Sparse Wavelet Transform for Underwater Acoustic Image Compressed Sensing

In this paper, the estimation of doubly spread underwater acoustic (UWA) channels is investigated. The UWA channels are characterized by severe delay spread and significant Doppler effects, and can be well modeled as a multi-scale multi-lag (MSML) channel. Furthermore, exploiting the sparsity of UWA channels, MSML channel estimation can be transformed into the estimation of parameter sets (amplitude, Doppler scale factor, time delay). Based on this, the orthogonal matching pursuit (OMP) algorithm has been widely used. However, the estimation accuracy of OMP depends on the size of the dictionary, which is related with both delay spread and Doppler spread. Thus it requires high computational complexity. This paper proposes a new method, called wavelet transform (WT) based algorithm, for the UWA channel estimation. Different from OMP algorithm which needs to search in both time domain and Doppler domain, WT-based algorithm only needs to search in time domain by using the Doppler invariant characteristic of hyperbolic frequency modulation (HFM) signal. The performance of the proposed algorithm is evaluated by computer simulations based on BELLHOP. The simulation results show that WT-based algorithm performs slightly better than OMP algorithm in low signal to noise ratio (SNR) while can greatly reduce computational complexity.

The fast temporal variations, long multipath delay spreads, and severe frequency-dependent attenuations of underwater acoustic communication channels are extremely complex that impedes underwater acoustic (UWA) data transmission. To alleviate this problem, channel coding is indispensable in UWA communication system to increase the reliability. In this paper, performances of LDPC codes with different parameters over different underwater acoustic communication channels are presented, which is to know how to adjust the encoding and decoding parameters according to different underwater acoustic channels. The results indicate that LDPC codes have a good performance of the estimated BER on the order of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> -10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> either in positive sound velocity gradient (PSVG) underwater channel or negative sound velocity gradient (NSVG) one, even invariable sound velocity gradient (ISVG) one. In addition, whatever the encoding or decoding parameters is adopted, performance of the LDPC codes over the NSVG underwater channel is the best, compared with PSVG one and ISVG one. Furthermore, in the desired performance of BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> , the encoding and decoding parameters according to the three different underwater channels specifications are summarized.

This paper details the architecture of a novel scale-lag rake receiver for the doubly selective underwater acoustic (UWA) channel. The shallow UWA channel is known to have a large Doppler spread. The cause of this is primarily due to the large spread of the angle of arrival of the received signal's paths. The Doppler scale value is dependent on the angle of arrival of the received signal. The Doppler spread is significant, and multiple Doppler scales are present in the UWA channel. Therefore, the receivers operating with only a single Doppler scale compensation perform sub-optimally. The optimal receiver should incorporate all possible Doppler scales for better performance. The receiver needs to have multiple sampling rates to incorporate all Doppler scales. It is usually done by having multiple receive channels, one for each sampling rate. It requires tremendous resources as its complexity increases exuberantly. This paper shows that these Doppler scales are clustered and that an optimal receiver is implemented using fewer receiver channels, each corresponding to one such cluster. It reduces the receiver's complexity. The simulation results demonstrate that using the Doppler scale value associated with the path of the highest magnitude per cluster yields the best performance.

The measurements of delay and Doppler (DD) spreading in underwater acoustic channels (UACs) have multiple applications, including communications as well as the development of a dynamic UAC simulator. However, these measurements suffer from the difficulties of fast time variations and large data sets. This paper addresses an efficient compressed sensing (CS) method to solve these problems. First, the DD spreading in UACs is studied by using a doubly spread model; second, the least-square criterion is implemented and its limit is analyzed. Subsequently, the matching pursuit (MP) method is applied to the problem by exploiting the sparsity of the DD model-based UACs. Although the MP method improves the performance of the LS method, it has unavoidable deficiencies, e.g., the redundant selections of bases that lead to a limited measurement of DD spreading. Thus, this paper proposes an improved version by inserting a projection matrix. The projected MP (PMP) method adopts QR decomposition for an efficient computation. Finally, at-sea data-based comparisons among the abovementioned three methods are conducted to verify the superiority of the PMP method.

