Time-varying Underwater Acoustic Channels Research Articles

Deep Learning Prediction of Time-Varying Underwater Acoustic Channel Based on LSTM with Attention Mechanism

Deep Learning Prediction of Time-Varying Underwater Acoustic Channel Based on LSTM with Attention Mechanism

An iterative subblock-based receiver for SC-FDE systems in time-varying underwater acoustic channels

Traditional single-carrier frequency domain equalization (SC-FDE) systems assume time-invariant channels that are difficult to realize in underwater acoustic (UWA) communication over block-based durations, leading to inter-frequency interference (IFI). Currently available approaches to resolving this issue involve shortening the block or inserting frequent training sequences at the cost of additional information from the channel and reduced spectral efficiency. This paper proposes an iterative subblock-based receiver algorithm that divides each time-varying block into multiple quasi-static subblocks. The designed receiver has a two-step structure consisting of block processing and cascaded subblock processing, where the former generates prior symbolic knowledge and the latter iteratively weakens IFI. We consider smoothly variant channels between adjacent subblocks and track them using a Kalman filter, leading to a more accurate estimation of the IFI and better equalization. The proposed algorithm was tested through simulations and experiments in Qiandao Lake and the Yellow Sea using blocks of different lengths and numbers of subblocks and elements in the array. The results provide a low bit error rate.

Underwater Acoustic Channel Estimation via an Orthogonal Matching Pursuit Algorithm Based on the Modified Phase-Transform-Weighted Function

In the context of torpedo guidance systems, the performance of active sonar in channel parameter estimation and target detection and recognition is significantly degraded by the multipath effect and the time-varying characteristics of the underwater acoustic (UWA) channel. Therefore, it is urgent to propose an algorithm that can accurately estimate the channel parameters in multipath time-varying UWA channels. To solve these problems, this study developed a modified phase transform (PHAT)-weighted function and applied it to the orthogonal matching pursuit (OMP) algorithm, named M-PHAT-OMP. The proposed algorithm is more robust, improves the resolution of the time delay and further improves the estimation accuracy of the parameters in the case of motion. Furthermore, with the aim of solving the problem of the difficulty that the traditional OMP algorithm has in determining sparsity, this study proposes a joint-threshold method, where the threshold value serves as the condition for terminating the algorithm’s iteration. The simulation results demonstrate that the M-PHAT-OMP algorithm proposed in this study exhibits a superior performance compared to other algorithms, as evidenced by its lower root mean square error (RMSE) for delay. Moreover, the experimental results also validate that the proposed algorithm has superior robustness and resolution of the time delay in practical applications.

Iterative double-differential direct-sequence spread spectrum reception in underwater acoustic channel with time-varying Doppler shifts.

Conventional double differential phase-shift keying modulation amplifies the phase noise and performs poorly under the time-varying direct-sequence spread-spectrum (DSSS) communication system. Therefore, the authors propose an iterative reception for DSSS communication in time-varying underwater acoustic channels. First, bit-interleaved coded modulation with iterative decoding integrated with multi-symbol differential detection is used. Second, this paper uses cross correlation method to estimate and track the Doppler shift of each symbol. Based on Doppler estimates, a dynamic linear prediction model is proposed to estimate and track the channel phase variation. Third, an algorithm for adaptive selection of reference signals is utilized to recover the magnitude attenuation of correlation peaks. Numerical simulation results demonstrate that the proposed reception achieves around 9 dB gain compared to conventional differential decision reception under constant acceleration of 0.14 m/s2. During the acoustic communication experiment in Songhua Lake, the proposed reception was tested by using a moving source at a speed of 1-6 knots at 2-m depth and the farthest distance between the transceivers is 2.8 km. The proposed reception achieves only one frame error from a total of 205 frames collected in the lake experiment, and it also achieves error-free communications over 96 frames during a 10 km depth deep-sea experiment.

