A wideband Doppler Effect is a significant challenge for underwater acoustic communications (UAC). This paper proposes a new two-stage structure of direct adaptive multi-resampling turbo equalizer (DAM-TEQ) for solving the problem of large timescale errors in time-varying channels, which uses an innovative adaptive time-domain resampling method for Doppler estimation and compensation. In this equalizer, the received signal is first fed into the first-stage structure, in which an adaptive resampling is performed using equalization coefficient detection to achieve a Doppler rough estimation. After the processing is completed, it is fed into the second-stage structure for joint equalization and decoding, effectively reducing the error of information transmission. Compared with the conventional turbo equalizer (TEQ) based on timescale estimation, the proposed equalizer can avoid the problem of the Doppler Effect not being accurately estimated in time-varying channels, with only a slight increase in complexity. Simulations and lake trails show that the equalizer can effectively perform a Doppler estimation and compensation in time-varying channels, and has a better bit error rate (BER) performance than the traditional timescale-based TEQ.

By transferring external information between the equalizer and the decoder iteratively, the performance of turbo equalization is close to the channel capacity. Conventional turbo equalization (CTE) relies on channel coding, while the transmission of external information is a problem in an uncoded system, and turbo equalization without channel coding (TECC) remains unexplored. Therefore, this paper introduces a TECC framework with a virtual decoder constructed by bidirectional processing. The main innovation is that the existence of the virtual decoder enables the transmission of external information. Under this new framework, we implement it with a minimum mean square error decision feedback equalizer (MMSE-DFE) and evaluate its performance across stationary channels and multipath fading channels. Simulation results demonstrate significant communication performance enhancement after three to four iterations, surpassing both conventional bidirectional and unidirectional equalization. In addition, the proposed TECC is verified through underwater acoustic communication in a sea trial. The results also demonstrate that the TECC achieves better bit error performance.