# Deep Learning-Based Cyclic Shift Keying Spread Spectrum Underwater Acoustic Communication
## 2 System Structure
### DL-Based CSK-SS UWA Communication System Structure  
The structure of the DL-based CSK-SS UWA communication system is shown in Figure 5. Compared with the conventional system, in the receiving part of the DL-based system, the neural network model is used to replace the receiver module of the conventional system. The DL-based signal demodulation will be divided into the offline training stage and the online test stage. In the offline stage, the transmitter completes the modulation of the known source information, reaches the receiver of the system through the UWA channel, and completes the training of the neural network model by receiving the signal data samples. In the test stage, the synchronized unknown received signal is input to the trained neural network model to complete the signal demodulation. This paper selects unidirectional standard LSTM and BiLSTM as the neural network model in the system. In addition, two different schemes will be proposed for whether there is channel equalization preprocessing. In scheme A, the CSK-SS signal through the UWA channel is directly input to the DL-based system after signal synchronization. The neural network model training and the demodulation of the received signal are completed in two stages. In scheme B, the preprocessing operation of the received signal is added. Firstly, the channel estimation is completed by the orthogonal matching pursuit (OMP) algorithm [26], then the channel equalization is realized by the virtual time-reversal mirror (VTRM) technology [27], and finally, the preprocessed received signal is processed. In the two stages, the training of the neural network model and the demodulation of the received signal are completed. In the offline training stage of scheme A, the known information sequence generates signal samples after CSK-SS modulation. Multiple UWA channel samples for training are generated by using BELLHOP. The training dataset consists of the CSK-SS signal passing through the UWA channel, which can be expressed as  
\[r(t)=s(t)\otimes h(t)+n(t), \tag{14}\]  
where \(s(t)\) is the CSK-SS signal transmitted by the transducer, \(h(t)\) is the CIR of the UWA channel, \(n(t)\) is the noise interference, and \(\otimes\) is the convolution operation. In the offline training stage of scheme B, in order to suppress the ISI caused by multipath expansion of the UWA channel and reduce the impact of channel fading, channel equalization preprocessing can be carried out before the received signal is fed to the neural network model. Based on the reciprocity theorem [28], the time-reversal mirror technology matches the UWA channel of acoustic transmission and guides spatial focusing and time compression [29; 30]. VTRM technology can make the multipath signals generated by the acoustic channel superimpose in phase simultaneously, compress the signal in the time domain, suppress the ISI caused by multipath spread, obtain the focusing gain, and improve the SNR. Especially in constructing a UWA communication network, when the nodes are fixedly arranged under the complex shallow water acoustic channel conditions, a better communication performance will be obtained by using VTRM technology. In addition, since the focusing effect of VTRM is related to the accuracy of UWA channel estimation, the  
Figure 5: Structure of DL-based CSK-SS UWA communication system. OMP algorithm is used to estimate the channel. The received signal processed by VTRM will be used as the training dataset of the neural network, which can be expressed as  
\[ \begin{array}{l}r^{\prime}(t)=[s(t)\otimes h(t)+n(t)]\otimes h^{\prime}(-t)\\ =s(t)\otimes[h(t)\otimes h^{\prime}(-t)]+n(t)\otimes h^{\prime}(-t)\\ =s(t)\otimes\hat{h}(t)+n(t)\otimes h^{\prime}(-t),\end{array}  \tag{15}\]  
where \(h^{\prime}(-t)\) is the CIR estimation result after inversion, \(\hat{h}(t)\) is the cross-correlation function between the CIR \(h(t)\) and its estimated value \(h^{\prime}(-t)\), also known as the virtual time-reversal channel.