Under water acoustic (UAC) channel is subjected to large delay spread compared to radio frequency (RF) channels. In order to capture this large delay spread and avoid ISI, the UAC symbol duration needs to be considerably large reducing the transmission data rate. Unlike other RF systems, in Ultra-wideband (UWB) RF systems, small pulse width in the order of nano seconds is used to transmit information. This in turn, gives high resolution multipaths. In a time hopping UWB system, to avoid multipath overlap, the chip duration and the frame duration are kept equal to or larger than the maximum delay spread of the channel. This results in large UWB symbol duration and hence reduces the data rate. In order to increase the data rate, the chip duration, and frame duration can be reduced to less than the maximum delay spread. In addition, to farther increase the data rate, guard interval between consecutive symbols can be reduced/removed allowing consecutive symbols to overlap. This results in intersymbol interference (ISI). Surprisingly, this type of overlap doesn't degrade UWB system performance significantly. In this paper, the same concept is applied to various UAC channels. In order to increase the data rate, consecutive UAC symbols are allowd to overlap. Performance under ISI is then evaluated.

The achievement of efficient data transmissions via underwater acoustic channels, while dealing with large data packets and real-time data fed by underwater sensors, requires a~high data rate. However, diffraction, refraction, and reflection phenomena, as well as phase and amplitude variations, are common problems experienced in underwater acoustic (UWA) channels. These factors make it difficult to achieve high-speed and long-range underwater acoustic communications. Due to multipath interference caused by surface and ocean floor reflections, the process of modeling acoustic channels under the water's surface is of key importance. This work proposes a~simple geometry-based channel model for underwater communication. The impact that varying numbers of reflections, low water depth values, and distances between the transmitter and the receiver exert on channel impulse response and transmission loss is examined. The high degree of similarity between numerical simulations and actual results demonstrates that the proposed model is suitable for describing shallow underwater acoustic communication environments.

The paper presents a brief survey on the underwater acoustic communication channel estimation of orthogonal frequency division multiplexing using deep learning techniques. In recent times, deep learning has shown great potential in the field of communication. The underwater acoustic channel is a highly challenging system as it has a restricted bandwidth, enlarged multi-path, medium refractive characteristics, acute fading, rapid time variation, large Doppler shifts, etc. For the UWA-OFDM communication model, DL-based receivers can be elucidated as a deep neural network for a better estimation than the conventional techniques. Sufficient training is required for the recovery of the transmitted symbols. It does not require any explicit CE or equalization and balancing. The estimation is accomplished in two stages. The first one is training stage. For training, this deep neural network-transmitted data, the signal received in the unknown channel, etc., are used as labeled data. The second one is test stage, where the deep neural network receiver recovers transmitted symbols, given the received signal. The accuracy and the computational complexity, these two have been a great challenge for the underwater acoustic channel estimation with the existing traditional channel estimation methods. The deep learning method is useful to solve these problems. This survey is to find out a few optimum methods of deep learning to estimate the UWA channel in an efficient way.

Spread spectrum technology has been widely employed for positioning and communicating with autonomous underwater vehicles (AUVs), but conventional spread spectrum sequences lack confidentiality and reliability in UWA channel. Considering the limitations of conventional sequences and the characteristics of underwater acoustic (UWA) channel, a composite chaotic orthogonal sequence (CCOS) based on the UWA channel is proposed. The confidentiality of the CCOS is superior to that of the m‐sequence, while the autocorrelation performance of the CCOS is superior to that of the orthogonal sequence. Moreover, the CCOS can compensate for the imbalance of logistic chaotic sequence when assigned certain initial values. Acquisition is a crucial component of accessing the spread spectrum signal; therefore, the acquisition performance indicates the applicability of the CCOS. The source–target model is established to simulate communication with an underwater moving target. To simulate the acquisition process, a parallel algorithm based on fast Fourier transform is adopted, and the entire simulation process is completed based on the BELLHOP ray acoustic model. Through data processing, the Doppler shift error is less than half of the frequency‐search element. Furthermore, the acquisition probabilities of the CCOS with different numbers of bits are over 90%, which demonstrates the reliability of the CCOS.