Underwater Acoustic Channel Tracking with Cluster Variation Learning for Acoustic Mobile OFDM Communication

In this paper, we propose a channel tracking method with cluster variation learning in multicarrier communications, by exploiting the cluster-specific channel coherence for time-varying underwater acoustic (UWA) channels. We develop a cluster variation model due to the cluster-specific channel coherence. In the cluster variation model, the path delay and the Doppler scale assemble the range and the velocity in the target movement. Inspired by the target tracking for its movement, we propose a channel tracking method which can incorporate the cluster variation model with the measurement model efficiently through Kalman filtering. The cluster variation model can learn its parameters block by block through pilots, therefore reduce its model mismatch adaptively. The proposed method has a moderate computational complexity, since it eliminates the explicit Doppler scale estimation and Doppler variation model comparing to the conventional channel estimation. Using simulated data as well as experimental data in mobile UWA communications with one phone element, we study the system performance in term of mean square error (MSE) and symbol error rate (SER) performance, and show that the proposed channel tracking method improves the performance significantly.

Fast Sparse Bayesian Learning-Based Channel Estimation for Underwater Acoustic OFDM Systems

Harsh underwater channels and energy constraints are the two critical issues of underwater acoustic (UWA) communications. To achieve a high channel estimation performance under a severe underwater channel, sparse Bayesian learning (SBL)-based channel estimation was adopted for UWA orthogonal frequency division multiplexing (OFDM) systems. Accurate channel estimation can guarantee the successful reception of transmitted data and reduce retransmission occurrences, thereby, leading to energy-efficient communications. However, SBL-based algorithms have improved performances in iterative ways, which require high power consumption. In this paper, a fast SBL algorithm based on a weighted learning rule for hyperparameters is proposed for channel estimation in a UWA-OFDM system. It was shown via numerical analysis that the proposed weighted learning rule enables fast convergence and more accurate channel estimation simultaneously. Simulation results confirm that the proposed algorithm achieves higher accuracy in channel estimation with much fewer iteration numbers in comparison to conventional SBL-based methods for a time-varying UWA channel.

A Block Sparse-Based Dynamic Compressed Sensing Channel Estimator for Underwater Acoustic Communication

Due to the complex ocean propagation environments, the underwater acoustic (UWA) multipath channel often exhibits block sparse time-varying features, and while dynamic compressed sensing (DCS) can mitigate the time-varying effects of the UWA channel, DCS-based algorithms have limited performance for the UWA channel with block sparsity. In this study, by formulating the UWA channel with blocks concatenation, a block sparse-based DCS approach (BS-CS) is proposed to explore the block and time-varying sparsity of UWA channel simultaneously. In detail, we firstly adopt a block sparse recovery algorithm, block orthogonal matching pursuit (BOMP), to compute the temporary estimate. Then, the CS approach is applied to compute the support additions, which are caused by the time-varying components of the UWA channel. Next, we use the selected support to perform the BOMP estimate, and obtain the estimated channel response. Finally, the numerical simulation and the sea experiment were carried out to verify the superior performance of the proposed BS-CS algorithm in the block sparse time-varying UWA channels.

Accurate Channel Estimation and Adaptive Underwater Acoustic Communications Based on Gaussian Likelihood and Constellation Aggregation

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.

Frequency domain direct adaptive turbo equalization based on block least mean square for underwater acoustic communications

In this paper, a novel frequency domain direct adaptive turbo equalizer (FDDA-TEQ) is proposed for time-varying underwater acoustic (UWA) channels. The proposed equalizer uses a modified frequency domain block normalized least mean square (FBNLMS) algorithm to update filter coefficients, which can effectively solve the problem of insufficient filter length in traditional adaptive frequency domain equalization. A sliding window strategy is adopted to deal with the rapid time-varying characteristic of UWA channels. Meanwhile, an iterative structure in the equalizer is proposed to further improve performance. The proposed method (FDDA-TEQ) is tested by simulation and the data collected in the real-world underwater experiments. Both simulation and experimental results can prove the effectiveness and superiority of the proposed method.

