## 6 Simulation and Ocean Experiments
### Simulation Result  
For the learning process, the whistles with the Additive White Gaussian Noise (AWGN) channel and with the time varying multipath channel of a shallow water in Figure 11(a) were utilized. The simulation models of the ocean depths, the distance between the transmitter and the receiver, and  
Figure 11: Trained network coefficients (**a**) DNN: Conv layer1 (\(48\times 48\)); (**b**) DAG-net1: Conv layer1 (\(48\times 48\)); (**c**) DAG-net1: Conv layer1 (\(128\times 128\)); (**d**) DNN Conv layer5 (\(24\times 24\)); (**e**) DAG-net1: Conv layer5 (\(24\times 24\)); (**f**) DAG-net2: Conv layer10 (\(24\times 24\)).  
the depth of each transmission source and receiver hydrophone are also shown in Figure 11(a). For the UWA channel, SNRs vary from \(-16\) dB to \(14\) dB by a \(2\) dB step, and \(150\) cases were generated for a SNR to obtain statistical reliability. At every iteration, Doppler frequencies of each multipath randomly and independently varied from \(0\) Hz to \(2\) Hz. These procedures were executed for all \(704\) whistles. Thus, \(3.4\) million training samples were utilized to train the D-LSTM network. Please note that the UWA channel had long multi-path delay times, which covered other conventional UWA channels. The efficacy of this learning process was proven in computer simulations and ocean experiments. For the over-fitting problem of the machine learning performance test, the different ocean environments with different multipath channels, given in Figure 11(b), were also used.  
In Figure 13, the BER performances of the tested algorithms are displayed. The dashed lines denote the BERs of whistle-by-whistle detections. The solid lines denote the BERs of the proposed link information aided detection methods. The black, the green, the pink, and the blue dashed lines denote the BERs of the conventional ML detectors, the conventional DNN, DAG-net1, and DAG-net2, respectively. The pink and the blue solid lines denote the BERs of the D-LSTM1, and the D-LSTM2, respectively. Figure 12(a)-c exhibits the BERs of the AWGN channel, the UWA channel of Figure 11(a), and the different UWA channel of Figure 11(b), respectively.  
In Figure 13, all BER results of the dashed lines exhibited the error flows by the limitation of the whistle-by-whistle detection. The error-floors started with \(10^{-2}\), which were considered as a low value in the conventional image detection applications. These values, however, may not be acceptable for the communications. Among the tested whistle-by-whistle detectors, the DAG-net1 and the DAG-net2 showed better BER performances than the other conventional algorithms, and had error-floors at \(10^{-3}\). As the number of the DAG-net stages increased, the detection performance also increased. Thus, the proposed D-LSTM1 and D-LSTM2 were tested for detection of the link information. In Figure 13, the proposed D-LSTM2 method demonstrated better BER performance than other algorithms, and did not have the error-floor. In Figure 12(c), the BER results were obtained by the UWA channel in Figure 11(b), which was not used for the training. Even though the trainings were executed by AWGN and the UWA channel in Figure 11(a), the BER results of the proposed method for the different UWA channel in Figure 11(b), also demonstrated the lowest BER value. Please note that the multipath of the UWA channel severely distorts the transmitted signals and the maximum delay time of the multipath is one of the important parameters of the UWA communications. The multipath delay time of the trained UWA channel in Figure 11(a) was larger than that of Figure 11(b). Therefore, the proposed algorithm was expected to attain the good BER results for practical ocean experiments. In the next subsection, the BERs of the practical ocean experiments are demonstrated.  
Figure 12: UWA channel (**a**) for training; (**b**) for tests.