Underwater Acoustic Communication Channel Modeling using Reservoir Computing

Underwater wireless communication has rapidly grown in importance for numerous ocean monitoring and information exchange applications in civil and military use in recent years [1]. Acoustic technology has also been shown as a useful tool for a wide range of underwater activities and applications. Ocean exploration, scientific data collection, and transmission are some of the most prevalent applications for underwater acoustic (UWA) communications. Furthermore, underwater communications have benefited the maritime sector by making process management and monitoring easier and more efficient [2]. Underwater operations including undersea marine biology study, undersea mining, pipeline laying, underwater maintenance, and geological surveys have fueled the increased demand for underwater channel and environment research [3]. In general, the behavior of the channel has a significant impact on acoustic signal transmission, therefore having a deep understanding of the channel characteristics is critical for implementing an effective underwater communication system [2].

The underwater environment presents a unique set of challenges for wireless communications [4], and UWA channels are widely regarded as one of the most challenging communication media now in use [1]. While low frequencies are excellent for acoustic propagation, the bandwidth available for communication is extremely limited. Furthermore, a UWA channel has low physical link quality and high latency, and it suffers from large multipath delay spread and frequency selective fading [5], making modeling of the UWA channel quite challenging [6, 7, 4, 8, 9]. A typical UWA communication scenario is depicted in Figure 1. As illustrated in the figure, variations in sound velocity, roughness of the ocean bed, multi-path propagation of acoustic signals, and ambient ocean acoustic noises created by aquatic creatures and human activities make it even more challenging to model UWA channel [2, 8].

Many physics-based UWA channel models have been developed. The most commonly used one is the BELLHOP model, which is an open-source beam/ray-tracing model for predicting acoustic pressure fields in the underwater environment [8]. The BELLHOP ray model is an intuitive and straightforward means for modeling sound propagation in the ocean among the various existing mathematical UWA channel models based on ray, normal-mode, and parabolic curve [1]. The majority of these models, however, are based on mathematical assumptions and approximations rather than real underwater communication data. As a result, they do not work well in reality [1].

Machine learning has seen considerable success in fields such as image and voice recognition, language processing, medical diagnosis, and wireless communications. This is due largely to its capacity to learn and intelligently respond to changing and complex operating conditions, such as those found in the UWA communication channel. Specifically, it is shown that modeling the UWA channel by replicating the effect of real water environment characteristics on the channel is effective [1]. However, there has not been much research work done in the domain of UWA communications using machine learning because of the complex nature of the underwater environment and the lack of sufficient and high-quality data. This motivated us to leverage the capability of collecting real-world data of UWA communications from Lake Tahoe in Reno, Nevada, and apply a data-driven approach to modeling the UWA channel using machine learning on the collected datasets [11].

RC is explored to model UWA channel in this paper. It has been shown that RC is capable of modeling dynamical systems [12, 13] and predicting chaos [14]. RC is a time-dependent data processing paradigm influenced by neuroscience [15]. It is a type of recurrent neural network model in which the recurrent component is initialized randomly and subsequently fixed thus incurring less computation and reducing training time [16, 17]. Despite this significant simplification, the recurring element of the model, the reservoir has a huge number of dynamic properties that can be used to solve a wide range of problems [18].

In this work, we seek to leverage these properties of RC and provide a data-driven approach to modeling the UWA communication channel using the Echo State Network (ESN), which is one of the two pioneering RC approaches. Using this approach significantly reduced the implementation complexity and the training time. The contributions of this paper are:

1. 1.

   A data-driven approach for UWA channel modeling is proposed to take advantage of the real-world experimental UWA datasets and avoid the unrealistic assumptions made by physics-based mathematical models.

2. 2.

   UWA channel modeling using ESN, an approach of RC and transfer learning have been carried out. Observations and insights are provided based on the experimental results.

3. 3.

   The effects of different setups of the ESN on the model performance, in terms of the reservoir initialization method, the size of the reservoir, the activation function, and the regression algorithms used at the readout layer, have been examined and suggestions are made to improve the performance of ESN for UWA channel modeling.

4. 4.

