their low computation cost [15; 16]. Enhanced variants like Stagewise OMP (StOMP) [17] and the more recent Gram-Schmidt OMP (GSOMP) [13], have improved the efficiency and accuracy of the original OMP by refining atom selection strategies and optimizing termination conditions. However, greedy methods typically yield sub-optimal solutions, and their performance often relies on having prior knowledge of the sparsity level of the channel [18]. Convex relaxation methods, represented by \(\ell_{1}\)-norm relaxation or Basis Pursuit Denoising (BPDN), provide more stable solutions in noisy UWA environments, supported by their stronger theoretical guarantees and global optimality [19]. Classic BPDN solvers like the Interior-Point Method (IPM), despite being computationally intensive, are known for their high accuracy and convergence speed [20; 21]. For large-scale problems or in scenarios where real-time processing is paramount, advanced solvers such as the Proximal Gradient Method (PGM) [22; 23] and the Alternating Direction Method of Multipliers (ADMM) [24; 25] offer a desirable compromise between computational efficiency and the precision required for effective channel estimation. Despite the success of the aforementioned methods in UAC applications, their effectiveness is largely predicated on the assumption of Additive White Gaussian Noise (AWGN) [26]. This assumption, however, does not always hold in real-world scenarios as UWA channels often contain interference, especially impulsive noise from various natural sources and human activities [27]. Addressing this, our previous work in [28] introduced a low-complexity, easily implementable ADMM-based algorithm. Recent developments in Deep Learning (DL) have offered promising solutions to the UWA channel estimation. In [29], a five-layer neural network trained on offline simulated data is developed for channel estimation and symbol detection in wireless Orthogonal Frequency Division Multiplexing (OFDM) systems. For UWA OFDM systems, [30] introduces a DL-based channel estimator that demonstrates improved performance over traditional methods such as LS and MMSE. Meanwhile, DL is also employed in UWA channel prediction. In [31], [PERSON] et al.