The vector approximate message passing (VAMP) soft frequency-domain equalizer (SFDE) has been proposed for turbo equalization. It consists of an inner soft equalizer (ISE) and an inner soft slicer (ISS), which iteratively exchange block-wise extrinsic information to improve the equalization performance, analogous to the outer turbo iteration between a soft equalizer and a soft decoder. However, a comparison of the VAMP-SFDE with other types of self-iterative SFDEs, including the self-iterative block-wise soft interference cancellation (SI-BSIC) SFDE and the generalized approximate message passing (GAMP) SFDE, is lacking. Moreover, a comprehensive performance analysis for the VAMP-SFDE is yet to be performed. In this paper, relations among the VAMP-SFDE, the SI-BSIC-SFDE, and the GAMP-SFDE, are first revealed. After that, the performance analysis is provided for the VAMP-SFDE and it leads to an improved semi-adaptive damping (SAD) scheme for maintaining the independence between the ISS and ISE. The resulting SAD-VAMP-SFDE shows improved mean square error (MSE) evolution curves compared with the original VAMP-SFDE. The SAD-VAMP-SFDE based turbo equalization outperforms those using the SI-BSIC-SFDE or GAMP-SFDE, and approaches the matched filter bound (MFB) over low signal-to-noise ratio region. To further demonstrate its superiority, the SAD-VAMP-SFDE is employed to enable a near-capacity transceiver design, which adopts the serial concatenation of an irregular convolutional code and a unity-rate code on the transmitter side.

Vertical underwater acoustic (UWA) communications play a crucial role in deep-sea applications. A vertical UWA channel generally features a moderate multipath but with time-varying Doppler shifts as well as loud impulsive noise. To achieve a robust vertical single-carrier UWA communication, this paper proposes an enhanced iterative receiver. First, a spline interpolation-based timing estimation approach is proposed to compensate for the time-varying Doppler effects efficiently. Then, the residual timing errors and the multipath interference are tackled by a fractionally spaced self-iterative soft equalizer (SISE) based on the vector approximate message passing (VAMP) algorithm. The VAMP-SISE consists of four parts: an inner soft slicer and an inner soft equalizer for symbol detection as well as a denoiser and a minimum mean-squared error estimator for impulsive noise suppression. Different parts iteratively exchange extrinsic information to improve the equalization performance. Last, a channel-fitting irregular convolutional code and a unity-rate code are employed at the transmitter to lower the signal-to-noise ratio threshold for reliable communications. Deep-sea experiments verify the performance superiority of the proposed receiver over existing schemes.

The Shipborne acoustic communication system of the submersible Shenhai Yongshi works in vertical, horizontal and slant channels according to the relative positions. For ease of use, an array combined by a vertical-cone directional transducer and a horizontal-toroid one is installed on the mothership. Improved techniques are proposed to combat adverse channel conditions, such as frequency selectivity, non-stationary ship noise, and Doppler effects of the platform’s nonlinear movement. For coherent modulation, a turbo-coded single-carrier scheme is used. In the receiver, the sparse decision-directed Normalized Least-Mean-Square soft equalizer automatically adjusts the tap pattern and weights according to the multipath structure, the two receivers’ asymmetry, the signal’s frequency selectivity and the noise’s spectrum fluctuation. The use of turbo code in turbo equalization significantly suppresses the error floor and decreases the equalizer’s iteration times, which is verified by both the extrinsic information transfer charts and bit-error-rate performance. For noncoherent modulation, a concatenated error correction scheme of nonbinary convolutional code and Hadamard code is adopted to utilize full frequency diversity. Robust and low-complexity synchronization techniques in the time and Doppler domains are proposed. Sea trials with the submersible to a maximum depth of over 4500 m show that the shipborne communication system performs robustly during the adverse conditions. From the ten-thousand communication records in the 28 dives in 2017, the failure rate of the coherent frames and that of the noncoherent packets are both below 10%, where both synchronization errors and decoding errors are taken into account.

In the cableless seafloor observation networks (SONs), the links among network nodes rely on underwater acoustic communication (UAC). Due to the energy constraint and the high-reliability requirement of the cableless SONs, the noncoherent UAC has been a preferred choice, even though a noncoherent UAC scheme generally suffers from low spectral efficiency. In this paper, we propose a high-spectral-efficiency noncoherent UAC transmission scheme which is implemented as an orthogonal frequency-division multiplexing (OFDM) system adopting the on-off keying (OOK) modulation. To simultaneously achieve high performance at a low energy consumption, an irregular recursive convolutional code (IrCC) is employed and an accumulator (ACC) is introduced to achieve a modulation with memory at the transmitter side. The ACC enables a turbo iteration between the soft demapper called the ACC-OOK demapper and the soft decoder on the receiver side, and also reduces the decoding error floor. To account for the unknown signal-to-noise ratio (SNR), an iterative threshold estimation (ITE) algorithm is proposed to determine a proper decision threshold for the ACC-OOK demapper. The IrCC is designed to match the extrinsic information transfer (EXIT) curve of the ACC-OOK demapper, lowering the SNR threshold of the aforementioned turbo iteration. Simulations and experimental results verify the superiority of the proposed noncoherent UAC scheme over conventional ones.