Joint time-frequency domain equalization of MSK signal over underwater acoustic channel

Minimum shift keying (MSK) shows better bandwidth efficiency than the phase shift keying owing to its high bandwidth usage efficiency and constant envelope property. The performance of frequency-domain block linear equalization (FD-BLE), which is commonly used for MSK communication, is limited in complex time-varying underwater acoustic (UWA) channel. In this paper, a time-domain adaptive decision feedback equalization (TD-ADFE) is proposed to address issues pertaining to MSK communications over UWA channel. Further joint time–frequency domain equalization (JTFDE) built on TD-ADFE and BLE is proposed to further reduce the bit error rate (BER). The proposed method can effectively track the time-varying UWA channel through the updated equalizer coefficient according to the output of de-mapper. Numerical simulation shows that the JTFDE performed better than TD-ADFE and FD-BLE over time-varying UWA channel by approximately 2 dB when the BER was 1 × 10−3.The sea trial results verified the proposed JTFDE and demonstrated that the BER of JTFDE was 82.5% and 88.9% lower than that of TD-ADFE and FD-BLE, respectively.

Exploiting Rapidly Time-Varying Sparsity for Underwater Acoustic Communication

Due to the combined effects of different acoustic propagation, reflection patterns in different time-scale, time-varying underwater acoustic (UWA) channel generally exhibits hybrid sparsity, i.e., contains not only rapidly time-varying elements, but also stationary or slowly time-varying ones. While the classic sparse reconstruction algorithms such as orthogonal matching pursuit (OMP) generally do not take it into account, the existence of static multipath will unavoidably hinder the tracking of rapid time variations. In this paper, a sequential adaptive observation length orthogonal matching pursuit (SAOLOMP) approach is proposed to sequentially explore rapidly time-varying sparsity in a two-step sequential manner. Specifically, the static components are firstly separated via simultaneous orthogonal matching pursuit (SOMP) among continuous measurements. Upon the residual error of the SOMP, the measurement-wise OMP is applied for estimating the remained dynamic components. As the variation of the SOMP residual error indicates how rapidly the remained dynamic multipath components vary, the observation length of the OMP is adjusted according to the gradient of residual error to adapt to rapidly time-varying components. Finally, both types of sparse components are summed up to obtain the whole channel response. Numerical simulations as well as experimental results from field UWA communication data show that the proposed algorithm exhibits better performance in exploiting rapidly time-varying sparsity than the state-of-the-art compressive methods do under UWA channel.

Time-varying carrier frequency offset estimation in OFDM underwater acoustic communication

We consider the problem of carrier frequency offset estimation in OFDM underwater acoustic communication. In our previous work, we suggested transmitting equi-power and equi-spaced pilot tones which led to a simple carrier frequency offset estimator. Here, we extend this work in two directions: First, equi-power pilots may result in a large peak to average power at the transmitter. Thus, we propose a method to design the phases of the pilot tones so as to keep the peak to average power low, while still obtaining large enough pilot to data ratio needed to decode the pilot symbols. The design method is based on ideas adopted from phase retrieval techniques. Second, we modify the previous carrier frequency offset estimators to the case of a time-varying underwater acoustic channel. These modifications are based on modeling the carrier offset by polynomial and piece-wise models. The estimators use the correlations and intervals between the pulses, and approximate the frequency offsets by small order polynomials. Simulations results show that for constant offsets, the proposed estimators achieve similar performances as state-of-the-art techniques, while for time-varying offsets the proposed estimators are superior.

Bayesian Learning-Based Clustered-Sparse Channel Estimation for Time-Varying Underwater Acoustic OFDM Communication.