   A novel approach of designing the reservoir using a pre-trained deep learning model as the reservoir has been proposed in this study. Experimental results demonstrate that ESN using pre-trained deep learning models as reservoir outperform the deep learning models for modeling the UWA channel. Although this may not be advantageous if the reservoir of the ESN can be designed properly using randomized weights, it provides a systematic way to set up the reservoir, which is valuable because there does not exist a systematic way for the design of reservoir for diverse real-world applications.

5. 5.

   Transfer learning using simulated radio frequency (RF) data and Bellhop-based simulated UWA channel data has been performed. It is observed that the performance of transfer learning using RF data is poor because of the significant differences in characteristics between RF channel and UWA channel. On the contrary, the performance of transfer learning using Bellhop-generated data is pretty good, although the Bellhop model itself is a simplified mathematical model and it does not take into account the various uncertainties in a real-world scenario.

The remainder of this paper is structured as follows. Some related works are discussed in Section II. Section III describes the data generation and collection process and gives the description of the datasets used in this work. Section IV discusses RC and the ESN approach used in this experiment. Detailed experimental results and analysis are given in Section VI and observations and insights from the results are discussed. Section VII concludes the paper.

Many mathematical models have been built and used for different purposes in theUWA domain including but not limited to investigating and tracking channel properties, sound propagation characteristics, the behavior of acoustic signals for different transmission frequencies, and the computation of some channel parameters such as the route loss. For example, in [1], a BELLHOP ray model was used to model the UWA channel in order to examine sound propagation characteristics while taking into account the rough nature of sea surfaces and bottoms for various oceanic conditions. It was also used to examine the behavior of an acoustic signal with transmission frequencies in the range of 9K to 90KHz in [19]. Channel properties for an autonomous underwater vehicle (AUV) wireless communication system were mathematically quantified by modeling the UWA channel in [3]. The model was created using the $AN$ product, signal-to-noise ratio (SNR), and band selection, where $A$ represents attenuation and $N$ represents ambient noise. In [9], simulations using ray-theory-based multipath Rayleigh underwater channel models for shallow and deep waters are carried out to investigate transmission losses between transceivers, the effects of bit error rate, maximum internode distances for different networks and depths, the effect of weather season, and variability of ocean environmental factors. The authors in [20] proposed a channel model for tracking dynamic UWA channels by using the channel’s correlation as the state-space model in the Kalman filter in order to improve tracking. The authors of [6] calculated the channel route loss, changed the log-distance model to produce a model suitable for an underwater IoT network, and created an empirical channel model for medium-distance UWA channels based on real measurement data. In [21], a non-stationary two-dimensional wideband channel model was designed for UWA communication and evaluated with measurement data.

Various deep learning models have been proposed to model UWA communication channels. For example, in [22], a deep learning network based signal detection was employed for full-duplex cognitive UWA communication with self interface cancellation. Automatic modulation classification of underwater communication signals using a combination of the convolutional neural network (CNN) and LSTM [23]. A similar task has been done in [24] using blind equalization in conjunction with a CNN. Because it is difficult to identify modulation during actual communication due to the complex and unstable nature of UWA communication systems, several machine learning methods were used in [25] to classify the modulation type in their quest to find an efficient link adaptation method based on channel quality of an underwater communications network. In [26], the authors employed a DNN to create a deep learning-based receiver for single carrier communication in a UWA channel utilizing data from the sea. When compared to the traditional channel-estimate based decision feedback equalizer, the DNN based receiver consistently performed better. The authors in [27] also utilized the DNN to estimate channel parameters based on data from the Bellhop Ray model simulation of the UWA environment. When compared to traditional channel estimation methods such as least square and minimum mean square error (MMSE), the DNN outperformed the LS algorithm and is comparable to the MMSE algorithm in terms of bit error rate and normalized mean square error. A deep learning-based UWA orthogonal frequency-division multiplexing (OFDM) communication system was constructed by representing the receiver as a DNN in [28] and [29]. The deep learning UWA communication systems could easily recover the transmitted symbols after training without using explicit channel estimation and equalization. In [30], the authors developed a depth learning-based underwater target recognition approach employing CNN and an extreme learning machine for UWA target classification and recognition.

