# End-to-End Underwater Acoustic Communication Based on Autoencoder with Dense Convolution
## 4 Simulation Analysis  
In order to demonstrate the effectiveness of the proposed convolutional-autoencoder-network-based communication method for underwater acoustic FBMC systems, the channel impulse response measured by linear-frequency-modulated signals at a certain moment in the Qingjiang experiment in July 2017 is used for simulation. The water depth at the experimental site is about 100 m, the transmitting and receiving vessels are about 1.5 km apart and both are in free drifting conditions. The transmitting transducer and receiving hydrophone are suspended at a depth of 30 m and 10 m, respectively. The channel impulse response is shown in Figure 5. The system parameters of the underwater acoustic FBMC modulation and the hyperparameter setting for the Conv1D autoencoder network are shown in Tables 2 and 3. To pursue a compromise between detection efficiency and accuracy, \(n_{b}=256\) bits are predicted at a time. The training samples and test data are divided by 9:1. The LS estimation algorithm and VTRM equalization algorithm are usually used in traditional signal detection based on pilots. The advantage of the LS algorithm is its simple structure and low computational effort. The VTRM algorithm first requires accurate Doppler compensation of the received signal, and the channel characteristics are estimated from the compensated received signal. The estimated channel is then time-inverted and convolved with the compensated received signal. In this paper, the BER performance of the system is analyzed in a signal-to-noise ratio (SNR) from 0 dB to 30 dB. Figure 6 compares the BER performance of the Conv1D autoencoder underwater FBMC communications when \(D=5\times 10^{4}\) samples are generated. \(\left(m_{1}^{e},m_{2}^{e},m_{3}^{e}\right)=\left(8,4,2\right)\) for the encoder network, and \(\left(m_{1}^{d},m_{2}^{d},m_{3}^{d}\right)=\left(2,4,8\right)\) for the decoder network. The proposed scheme is much better than that of the conventional method, and the performance of the system is further improved when dense connections are adopted between convolutional layers in the decoder. The advantage is even more obvious when the SNR is greater than 15 dB. This indicates that, by training with plenty of communication data, the proposed scheme is able to achieve similar constellation mapping at the transmitter and a better demodu  
Figure 7 compares the effects of different data sample sizes on the system's BER performance under the same network parameter settings. The kernel size of each convolutional layer remains unchanged, and the system is evaluated when the sample size is \(1\times 10^{4}\), \(2\times 10^{4}\), \(5\times 10^{4}\) and \(2\times 10^{5}\). The simulation results show that the BER performance of the proposed scheme decreases significantly with the increase in the number of training samples and is superior to the hand-crafted schemes in all cases. It indicates that the data-driven communication system is sensitive to the number of training samples. To explore the effect of the network structure, especially the effect of the number of convolution kernels on the system performance, we set up two comparisons: case1 with \(\left(m_{1}^{e},m_{2}^{e},m_{3}^{e}\right)=(4,2,2)\), \(\left(m_{1}^{d},m_{2}^{d},m_{3}^{d}\right)=(2,2,4)\) and case2 with \(\left(m_{1}^{e},m_{2}^{e},m_{3}^{e}\right)=(32,8,2)\), \(\left(m_{1}^{d},m_{2}^{d},m_{3}^{d}\right)=(2,8,32)\). The BER curve is shown in Figure 8. When \(D~{}=~{}2\times 10^{4}\), the BER performance gain of case2 compared with that of case1 slightly increases with an improvement in SNR. The deeper model performs better with a handful of training data. When \(D~{}=~{}2\times 10^{5}\), case2 and case1 show similar performances when the SNR is lower than 15 dB. This indicates that the proposed scheme is also influenced by the complexity of the model, and the gain from a deeper model is limited when the amount of data is sufficient.