Underwater acoustic noise with generalized Gaussian statistics: Effects on error performance

Underwater acoustic (UWA) communication in shallow water areas is often affected by the impulsive components of ambient noise. The noise statistics in such cases does not follow the traditional Gaussian behavior. On the other hand, most communication receivers are designed with Gaussian noise assumption. Performance of such systems may not be optimum in the presence of non-Gaussian noise in a UWA channel, and, so, the scenario demands an investigation. Among the several non-Gaussian noise models proposed in various literature, the Gaussian Mixture (GM) distribution is popular due to its "universal approximation" properties. However, despite its popularity in modeling UWA noise, none has yet reported any analytical analysis of error probability assuming GM noise statistics in the UWA channel, to the best of our knowledge. In this paper, we present a study on the error performance of a UWA communication system considering channel noise to be a mixture of Gaussian components. We derive the analytical expressions of probability of error for BPSK, QPSK and M-PAM constellations. We also simulate a UWA system where the performance of a traditional Gaussian receiver is studied in the presence of GM noise. It has been observed that in the presence of GM noise, the system performance degrades significantly from the usual one expected in a Gaussian noise environment and becomes a function of the mixing coefficients of the GM distribution.

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.

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.

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.

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.

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.

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.

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 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 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.

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.

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.

Sonar plays a very important role in underwater detection and exploration. Sonar images can show the underwater scene which are transmitted through the underwater acoustic (UWA) channel. However, the UWA channel is challenging to transmit images because of the characteristics of the channel, such as doppler spread, multipath effect, and especially limited bandwidth. In order to transmit images efficiently, in recent years, compressed sensing (CS) has been widely used as an image compressed method. The sparse representation in CS can be performed by the wavelet transform and other transforms which can generate sparse signal. In this paper, a novel signal transform called sparse wavelet transform (SWT) is proposed to find the most sparse representation of signal. The proposed algorithm can transmit sonar images with less data and thus improve the bandwidth utilization. Sparse wavelet transform is compared with Bandelets transform and wavelet transform in an experiment. The results show that the peak signal to noise ratio (PSNR) and the structural similarity (SSIM) index of sparse wavelet transform are higher than that of wavelet transform and Bandelets transform at the same sample rate.

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.

Due to the simultaneous existence of severe difficulties caused by multi-path, Doppler, and environmental noise caused by underwater acoustic channels, designing a stable and reliable underwater acoustic communication system (UWACS) is a challenging task. In addition to channel estimation and equalization, the technique of channel codes, which is capable of approaching Shannon’s capacity at a low encoding and decoding complexity, offers an efficient and reliable solution to improve the performance of the UWACS and thus draws extensive attention from the research community. By seeking a balance between communication efficiency and channel tolerance via multiple coding rate tuning, it has been recognized that the rate-compatible codes can achieve smooth rate-adaptive transmission under highly diverse underwater acoustic channel states. While there has been a substantial number of investigations on rate-compatible channel codes for the UWACS, in this paper, the research of rate-compatible channel codes has been summarized, reviewed, and compared, mainly focusing on the low-density parity-check (LDPC) and polar codes, which render flexibility in terms of code length and rate. Furthermore, typical research was evaluated and compared from the practical viewpoint of performance under real noise in a shallow water environment. Finally, problems encountered by the LDPC and polar codes for the UWACS were highlighted, and several future research issues were discussed.