# WhistleGAN for Biomimetic Underwater Acoustic Covert Communication
## 3 Analysis of Experimental Results
### Whistle Generation Results  
For the training of the proposed WhistleGAN, the whistles from the \"Watkins Marine Mammal Sound Database (WMMSD)\", and \"voice in the sea and discovery of sound in the sea\" were used [24; 25]. The data of about 239 single whistles were increased to 10,000 whistles by changing the time and frequency and used as the training set. To compare the computational complexity and accuracy between the proposed WhistleGAN and the conventional methods, the DCGAN (256) and the proposed WhistleGAN were trained, and DCGAN (128) was also trained with the same whistles of the same size for a fair comparison. The whistle inputs for DCGAN (256) and DCGAN (128) were set to 256 \(\times\) 256 \(\times\) 3 and 128 \(\times\) 128 \(\times\) 3, respectively, according to frequency, time, and color. Note that the proposed WhistleGAN with a 128 Mel filter bank was trained by reduced whistle image to 128 \(\times\) 128 \(\times\) 3, which was four times smaller than the DCGAN (256) input image size. The frequency scale of the input whistles of the proposed method was transformed into a logarithmic Mel scale with equal intervals from the linear scale. For training the proposed WhistleGAN and the conventional DCGAN, the input whistles were normalized between \(-\)1 and 1. The WhistleGAN and DCGAN were implemented on Pytorch 1.12.0 and trained using RTX 4090 (NVIDIA, SCL, Santa Clara, CA, USA). Both methods used the same learning parameters for a fair comparison in Table 4. The bench test results of the computational complexity of DCGAN and the proposed WhistleGAN are shown in Table 5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Kernel** & **Stride** & **BN** & **Activation Function** \\ \hline Input & 4 \(\times\) 4 & 2 & N & LeakyReLU \\ Conv1 & 4 \(\times\) 4 & 2 & Y & LeakyReLU \\ Conv2 & 4 \(\times\) 4 & 2 & Y & LeakyReLU \\ Conv3 & 4 \(\times\) 4 & 2 & Y & LeakyReLU \\ Conv4 & 4 \(\times\) 4 & 2 & Y & LeakyReLU \\ Conv5 & 4 \(\times\) 4 & 2 & Y & LeakyReLU \\ Output & 2 \(\times\) 2 & 2 & N & Sigmoid \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The specific structure of the WhistleGAN’s discriminator network. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **128 \(\times\) 128 \(\times\) 3** & **256 \(\times\) 256 \(\times\) 3** \\ \hline DCGAN [20] & 10 million & 30 million \\ ProGAN [21] & 140 million & 420 million \\ BigGAN [22] & 500 million & 1500 million \\ VQGAN+CLIP [23] & 50 million & 150 million \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The number of nodes in generation models according to input size. In Table 5, the average batch time of the proposed WhistleGAN was 1.63 times faster than that of the conventional DCGAN (256). The number of images processed per second of the proposed method was 3.25 times higher. The total parameter size of the proposed method was 1.88 times smaller. Thus, the proposed WhistleGAN has 47% less computation than the conventional DCGAN (256) using smaller-sized whistles, even with additional filters and the learning process. On the other hand, the conventional DCGAN (128) with the same size whistle input used in the proposed method required less computational complexity than the proposed WhistleGAN because the conventional DCGAN (128) did not use the bilateral filter. Figures 3 and 4 depict examples of whistles generated by the DCGAN (256) and DCGAN (128), and Figure 5 displays examples of whistles generated by the proposed WhistleGAN. Figure 3 shows the whistle of size 256 \(\times\) 256 \(\times\) 3, and Figures 4 and 5 show the whistle of size 128 \(\times\) 128 \(\times\) 3. In Figure 5, the y-axis denotes the Mel frequency scale, while others utilize linear scale. The whistles generated by the DCGAN and the proposed WhistleGAN are noise-free and generated various whistle contours such as flat, up-chirp, down-chirp, and fluctuations, etc. [26]. Since the method generated new whistle patterns, the conventional correlation assessment between real and generated whistles cannot be applied.