Orthogonal frequency division multiplexing (OFDM) has been widely adopted in underwater acoustic (UWA) communication due to its good anti-multipath performance and high spectral efficiency. For UWA-OFDM systems, channel state information (CSI) is essential for channel equalization and adaptive transmission, which can significantly affect the reliability and throughput. However, the time-varying UWA channel is difficult to estimate because of excessive delay spread and complex noise distribution. To this end, a novel Bayesian learning-based channel estimation architecture is proposed for UWA-OFDM systems. A clustered-sparse channel distribution model and a noise-resistant channel measurement model are constructed, and the model hyperparameters are iteratively optimized to obtain accurate Bayesian channel estimation. Accordingly, to obtain the clustered-sparse distribution, a partition-based clustered-sparse Bayesian learning (PB-CSBL) algorithm was designed. In order to lessen the effect of strong colored noise, a noise-corrected clustered-sparse channel estimation (NC-CSCE) algorithm was proposed to improve the estimation accuracy. Numerical simulations and lake trials are conducted to verify the effectiveness of the algorithms. Results show that the proposed algorithms achieve higher channel estimation accuracy and lower bit error rate (BER).

Iterative adaptive frequency-domain equalization based on sliding window strategy over time-varying underwater acoustic channels.

This letter provides a novel iterative adaptive frequency-domain equalization for time-varying underwater acoustic (UWA) channels. The proposed scheme adopts a modified frequency-domain block least mean square algorithm to update the filter weights. A sliding window strategy is developed to deal with the rapid time-varying characteristics of UWA channels. The proposed method enhances the performance through an iterative structure. Experimental results show that the bit error rates of the proposed method can be one order of magnitude lower than those of conventional schemes.

Inter-carrier interference-aware sparse time-varying underwater acoustic channel estimation based on fast reconstruction algorithm

In this paper, a fast orthogonal matching pursuit (OMP) algorithm based on optimized iterative process is proposed for sparse time-varying underwater acoustic (UWA) channel estimation. The channel estimation consists of calculating amplitude, delay and Doppler scaling factor of each path using the received multi-path signal. This algorithm, called as OIP-FOMP, can reduce the computationally complexity of the traditional OMP algorithm and maintain accuracy in the presence of severe inter-carrier interference that exists in the time-varying UWA channels. In this algorithm, repeated inner product operations used in the OMP algorithm are removed by calculating the candidate path signature Hermitian inner product matrix in advance. Efficient QR decomposition is used to estimate the path amplitude, and the problem of reconstruction failure caused by inaccurate delay selection is avoided by optimizing the Hermitian inner product matrix. Theoretical analysis and simulation results show that the computational complexity of the OIP-FOMP algorithm is reduced by about 1/4 compared with the OMP algorithm, without any loss of accuracy.

An iterative receiver for time-domain oversampled OFDM system over time-varying underwater acoustic channels

This paper investigates an iterative receiver for time-domain oversampled orthogonal frequency division multiplexing (OFDM) over time-varying underwater acoustic channels for both single-input, single-output (SISO), single-input, multiple-output (SIMO) and multiple-input, multiple-output (MIMO) scenarios. We extend two widely used parametric models for time-varying channels: (i) Doppler rate model (DRM) and (ii) basis expansion model (BEM) to work with oversampled OFDM systems. To exploit the inherent sparsity of underwater acoustic channel, iterative orthogonal matching pursuit (OMP) algorithm is adopted for channel estimation. To further reduce computational complexity, fast Fourier transform (FFT) based low-complexity implementations for iterative OMP algorithm are proposed for both BEM and DRM. The proposed receiver is evaluated by sea trial conducted in the Trondheim Fjord, Norway. Both 8-phase shift keying modulation scheme and 16-quadrature modulation (16-QAM) scheme are carried out during the sea trial. The experimental results show that the proposed iterative time-domain oversampled OFDM receiver achieves lower bit error rates (BERs) than conventional iterative symbol rate sampled OFDM receiver.

Joint Channel Estimation and Generalized Approximate Messaging Passing-Based Equalization for Underwater Acoustic Communications

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.

