Acquiring accurate channel state information and mitigating severe intersymbol interference are challenging for underwater acoustic communications with moving transceivers due to the rapid changes of the underwater acoustic channels. In this work, we address the issue using a superimposed training (ST) scheme with a powerful channel estimation method. Different from the conventional time-multiplexed training, training sequences with a small power are superimposed with symbol sequences. The training signals are transmitted over all time, leading to enhanced tracking capability to deal with time-varying channels at the cost of only a small power loss. To realize this, based on the belief propagation, we develop a message-passing-based bidirectional channel estimation (BCE) algorithm, where all messages are Gaussian, enabling efficient implementation. In particular, the channel correlations are fully exploited through a forward recursion and a backward recursion, thereby achieving accurate channel estimation. Moreover, the ST-based BCE is combined with channel equalization (in the frequency domain) and decoding, and they are performed jointly in an iterative manner to significantly enhance the overall system performance. Field experiments were carried out in Jiaozhou Bay in 2019, and the results verify the effectiveness of the proposed scheme and algorithm.

Acquiring channel state information and mitigating multi-path interference are challenging for underwater acoustic communications under time-varying channels. We address the issues using a superimposed training (ST) scheme with a least squares (LS) based channel estimation algorithm. The training sequences with a small power are linearly superimposed with the symbol sequences, and the training signals are transmitted over all time, resulting in enhanced tracking capability to deal with time-varying underwater acoustic channels at the cost of only a small power loss. To realize the full potentials of the ST scheme, we develop a LS based channel estimation algorithm with superimposed training, where the Toeplitz matrix is used, which is formed by the training sequences, enabling channel estimation with superimposed training. In particular, a low-complexity channel equalization algorithm based on generalized approximate messaging passing (GAMP) is proposed, where the a priori, a posteriori, extrinsic means and variances of interleaved coded bits are computed, and then convert them into extrinsic log likelihood ratios for BCJR decoding. Its computational complexity is only in a logarithmic order per symbol. Moreover, the channel estimation, GAMP equalization and decoding are performed jointly in an iterative manner, so that the estimated symbol sequences can also be used as virtual training sequences to improve the channel estimation and tracking performance, thereby remarkably enhance the overall system performance. Moving communication experiments in Jiaozhou Bay (communication frequency 12 kHz, bandwidth 6 kHz, sampling frequency 96 kHz, symbol transmission rate 4 ksym/s) were carried out, and the experimental results verify the effectiveness of the proposed technique.

The Least Mean Squares Blind Adaptive Multi-user Detection algorithm, the Recursive Least Squares Blind Adaptive Multi-user Detection algorithm, and the Kalman Filter Blind Adaptive Multi-user Detection algorithm, for under-ice communication networks with rising and diving interfering users, are investigated in this paper. Under-ice random asynchronous multi-user communication experiments with rising and diving interfering users were carried out (7 users, 15.7 bit/s per user, 1.2 km under-ice acoustic channels in the Bohai Sea). Good experimental results verified the feasibility and effectiveness of the proposed algorithms in mitigating inter-symbol interference and multiple access interference.

Achieving accurate channel estimation and adaptive communications with moving transceivers is challenging due to rapid changes in the underwater acoustic channels. We achieve an accurate channel estimation of fast time-varying underwater acoustic channels by using the superimposed training scheme with a powerful channel estimation algorithm and turbo equalization, where the training sequence and the symbol sequence are linearly superimposed. To realize this, we develop a ‘global’ channel estimation algorithm based on Gaussian likelihood, where the channel correlation between (among) the segments is fully exploited by using the product of the Gaussian probability-density functions of the segments, thereby realizing an ideal channel estimation of each segment. Moreover, the Gaussian-likelihood-based channel estimation is embedded in turbo equalization, where the information exchange between the equalizer and the decoder is carried out in an iterative manner to achieve an accurate channel estimation of each segment. In addition, an adaptive communication algorithm based on constellation aggregation is proposed to resist the severe fast time-varying multipath interference and environmental noise, where the encoding rate is automatically determined for reliable underwater acoustic communications according to the constellation aggregation degree of equalization results. Field experiments with moving transceivers (the communication distance was approximately 5.5 km) were carried out in the Yellow Sea in 2021, and the experimental results verify the effectiveness of the two proposed algorithms.

To mitigate the inter-symbol interference (ISI), multiple access interference (MAI), and the effect of different Doppler shifts within a data package incurred in variably mobile asynchronous underwater multiuser communications (VMAUMC), a Kalman filter-based chip differential blind adaptive multiuser detection (D-KF-BAMUD) algorithm is proposed in this paper. The Kalman filter-based blind adaptive multiuser detection (KF-BAMUD) algorithm has been adopted to combat ISI and MAI in the scenario of static users, and underwater and under-ice multiuser communication experiments have been carried out to verify the effectiveness of the KF-BAMUD algorithm. To tackle the more challenging VMAUMC, a differential modulation and demodulation technique operating at the chip level is proposed to reduce the impact of Doppler shift residues after the Doppler compensation with an average Doppler frequency offset within each data package. The technique is combined with the KF-BAMUD algorithm, leading to the D-KF-BAMUD algorithm, which is able to effectively handle ISI, MAI, and the effect of Doppler shift residues simultaneously in VMAUMC. This paper reports our experiments on VMAUMC carried out in Songhua River in April 2016 (seven users, data rate 7.87 bit/s, up to 2 m/s variably relative velocity in each data package, and horizontal distance 200-m shallow-water channel between transducer and hydrophone), and the encouraging experimental results demonstrate the effectiveness of the proposed system and the D-KF-BAMUD algorithm.