The underwater acoustic (UWA) channel causes large propagation delays and reduces the bit error rate (BER) of wireless communication systems. The t-distribution is the optimal distribution to perform UWA noise. In this study, polar-coded differential chaos shift keying (DCSK) and quadrature chaos shift keying (QCSK) communication with UWA noise are considered. First, we have proposed a PDF for the UWA noise channel, and based on this PDF, the theoretical BER is derived. Second, polar coding’s performance is determined to demonstrate the improvement in the BER performance compared to the uncoded UWA system by means of Monte Carlo simulations. The experimental results prove that the nearest model that is applicable to the UWA channel is a t-distribution with five and six degrees of freedom. The BER formulas of the proposed systems are derived and compared with the simulation results. The results confirm the performance improvement of the polar-coded chaotic modulation systems over uncoded systems in UWA channels.

Underwater acoustic (UWA) communication is a critical part of information exchange among marine equipment in the Internet of Underwater Things (IoUT). The impact of the marine environment on UWA communication manifests through physical channels, which exhibit multipath propagation, Doppler spread, and time-varying characteristics. The dynamic compressed sensing (DCS) framework, represented by Kalman Filtered CS (KF-CS) algorithm, is introduced to dynamically adapt support sets by real-time tracking of observations. Meanwhile, channel modeling in Delay-Doppler (DD) domain offers a more stable representation for doubly-selective UWA channels, revealing a potential for channel estimation. In this paper, we transform the time-domain channel estimation into the DD domain channel estimation, and formulate the DD domain channel estimation under the DCS framework to exploit the time-varying sparsity of the UWA channel in the DD domain. In addition, to solve the DD model, the classic algorithms need to search for the sparse solution in the extremely large two-dimensional space of the entire UWA channel. Since only a few multipath arrivals within the large time-delay spread of the entire UWA channel have the Doppler value, we propose the multipath arrivals-Doppler function-based DCS channel estimation approach (DCS-MAD) to solve the DD model. The proposed DCS-MAD can remodel the traditional DD model as multipath arrivals and Doppler model, and search for the sparse solution in the two-dimensional space of multipath arrivals, instead of on the entire channel, so as to effectively reduce system complexity and better focus on Doppler value estimation at the UWA channel’s multipath arrivals. Specifically, we first estimate the multipath arrival delay of the UWA channel using the DCS algorithm. Then, the two-dimensional space search is performed specifically at the multipath arrivals and Doppler domains under the DCS framework to exploit the time-varying sparsity. Finally, the results of numerical simulation and sea experiments validate the superiority of the proposed schemes, compared to the benchmark algorithms.

Multicarrier acoustic communication has enabled wireless underwater transmission at higher data rates. Several multicarrier modulation systems have been explored in the past for data transmission. Orthogonal frequency division multiplexing (OFDM) fights-off inter-symbol-interference due to orthogonality of the carriers. However, it is susceptible to time variations which introduces inter-carrier-interference. Being double selective, the underwater acoustic (UWA) channel is both time and frequency variant. Time variations and multipath fading makes it a complex channel to estimate. In this paper, we explore linear frequency domain equalization techniques available for radio OFDM systems and compare their performance for a shallow underwater acoustic channel. The underwater channel model used is based on Rician shadowed distribution with Doppler shifts. We compare the performance of a linear equalizer with pilot estimated channel against a zero-forcing equalizer where the channel is assumed to be known. Results collected through Monte Carlo simulations show that for a 128-subcarrier OFDM system and a transmitter-receiver separation of 800 m, a gain of almost 7dB is obtained at a BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> when a zero-forcing equalizer is used. Moreover, when the subcarriers are increased to 256, this gain almost doubles. In conclusion, the zero-forcing equalizer outperforms the LS equalizer for an underwater acoustic channel.

