## 1 Introduction
The training-sequence-based method performs the channel estimation by utilizing the known training sequence part of the received signals [19]. The training-sequence-based channel estimation method has been widely studied and adopted owing to its low computational complexity and good performance. Moreover, the channel estimation method based on compressed sensing (CS), making full use of the sparsity of the underwater multipath channel, has become a hot research topic [20]. Among the CS-based channel estimation algorithms, orthogonal matching pursuit (OMP) [21] stands out as the most representative with the potential to achieve high estimation accuracy, as well as keeping the computational cost low [20]. However, in the OMP algorithm, determination of the iteration termination condition is a fundamentally challenging problem. Without an appropriate termination condition, not only accuracy but also computational complexity will deteriorate. Considering that the time-varying UWA channel contains both rapidly time-varying and stationary (or slowly varying) components, a sequentially adaptive observation length OMP (SAOL-OMP) algorithm was proposed in [22]. Although the SAOL-OMP algorithm exhibits better performance than the OMP, the iteration termination condition problem was not resolved. To determine the iteration termination condition, an adaptive OMP (A-OMP) algorithm was proposed in [23], where the recovery sparsity was exploited to derive a closed-form expression for the termination condition. However, the A-OMP algorithm has not been validated using sea trial experiments. The sparse-Bayesian-learning-based channel estimation method has been proposed [24; 25]. In [24], sparse-Bayesian-learning-framework-based channel estimation methods were investigated, where the convergence error is avoided by utilizing the sparsity of the channel. Meanwhile, better channel estimation performance and lower output bit error rate (BER) were obtained compared to the CS-based method. In [25], a fast channel estimation algorithm based on sparse Bayesian learning using the fast marginal likelihood maximization was proposed. However, although the sparse-Bayesian-learning-based channel estimation method performs well, the computational complexity is much higher, in terms of long computing time and large power consumption. In this paper, we investigate the Doppler and channel estimation problem for UWA communication using a dedicated preamble signal. In more detail, a preamble signal based on the superimposed LFMs is designed for Doppler and channel estimation. According to the designed preamble signal, we further propose the corresponding Doppler estimation algorithm and channel estimation algorithm. The main contributions of this paper are summarized as follows:  
1. To achieve Doppler and channel estimation using the preamble signal, a preamble signal based on the superimposed LFMs is designed. Specifically, the designed preamble signal is composed of an up-sweeping LFM signal and a down-sweeping LFM signal, which are superimposed in the time domain. Differing from the traditional frame structure that inserts two identical LFM signals before and after the data block, the designed preamble signal can achieve real-time estimation. Compared with the preamble signal using HFM signals, the designed preamble signal is easy to generate and does not increase the time duration. 2. As revealed in [14], under the influence of the Doppler factor, the LFM signal has an approximate linear relationship between the correlation peak shift and the Doppler factor. Hence, a Doppler estimation method is proposed utilizing the relationship between the relative correlation peak shift of two superimposed LFM signals and the Doppler factor. Moreover, once the Doppler factor is estimated, the timing synchronization can be realized simultaneously. 3. An improved OMP channel estimation algorithm utilizing the designed preamble signal is proposed. Since the preamble signal is composed of two LFM signals, it also has excellent autocorrelation characteristics.