# Deep Learning-Based Signal Detection for Underwater Acoustic OTFS Communication
###### Abstract  
Orthogonal time frequency space (OTFS) is a novel two-dimensional (2D) modulation technique that provides reliable communications over time- and frequency-selective channels. In underwater acoustic (UWA) channel, the multi-path delay and Doppler shift are several magnitudes larger than wireless radio communication, which will cause severe time- and frequency-selective fading. The receiver has to recover the distorted OTFS signal with inter-symbol interference (ISI) and inter-carrier interference (ICI). The conventional UWA OTFS receivers perform channel estimation explicitly and equalization to detect transmitted symbols, which requires prior knowledge of the system. This paper proposes a deep learning-based signal detection method for UWA OTFS communication, in which the deep neural network can recover the received symbols after sufficient training. In particular, it cascades a convolutional neural network (CNN) with skip connections (SC) and a bidirectional long short-term memory (BiLSTM) network to perform signal recovery. The proposed method extracts feature information from received OTFS signal sequences and trains the neural network for signal detection. The numerical results demonstrate that the SC-CNN-BiLSTM-based OTFS detection method performs with a lower bit error rate (BER) than the 2D-CNN, FC-DNN, and conventional signal detection methods. O 202202010 10 2022  
non-fading channel through a series of 2D transformations. In UWA OTFS communication, the fast time-variant UWA channel will still bring ICI and inter-symbol interference (ISI). To improve the communication performance of OTFS, channel equalization and signal detection can mitigate the interference. Signal detection algorithms generally include linear and nonlinear detection algorithms. Linear signal detection methods, such as the zero-forcing (ZF) algorithm [11] and linear minimum mean squared error (LMMSE) [12], have high complexity in practical implementation. Bayesian-based nonlinear algorithms assume the interference terms are approximately Gaussian distributed noise, such as message passing (MP) [13] and the Markov chain Monte Carlo algorithm. However, in actual UWA communication systems, the interference term may not obey the Gaussian distribution. Although the nonlinear algorithms can approximate the optimal performance with a large number of iterations, the complexity is much higher than that of the LMMSE algorithm. In UWA OTFS communication, signal detection has been studied by linear equalizers [14; 15; 16] under different UWA channels. Machine learning can be used in wireless communication for signal detection. In [17], supervised machine learning techniques were applied to decode the tag symbols. The input features that form the training data were explored and extracted from the received signal for machine learning-based detectors. In [18], support vector machine (SVM)-based data detection is proposed for optical OFDM in visible light communication. In this paper, the SVM detector contained multiple binary classifiers with different classification strategies. The experiment results presented that the SVM detection offered improved BER performance compared with the traditional direct decision method. In [19], the SVM in machine learning was used to jointly optimize the processing chain of signal detection, feature extraction and signal classification, and the simulation results show that the SVM had good performance. However, when the sample size is large, machine learning has difficulty dealing with the problems, and deep learning (DL)-based methods can solve such problems well. For example, the convolutional neural network (CNN) and its derivative algorithms can automatically learn the deep features of input digital information for subsequent classification [20]. The recurrent neural network (RNN) is also widely used due to its advantages in processing time series data [20]. In recent years, the DL-based method has shown its potential in communication systems [21]. [PERSON] et al.