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.

Channel equalization plays a crucial role in single-carrier underwater acoustic (UWA) communications. Recently, a frequency-domain turbo equalization (FDTE) scheme enabled by the vector approximate message passing (VAMP) algorithm, was proposed, and it outperformed classic linear minimum mean square error FDTE at acceptable complexity cost. The operation of the VAMP-FDTE requires knowledge of noise power, which is predetermined before the equalization starts. In practice, however, it is difficult to obtain prior knowledge of noise power due to factors of unknown channel estimation errors and dynamic underwater environments. Motivated by this fact, we propose an enhanced VAMP-FDTE scheme, which learns the noise power knowledge during the equalization process via the expectation-maximization (EM) algorithm. The EM-based noise power estimation makes use of intermediate results of the VAMP-FDTE and, thus, only incurs a small extra computational overhead. The improved VAMP-FDTE, named EM-VAMP-FDTE, was tested by experimental data collected in shallow-sea horizontal UWA communication trials with MIMO configuration. It showed better performance than the existing VAMP-FDTE scheme, attributed to the online noise power learning.

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.

Concatenated code based on nonbinary LDPC code and Hadamard code is used for noncoherent underwater acoustic communication system. 32-ary (620, 320) regular LDPC code and irregular LDPC code is constructed by quasi-cyclic extension method and Progressive edge-growth (PEG) algorithm, respectively. Under non-Gaussian noise model, Gaussian mixture model (GMM) is used to fit the noise, and the parameters in GMM is estimated by Expectation Maximization (EM) algorithm, the probability density of noise is further estimated. In Rayleigh fading channel, posterior probabilities of Hadamard code-words are calculated based on GMM, and nonbinary LDPC code is further decoded by Belief Propagation (BP) algorithm based on Tanner graph. It is verified by simulation that concatenated irregular LDPC code and Hadamard code has a 0.4 dB benefit than concatenated regular LDPC code and Hadamard code under white Gaussian noise; under Gaussian mixture noise, the EM algorithm based on GMM can exactly estimate the probability density of noise and improve the error correcting performance of concatenated code, the performance gap is 0.1 dB compared to results in known probability density condition. Noise samples were acquired by experiments carried out in deep sea and shallow lake. Under actual noise, the advantages of concatenated code based on GMM in practical application is verified.

Time synchronization plays an important role in the scheduling and position technologies of sensor nodes in underwater acoustic networks (UANs). The time synchronization (TS) algorithms face challenges such as high requirements of energy efficiency, the estimation accuracy of the time-varying clock skew and the suppression of the impulsive noise. To achieve accurate time synchronization for UANs, an energy-efficient TS method based on nonlinear clock skew tracking (NCST) is proposed. First, based on the sea trial temperature data and the crystal oscillators’ temperature–frequency characteristics, a nonlinear model is established to characterize the dynamic of clock skews. Second, a single-way communication scheme based on a receiver-only (RO) paradigm is used in the NCST-TS to save limited energy. Meanwhile, impulsive noises are considered during the communication process and the Gaussian mixture model (GMM) is employed to fit receiving timestamp errors caused by non-Gaussian noise. To combat the nonlinear and non-Gaussian problem, the particle filter (PF)-based algorithm is used to track the time-varying clock state and an accurate posterior probability density function under the GMM error model is also given in PF. The simulation results show that under the GMM error model, the accumulative Root Mean Square Errors (RMSE) of NCST-TS can be reduced from 10⁻⁴ s to 10⁻⁵ s compared with existing protocols. It also outperforms the other TS algorithms in the aspect of energy efficiency.