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This article investigates a robust receiver scheme for a single carrier, multiple-input–multiple-output (MIMO) underwater acoustic (UWA) communications, which uses the sparse Bayesian learning algorithm for iterative channel estimation embedded in Turbo equalization (TEQ). We derive a block-wise sparse Bayesian learning framework modeling the spatial correlation of the MIMO UWA channels, where a more robust expectation–maximization algorithm is proposed for updating the joint estimates of channel impulse response, residual noise, and channel covariance matrix. By exploiting the spatially correlated sparsity of MIMO UWA channels and the second-order a priori channel statistics from the training sequence, the proposed Bayesian channel estimator enjoys not only relatively low complexity but also more stable control of the hyperparameters that determine the channel sparsity and recovery accuracy. Moreover, this article proposes a low complexity space-time soft decision feedback equalizer (ST-SDFE) with successive soft interference cancellation. Evaluated by the undersea 2008 Surface Processes and Acoustic Communications Experiment, the improved sparse Bayesian learning channel estimation algorithm outperforms the conventional Bayesian algorithms in terms of the robustness and complexity, while enjoying better estimation accuracy than the orthogonal matching pursuit and the improved proportionate normalized least mean squares algorithms. We have also verified that the proposed ST-SDFE TEQ significantly outperforms the low-complexity minimum mean square error TEQ in terms of the bit error rate and error propagation. 

Orthogonal signal-division multiplexing (OSDM) is one of the generalized modulation schemes that bring the gap between orthogonal frequency division multiplexing (OFDM) and single carrier frequency domain equalization (SC-FDE). By performing encoding upon subvectors of each interleaved block, it enjoys a flexible resource management with low peak-to-average power ratio (PAPR). Meanwhile, the OSDM induces the intervector interference (IVI) inherently, which requires a more powerful equalizer. By deriving the input and output system model, this paper proposes a time domain soft decision feedback equalizer (SDFE) on per vector equalization with successful soft interference cancellation (SSIC). In addition, this paper takes the whole OSDM block to perform the channel encoding rather than on each vector of the OSDM. Simulation and experimental results demonstrate that the proposed SDFE with SSIC structure outperforms the conventional minimum mean square error (MMSE) equalizer and the block encoding (BE) scheme outperforms the vector encoding (VE) scheme, because theoretically the longer the encoded bit stream is, the more stable and more confident the maximum a posteriori probability (MAP) decoder will be.