The combination of orthogonal frequency division multiplexing (OFDM) and interleave division multiple access (IDMA), known as OFDM-IDMA, has been proposed as a promising multiple access scheme for wireless communications due to its low decoding complexity and potential of achieving high spectral efficiency. However, most of the work on OFDM-IDMA is in radio frequency (RF) communications scenarios and based on computer simulations. In this paper, we propose OFDM-IDMA over underwater acoustic (UWA) channels with experimental results. We also extend the original OFDM-IDMA to a multiple hydrophones scenario to improve the bit error rate (BER) performance. Experimental results show that with multiple hydrophones, the coded BER performance of OFDM-IDMA approaches zero after only a few iterations, validating the feasibility of our proposed approach over UWA channels.

Noise in an underwater acoustic (UWA) channel does not necessarily follow Gaussian statistics, especially in a shallow water environment which is dominated by impulsive noise sources. However most of the receivers are designed with the assumption that the channel noise is additive white Gaussian (AWGN). Such receivers may not be the optimum ones to deal with the non-Gaussian UWA noise. Several non-Gaussian statistics have been proposed in previous literature to model UWA noise among which the Generalized Gaussian (GG) model has been very popular due to its flexible parametric form. However, to the best of our knowledge, no analytical error analysis with the assumption of channel noise being generalized Gaussian has yet been reported. In this paper, we derive the analytical expression for probability of error considering the presence of GG noise in the UWA channel. We also try to study the performance of an AWGN receiver in the presence of non-Gaussian noise. We consider three different communication systems using BPSK, QPSK and M-ary PAM constellations, and observe, for all three of them, that if noise kurtosis is greater than the Gaussian kurtosis, the system performance degrades. Thus here is an initial phase of designing UWA system with GG noise assumptions instead of the traditional Gaussian receiver. It is still a matter of argument, due to all possible redesign complexities, whether it is worth taking all the redesign complexities or the performance degradation can be tolerated as per the requirements of system application.

Underwater acoustic (UWA) channel is bandwidth-limited owing to the low sound speed, severe time- and frequency-selective fading. We believe that improving the spectral-efficiency is a decent approach to increase the capacity of UWA systems. In this paper, we introduce a highly spectrum-efficient MIMO-OFDM system under UWA channel that uses blind channel estimation and elimination of phase ambiguity induced in equalization. We employ classic subspace algorithm (SPA) as the blind channel estimation method without the training sequences and pilot tones. To maximize the performance of SPA, a resampling-based solution to mitigate the channel Doppler shift is applied at the receiver. Considering the phase ambiguity introduced inherently in SPA, we use an interleaved symbol mapping schemes to eliminate the ambiguity, which achieves no rotational symmetry in the combined signal constellation. Numerical simulations verified that the phase error could be corrected without any data aiding and the spectrum efficiency of MIMO-OFDM UWA communications is greatly improved compared with pilot-based method.

An underwater acoustic multimedia communication (UWAMC) system is proposed with 2400 transmission modes according to time-varying multipath underwater acoustic (UWA) channel conditions. The orthogonal variable spreading factor (OVSF) scheme and Gold sequence (GS) scramble code are integrated into multi-input multi-output UWAMC system based on orthogonal frequency-division multiplexing to achieve the quality of service of multimedia transmission in the UWA channel. Binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK) adaptive modulation, direct mapping (DM) or space–time block code (STBC) transmission strategies, convolution channel code with rate 1/2 and 1/3, and a power assignment mechanism were adopted in the proposed system. Simulation results show that the bit error rate (BER) and power saving ratio (PSR) performance of the STBC strategy with transmission diversity is superior to that of the DM strategy without transmission diversity, and the performance of the BERs and PSRs of the transmission scheme with the GS scramble code surpasses that of the scheme without the code. The performance of the BERs and PSRs of BPSK modulation with a channel code rate of 1/3 is better than that of BPSK modulation with a channel code rate of 1/2, and the performances of BERs and PSRs of BPSK modulation with a channel code rate of 1/3 are better than that of QPSK modulation with a channel code rate of 1/3. As the length of the OVSF codes increases, the UWAMC system’s BERs decrease, and its PSRs increase. The UWAMC system can achieve either maximum transmission speed or maximum transmission power efficiency.