## 2 Related Works  
The UWA channel is severely band-limited, and exhibits time-varying excessive delay spread. To this end, the sparse structure of the UWA channel can be exploited to improve the estimation performance, as most channel energy of the UWA channel is concentrated on a few paths [18; 19]. The paths of the UWA channel also tend to be clustered-sparse [20], which has been frequently observed based on field experiments at different locations [9; 10; 11; 12; 13]. A detailed investigation on the variation of the significant paths in each cluster is presented in [21]. Based on the observation of channel sparsity, compressed sensing (CS)-based sparse channel estimation methods [22; 23; 24] have been studied, such as the greedy matching pursuit (MP) and orthogonal matching pursuit (OMP), which were adopted in [18; 25], aiming to estimate the UWA channel impulse response (CIR) and the channel delay-Doppler-spread function, respectively. In order to reduce the convergence error of the OMP algorithm, the compressed sampling matching pursuit (CoSaMP) algorithm is proposed in [26]. However, CoSaMP-based channel estimators require knowledge of the channel sparsity level, which is difficult to obtain accurately in advance in practical applications. The joint sparsity among adjacent OFDM blocks was exploited by the simultaneous OMP (SOMP) [27] for higher estimation accuracy, but only stable path delays were considered and the temporal correlation of path gains was ignored. Typical convex optimization algorithms including basis pursuit (BP) and basis pursuit denoising (BPDN) tackle the NP-hard \(l_{0}\) norm problem by transforming the \(l_{0}\) norm to a convex \(l_{1}\) norm. The BP algorithm was applied to estimate the path delays and Doppler scale factors of the UWA channel in [25], and the BPDN algorithm was proposed to estimate the slowly time-varying UWA channels in [28]. However, the global minimum of the cost function in BP or BPDN is not necessarily consistent with the sparsest solution. An empirical channel variation model, in which different clusters vary independently, was proposed in [14], and demonstrated that adaptation with multiple clusters outperforms that with one cluster for UWA channel estimation.  
In recent years, Bayesian learning (BL) has been used to improve the performance of channel estimation. Compared with the CS-based methods that provide point estimation, Bayesian techniques can give the interval estimation of channel response and have a desirable property of preventing structural errors [29]. By using BL-based methods, the high accuracy of channel estimation was achieved in OFDM systems [30; 31; 32; 33]. The temporal multiple sparse Bayesian learning (TMSBL)-based estimation method was further proposed in [32] to estimate the sparse channels by taking advantage of the channel coherence between consecutive OFDM blocks, and it can achieve better performance in strong correlated channels and maintains robustness in weak temporal correlated channels. Due to the high computational complexity of BL, some accelerated algorithms were proposed, such as the approximate message passing (AMP)-based method in [34]. More recently, some researchers utilized deep learning (DL)-based channel estimators for OFDM systems [35; 36; 37], which showed better channel estimation or equalization performance for nonlinear channel distortion. However, how to go about improving the generalization performance of pre-training DL models and reduce the complexity of training and inferring remain challenging.