# A Joint Denoising Learning Model for Weight Update Space-Time Diversity Method +
## 5 Evaluation and Result Analysis
### Simulation Results  
The simulation experiment used Bellhop [71] to simulate the transmit-receive scenario of the underwater array. Bellhop is a toolbox dedicated to underwater environment simulation, supporting a wide range of parameter settings. By editing the environment file \(*env\), we can implement the shock response simulation for the UWA channel. The transmitter is a single acoustic source, and its position will change twice, corresponding to angles of \(\theta 1=30^{\circ}\) and \(\theta 2=60^{\circ}\). Distance R = 100 m between the transmitting end and the center O. The receiver is a four-element uniform linear array (ULA). The sound field is limited to \(100\) m \(\times\) 300 m \(\times\) 150 m in the water. To simulate the tugboat's situation close to the communication array, we set the distance between the tugboatand the array to \(5\) m when the VURN is the main source of the noise. The transmit and receive settings for the simulation environment are shown in Figure 15(a). The sound velocity profile is shown in Figure 15(b). \begin{table}
\begin{tabular}{c c c} \hline
**Network** & **Components, Kernel Size** & **Component Number** \\ \hline \multirow{8}{*}{Complex-CGAN} & Conv, \(1\times 1\) & GM 3; DM 6. \\  & Conv, \(3\times 3\) & GM 3; DM 3. \\  & Conv, \(4\times 4\) & GM 1. \\ \cline{1-1}  & Pool, \(3\times 3\) & GM 1; DM 2. \\ \cline{1-1}  & CatBN & GM 1; DM 1. \\ \cline{1-1}  & CReLU & GM 1; DM 1. \\ \hline \multirow{8}{*}{RCL module} & Conv, \(1\times 1\) & 2 \\ \cline{1-1}  & Conv, \(3\times 3\) & 3 \\ \cline{1-1}  & Inception & 1 \\ \cline{1-1}  & Pool, \(3\times 3\) & 2 \\ \cline{1-1}  & CReLU & 2 \\ \hline \multirow{8}{*}{TDNN} & Conv, \(3\times 3\) & 2 \\ \cline{1-1}  & CReLU & 1 \\ \cline{1-1} \cline{1-1} \cline{2-4} \end{tabular}
\end{table} 
Table 2: Specific network parameter settings for the noise-reduction learning model. Accuracy and loss function are important metrics that describe the DL model during training and testing. Higher accuracy represents better performance, and faster convergence of the loss function represents better training and testing results. Figure 17 shows the accuracy and loss function statistics on the training and test datasets in the simulation experiments. Figure 17 shows that the noise-reduced learning model maintains a better processing advantage on both the training and test datasets. In the simulation experiments, we compared the performance of the proposed method with more typical algorithms in UWA signal processing. These algorithms are the Wiener filtering method, the KBM-ANC method, and the CNN method. The Wiener filtering algorithm uses finite-length Wiener filtering with time-domain processing. The KBM-ANC method uses the nonlinear-KLMS algorithm, which uses a Gaussian kernel function to compute the mean-squared error and can be considered a dictionary-based nonlinear sparse approximation problem. The definition of nonlinear-KLMS is as follows:  
\[\mu=\max_{i\
eq j}\left|\kappa\left(\mathbf{u}_{\omega_{i}},\mathbf{u}_{ \omega_{j}}\right)\right| \tag{28}\]  
Figure 16: The setup of the simulation test: (a) the transmit and receive settings for the simulation environment; (b) the sound velocity profile. Figure 17: Comparison of accuracy and loss function statistics for training and test datasets. where \(\kappa(. )\) is a normalized kernel function and \(\mathbf{u}\) is a dictionary element. The coherence coefficient criterion only allows the input \(\kappa\left(\mathbf{u}_{\omega_{i}},\mathbf{u}_{\omega_{i}}\right)\) to be added to the dictionary when it is below the threshold \(\mu_{0}\). The value of \(\mu_{0}\) is taken in the interval of [0,1], which controls the sparsity of the dictionary and was taken as 0.2 in the simulation experiment. The dictionary can be constructed by Equation (29), and M denotes the length of the dictionary, which is taken to be equal to the length of the data frame in the experiment.