Joint Multiple Turbo Equalization for Harsh Time-Varying Underwater Acoustic Channels

To address the problem of the harsh time-varying multi-path interference (TMI) incurred by moving underwater acoustic communications, a joint multiple turbo equalization (JMTE) algorithm is proposed. The superimposed training scheme and the single turbo equalization have been proposed to address the issue of the TMI. To tackle the more challenging fast TMI, the symbol block has been successfully divided into the segments, and the channel correlation between (among) the segments has been established, improving the tracking performance for fast time-varying channels. When the channels sharply change, the channel correlation between (among) the segments is broken, leading to decoding failure. Therefore, we develop the JMTE algorithm with the calculational complexity of the logarithmic order per symbol, where the channel of each segment is separately estimated, so that the establishment of the channel correlation is avoided, and the corresponding separate equalization results of the segments are combined to construct a joint equalization result. Unlike the Gaussian approximate process of the input symbols of the traditional linear minimum mean square error equalization, the discrete independent random variable form of the input symbols of the JMTE algorithm is retained to avoid input information loss. The ‘separate’ channel estimates, the JMTE and decoding are iteratively operated, where based on the low-complexity diagonal-matrix message passing, the information exchange between the JMTE equalizer and the decoder is carried out to dramatically enhance the equalization performance by utilizing the encoding redundant information. Moving underwater communication experiments were done in 2021 (the communication distance was about 5.5 km, and the relative speed was about 0.5 m/s), and the experimental results verify the effectiveness of the proposed algorithm.

Exploiting dynamic sparsity for time reversal underwater acoustic communication under rapidly time varying channels

Underwater acoustic (UWA) communication encounters significant difficulties posed by the simultaneous presence of multipath and time variations. It has been recognized that, under the assumption that channel keeps static within the processing windows, time reversal (TR) processing approach is capable of mitigating multipath via the spatial–temporal focusing. However, for a rapidly time-varying UWA channel, the replica channel impulse response in time reversal processor need to be updated frequently to avoid performance degradation, which leads to huge computational complexity and significant overhead. Consider that after time reversal processing the resulting time-reversed channel response exhibits much more slow time variations compared to the original channel impulse response, previously Kalman filtering has been adopted to track the time-reversed channel response to alleviate the requirement of frequent channel update. Under the framework of dynamic compressed sensing (DCS), in this paper the time-reversed channel is formulated as a sparse set consisting of constant and slowly time-varying supports to derive the Kalman Filtered Compressed Sensing (KF-CS) channel estimation algorithm for time reversal communication. Based on the receiver structure by coupling the KF-CS estimator driven time reversal processor with a single channel decision-feedback equalizer (TR-DCS-DFE), shallow water experimental results with field data are provided to demonstrate the effectiveness of the proposed algorithm, compared to the classic time reversal communication scheme.

Frequency-Domain Decision Feedback Equalization for Single-Carrier Transmissions in Fast Time-Varying Underwater Acoustic Channels

Frequency-domain equalization (FDE) is a computationally efficient method to recover underwater acoustic single-carrier transmissions in a multipath environment. The FDE receivers often operate in a block-by-block manner, assuming that the channel is time invariant during a block duration. This assumption implies that traditional block-based FDE receivers experience performance degradation in fast time-varying channel conditions, since the interfrequency interference (IFI) is often not considered. Here, we focus on the IFI cancelation (IFIC) in single-carrier transmissions. The IFI formulations are developed for a blockwise FDE receiver, where the time reversal (TR) processing is incorporated to alleviate the interblock interference. Based on the formulations, the IFI is estimated by the time-varying impulse responses, which are obtained from an adaptive basis expansion model. A soft two-step IFIC strategy is then employed to address the IFI. In the first step, the main IFI is removed by the time-varying TR processing and explicit IFI cancelation. The residual IFI is suppressed by the frequency-domain decision feedback equalization (FD-DFE) in the second step. To further enhance the communication performance, we develop a soft-symbol-based iterative receiver, referred to as IFIC-FD-DFE. The impulse responses, explicit IFI, and residual IFI are updated in an iterative fashion, based on the soft symbol estimates. The proposed receiver has been tested using the at-sea measurements collected at the Gulf of Mexico in August 2017. Communication packets at four ranges at the carrier frequency of 160 kHz with a symbol rate of 32 kHz have been decoded. The effectiveness of the IFIC-FD-DFE receiver has been demonstrated via comparisons with several FDE schemes in the current literature.