## 1 Introduction
Various equalizers have been proposed, such as a coherent receiver structure based on a Decision Feedback Equalizer (DFE) [17] and a turbo equalizer [18]. Furthermore, some improved methods such as minimum mean square error turbo equalization (MMSE-TEQ) [19; 20] and the direct adaptive turbo equalizer (DA-TEQ) [21; 22] have been proposed sequentially. They both have a low complexity. Among them, the DA-TEQ is widely used in communication systems because of its low complexity and simple implementation. These methods are suitable for the correction and compensation of small Doppler shifts. However, due to the constraint of equalizer convergence, the Doppler Effect can be compensated for in a small range. On this basis, a commonly used conventional TEQ based on timescale estimation first uses resampling technology to compensate for Doppler, and then sends the compensated signal to the TEQ for processing to correct the residual Doppler. This approach is effective in mitigating the Doppler Effect, but at the same time, it is still inevitably limited by the channel and the associated signal. Figure 1: The cross-correlation results of the signal. As described, time-domain resampling uses signal expansion or compression on the timescale for Doppler estimation. It has a low complexity and is widely used. However, good channels and accurate timescales are required. Sparse channel estimation requires a high level of complexity, while maintaining a high accuracy. In addition, it also requires the sparsity of the channel. Channel equalization can effectively address small-scale Doppler Effects, but it fails with larger scales. Therefore, combined with channel equalization technology [23; 24; 25; 26; 27; 28; 29; 30; 31], this paper proposes a DAM-TEQ, and uses the adaptive time-domain resampling method for Doppler estimation and compensation. Unlike conventional TEQ, the equalizer is divided into two-stage structures. The first-stage equalizer is an adaptive multi-resampling equalizer, which carries out channel pre-equalization and Doppler rough estimation. This equalizer detects the equalization coefficient and selects the most matching multi-sampling rate interval for the output, to achieve an adaptive resampling. The second-stage equalizer is a parallel turbo equalizer, which sends the multi-sampling signal output by the first-stage equalizer to the turbo equalizer for joint equalization and decoding. Verified by simulations and lake experiments, the equalizer can effectively carry out Doppler estimation and compensation, ensure robust and reliable UAC in a Doppler environment, and does not require auxiliary signals for timescale estimation, greatly saving time and energy costs. The contribution of this article is as follows:  
1. A two-stage adaptive multi-sampling turbo equalizer is proposed, which realizes robust and reliable underwater acoustic communication by combining an adaptive multi-resampling equalizer and parallel turbo equalizer. 2. An adaptive resampling method is proposed to adaptively update the resampling rate of the equalizer by detecting the equalization coefficient, to achieve Doppler estimation and compensation. The rest of this article is organized as follows. Section 2 introduces the model of a single-carrier (SC) UAC system and describes the structure of the proposed equalizer. Section 3 presents and analyzes the proposed adaptive resampling method. Simulation and experimental results are presented in Section 4 to evaluate the performance of the proposed equalizer compared with the conventional TEQ based on timescale estimation. Finally, a conclusion is drawn in Section 5.