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A virtual space-time diversity soft direct-adaptation turbo euqalization (SDATEQ) is proposed for single-input-single-output (SISO) underwater acoustic (UWA) communications based on soft fractionally-spaced decision-feedback equalizer (SFSDFE) and virtual time-reversal mirror (VTRM). The SFSDFE combined with recursive least-squares (RLS) algorithm is employed to achieve virtual space diversity and increases the mutual information (MI) of iterations for faster convergence. Bidirectional structure with VTRM is exploited to mitigate error propagation phenomenon of DFE. An interpolator and digital phase locked loop (DPLL) are embedded into the euqalizer to overcome the residual Doppler frequency shift and recover the timing distortion. Results of simulations and field lake trial show that the proposed algothrim achieves better performance than Soft-DATEQ under the same equalizer order, and the bit error rate (BER) of 1500-m lake trial decreases from 1.50×10 -2 to 2.22×10 -5 .

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Space–time diversity (STD) has been widely applied in underwater acoustic (UWA) communication due to its exceptional anti-multipath performance. However, underwater noise can seriously affect the processing results of STD. The conventional filtering algorithms cannot deal with the nonlinear components of underwater noise and may not work well for complex-type signals. This study proposes an improved STD method with a joint noise-reduction learning model for the above issues. We construct a noise-reduction learning model dedicated to complex-type UWA signals in the first stage. Complex-type features based on UWA data are extracted for pre-processing data, and a conditional generative adversarial network (CGAN) is used as the backbone network for noise-reduction. Residual learning is used to accomplish noise cancellation and yield noise-reduction estimates. In the second stage, an STD structure based on a weight update strategy is constructed. The STD structure can further constrain the weights of the signals from the main path, enhance the reception of the main path, and suppress the multi-access interference (MAI) caused by the spread spectrum communication. Finally, combining the signals on each path can improve the communication quality of the system based on the principle of the maximum signal-to-interference plus noise ratio (SINR). The simulation and experiments on a lake showed that the proposed method is more robust over the changing signal-to-noise ratio (SNR) and has a lower bit error rate (BER) than conventional methods.