# End-to-End Underwater Acoustic Communication Based on Autoencoder with Dense Convolution
## 3 Dense-Convolutional-Autoencoder-Based UWA FBMC Communications System
### System Model  
The idea of employing an autoencoder network is extended to the underwater acoustic FBMC system by placing the encoder network and the decoder network at the transmitter and the receiver, respectively, and the proposed scheme is shown in Figure 4. On the transmitter side, the encoder learns an appropriate mapping method to convert the binary bit stream to a complex symbol, which is then modulated by the integrated filter bank and sent to the underwater acoustic channel for transmission. No explicit channel estimation and equalization process is required on the receiver side, and the received complex symbols are directly input to the decoder after fast fourier transform (FFT) transformation to recover the original transmitted signal. The densely connected Conv1D layers are only employed in the decoder network because the initial Conv1D encoder networks are able to reproduce the constellations perfectly. Specifically, the binary bit stream \(b\) is randomly generated and entered into the well-trained encoder to map to a complex vector after a series of nonlinear operations. The parameter settings in the encoder and decoder with three Conv1D layers, respectively, are shown in Table 1, where \(m_{l}^{e}\) and \(m_{l}^{d}\) denote the number of convolutional kernel channels in the \(l-\)th layer of the coding network and decoding network. Batch normalization (BN) layers are used to speed up the training and convergence of the network and to prevent overfitting. The kernel size determines the dimension of the output features of the current convolution layer. Because only constellation mapping is replaced, the encoder has  
Figure 3: The Dense-Net structure. an input feature dimension of 1 for the first Conv1D layer and an output feature dimension of 2 for the last Conv1D layer. Then, the real and imaginary parts of the mapped symbols are staggered by half a symbol period, i.e., OQAM modulation. With the effect of the phase rotation factor, the adjacent real and imaginary parts at the TF points remain orthogonal in the real domain. After IFFT and filtering by a prototype filter bank with different offsets named the polyphase network (PPN), the data symbols are modulated onto \(M\) corresponding subcarriers, forming \(N\) FBMC symbols \(x_{FBMC}\). Typically, the prototype filter uses a non-rectangular pulse with length \(L_{g}=KT\), where \(K\) is the overlap factor and \(T\) is one FBMC symbol period. The prototype filter used in this paper is PHYDYAS [25] with overlapping factor \(K=4\). Finally, the signals on each subcarrier are superimposed through the underwater acoustic channel. The received signal is sent to the decoder for signal recovery after PPN and FFT. As the neural network cannot process complex data directly, the signal needs to be pre-processed. By taking the real part, the real and imaginary parts of the signal are stacked as all real tensors as from \(\pm a\pm bi\) to \([\pm a,\pm b]\), which also resists imaginary interference as in a traditional FBMC receiver. Dense-Net modules are constructed by using dense connections between each convolutional layer of a decoder to maximize feature sharing for better recovery of \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Layer Name**} & **Kernel Size** & **Stride** & **Input Features Dimension** \\ \hline \multirow{3}{*}{Encoder} & Conv1D + BN & \(m_{1}^{e}\) & 3 & 1 \\  & Conv1D + BN & \(m_{2}^{e}\) & 3 & \(m_{1}^{e}\) \\  & Conv1D + BN & 2 & 2 & \(m_{2}^{e}\) \\ \hline \multicolumn{4}{c}{Untrainable FBMC modulation} \\ \hline \multirow{3}{*}{Decoder} & Conv1D + BN & \(m_{1}^{d}\) & 2 & 2 \\  & Conv1D + BN & \(m_{2}^{d}\) & 3 & \(m_{1}^{d}\) \\ \cline{1-1}  & Conv1D + BN & \(m_{3}^{e}\) & 3 & \(m_{1}^{d}+m_{2}^{d}\) \\ \cline{1-1}  & Flatten + FC & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter settings of autoencoder network. Figure 4: Block diagram of UWA FBMC system based on convolutional autoencoder network. the original data.