RC has been applied in wireless communications for predicting wireless channel or state conditions, symbol detection, and measuring the channel SNR. For example, in [31], the performance of an extreme learning machine and an ESN for forecasting wireless channel conditions was compared. These two methods were used to forecast the SNR for single-input single-output systems in both pico-cellular and micro-cellular contexts. For multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems, an ESN-based symbol detector was used in [32]. The efficiency of the adopted symbol detector outperforms traditional symbol detectors based on channel estimation methods in terms of BER performance according to simulation results. In [33], a new RC-based detector called windowed ESN was designed for MIMO-OFDM symbol detection. This resulted in significant improvements in interference cancellation and nonlinear compensation, as well as the ability to improve short-term memory fundamentally. The authors in [15] looked at a simplified fading channel model, defined the transmission properties of satellite communication channels, and devised an ESN-based approach for measuring channel SNR. For the categorization of multivariate time series, the authors in [34] applied an unsupervised approach for creating multivariate time series (MTS) representations (also known as reservoir model space). The parameters of a one-step forward predictor that forecasts the future reservoir state rather than the future MTS input were used to create the reservoir model space. The results revealed that RC classifiers are substantially faster and achieve higher classification accuracy. In [35], an ESN was utilized to train an RNN to predict channel state information in a wireless OFDM system, which resulted in a significant decrease in training time, implementation, and computing complexity. RC has also been applied in UWA communications. For example, transfer learning was introduced to ESNs in [36] to develop a channel model that predicts shallow water dynamics. Experimental results showed that transfer learning helped improve the predictions.

In this work, we leveraged the capabilities of RC and deep learning to build a data-driven channel model using a real experimental UWA communications dataset collected from Lake Tahoe under various environmental conditions. Different from the existing works, the goal of this work is to model the UWA channel and be able to perform sequence-to-sequence prediction, i.e., when a sequence of transmitted data is fed into the model as input, the corresponding sequence of data is expected to be received at the receiving end of the UWA channel will be predicted. The obtained UWA channel model in this work would be very useful as a candidate plugin module when large scale simulations of UWA communications are needed, or a large amount of data need to be generated for UWA channels with high fidelity while it is difficult to obtain that kind of data from physical underwater data collections.

RC is a time-dependent data processing paradigm influenced by neuroscience [15]. It is a class of recurrent neural network (RNN) model in which the recurrent component is produced randomly and subsequently fixed [16, 17]. The RC methodology builds an RNN with random synaptic weights, dubbed the reservoir, in order to avoid the gradient-descent procedures of the training algorithms for a typical RNN. In [16] and [38], RC shows how an RNN with fixed connectivity can memorize and produce complicated Spatio-temporal sequences. RC has also been demonstrated to be a valuable tool for modeling and predicting dynamic systems [12, 13]. It was demonstrated in [14] that RC is capable of forecasting massive chaotic systems.

Despite this significant simplification, the recurring element of the model (the reservoir) has a huge number of dynamic properties that can be used to solve a wide range of problems [18]. It is also pertinent to state that RC involves less computation and thus has reduced training time dramatically. The normal workflow of solving a task using RC requires handling two key steps: (1) designing a suitable reservoir for the specific task under consideration, and (2) determining a readout function that will adequately map the state of the reservoir to a target output [39]. One of the concerns of RC is that the design is mainly driven by a succession of randomized model-building stages, leaving researchers to rely on a series of trials and errors [40]. In this work, a novel approach to designing the reservoir using a pre-trained deep learning model as the reservoir has been proposed. Although this may not be advantageous if the reservoir of the ESN can be designed properly using randomized weights, it provides a systematic way to set up the reservoir, which is valuable because there does not exist a systematic way for the design of reservoir for diverse real-world applications.

There are two popular RC approaches: the Liquid State Machines (LSM) and ESN [41, 42, 43]. Both architectures attempt to model biological information processing using similar principles [44]. In this work, ESN is chosen because of its close relationship to RNN/LSTM and allows direct performance comparison between these different models.

Transfer learning can be defined as the process of improving learning in a new task or domain by transferring knowledge acquired from another related task or domain that has already been trained. In other words, transfer learning relates to situations in which what has been learned in one domain is used to improve generalization in another domain [53]. In transfer learning, a base model is first trained on a base dataset and task. The learned features are then transferred to the target domain to be trained on a target dataset and task. This method is more likely to succeed if the features are generic, i.e., applicable to both the base and target domains, rather than being specific to the base domain. This approach is known as the “pre-trained model approach”. The purpose of transfer learning is to quickly obtain the learning model by leveraging commonalities between tasks. In this study, transfer learning for RC has been considered. Specifically, transfer learning using simulated RF data and Bellhop based simulated UWA channel data has been performed. In this case, the base domain is RF wireless communications or simulated UWA communications, and the target domain is real-world UWA communications.

In this section, we provide the experimental set up such as the hyperparameters’ settings in section VI.A. Then the detailed performance of ESN is evaluated in section VI.B. Performance evaluations of modified ESN and transfer learning are carried out in section VI.C and section VI.D, respectively. Together they provide a comprehensive performance analysis of the proposed schemes.

Two key objectives were pursued in this work. The first objective is to mitigate the approximations and unrealistic assumptions made by the mathematical models for UWA channel models by providing a data-driven approach to UWA channel modeling. To achieve this first goal, data generation and collection experiments were carried out in a water tank and in Lake Tahoe under different levels of disturbances. Then the obtained datasets were used to train deep learning models (DNN and LSTM) as well as the ESN to obtain models with high fidelity in a real-world scenario. It is observed that ESN performs better than DNN and LSTM in terms of prediction accuracy and has much less computational cost in terms of training time. The performance gap becomes larger when the data quality gets worse (more chaotic data), which is in agreement with previous studies in the literature that RC is very effective in modeling chaotic dynamical systems. The second objective is to examine how RC performs under various setups including different initialization methods of the reservoir, various spectral radii, the reservoir size, the activation function used, and the regression method used for training the output layer. It is shown that ESN is quite robust to these different settings as long as the spectral radius satisfy the echo state property. It is also observed that when the size of the reservoir matches the size of the input sequence, the ESN model performs better. Furthermore, the performance of transfer learning in ESN is also evaluated. Although Bellhop mathematical model has a very poor performance by itself, when ESN models trained with simulated Bellhop data were transferred and evaluated on real-world underwater data, there was a noticeable improvement in ESN performance. Lastly, a modified ESN implementation was examined where the reservoir of the ESN is replaced with a pre-trained deep learning model. Though this approach gives a slightly better performance when compared to pre-trained deep learning models, it is not as efficient as the conventional ESN.

In this study, the trained ESN model, using real-world UWA communications data, is a data-driven black box model that performs sequence-to-sequence or point-to-point prediction very well with time-series I/Q data as the input to the model. It could be used to carry out large scale simulations of UWA communications or obtain a large amount of high fidelity data when it is difficult to obtain that kind of data from physical underwater data collections. While it provides a more realistic model when compared to mathematical models, it may also be over specified due to the peculiarities of the measurement environment. It could also be generalized to model a network setting with multiple transceivers or could be refined to model the ocean environment or any other environment with time-series data. For instance, we can generalize the developed channel model to a network setting with multiple transmitting-receiving (Tx/Rx) pairs, as long as the multiple Tx/Rx pairs are orthogonal. If we consider multiple simultaneous transmissions in non-orthogonal UWA channels, new channel model must be trained based on new datasets that capture the mutual interference. The model can also be trained in the reverse direction to recover the transmitted signals based on the received signals, which may be an alternative implementation for the software-based receiver. This is one of our future efforts.

This research work is supported in part by the U.S. Army Research Office (ARO) under agreement number W911NF-20-2-0266 and the U.S. Office of the Under Secretary of Defense for Research and Engineering (OUSD(R&E)) under agreement number FA8750-15-2-0119. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the U.S. Army Research Office (ARO) or the Office of the Under Secretary of Defense for Research and Engineering (OUSD(R&E)) or the U.S. Government.