## 4 Experimental Results
### Training Results of the Proposed Models With or Without Pruning (Techniique)
#### 4.1.2 Experimental Results of Deep Neural Network Model  
To design a system suitable for the power-constrained environment of sonobuoys, pruning was applied only to the encoder among the encoder and RVQ. This is because pruning is challenging for RVQ due to its structural characteristics. RVQ operates based on a fixed codebook at each stage, and this codebook consists of static data that is not updated, like trainable weights, during the learning process. In contrast, the encoder is composed of a deep learning network, allowing pruning techniques to effectively reduce trainable weights and computational requirements. Therefore, pruning was applied to the encoder to design a lightweight model suitable for the constrained environment of sonobuoys. The pruning results are summarized in Table 3, where the computational requirements are measured in Mega Multiply-Add Operations per Second (MMACs) for processing \begin{table}
\begin{tabular}{c c c} \hline  & **CW** & **LFM** \\ \hline Center frequency (Hz) & 3500, 3600, 3700, 3800 & \\ Bandwidth (Hz) & - & 400 \\ Pulse duration (s) & 0.1, 0.5, 1 & \\ Sampling frequency (Hz) & 31,250 & \\ Total Time (h) & 43 & 43 \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters for the bistatic sonobuoy signal collection simulation. 1-second audio signals. The computational measurements for the encoder and RVQ in the proposed system show that additional RVQ parameters of 5.12 million and a computational requirement of 51.2 MMACs were introduced compared to the conventional method [6]. However, these values remain significantly lower than those of LightCodec [14], a state-of-the-art lightweight neural codec for audio signals, which requires 820 MMACs. These results demonstrate that the proposed system is efficient and well-suited for environments with limited power and computational resources, such as sonobuoy operations. To evaluate the performance of the proposed neural codec system, we quantitatively measured the Spectrogram MSE (MSE), Log Spectral Distance (LSD), and Signal-to-Noise Ratio (SNR) between the reconstructed signals and the original input signals. Additionally, a subjective comparison was conducted through visual analysis of the spectrograms. Performance evaluation was carried out using approximately 0.5 h of CW and LFM signals, which were not included in the training set, totaling 1 h of evaluation data. Additionally, the spectrogram MSE is calculated as the mean squared error between the amplitude spectra of the original and reconstructed signals. It is defined by the equation:  
\[MSE_{spectrogram}=\frac{1}{N_{frame}}\sum_{j=1}^{N_{frame}}\left(\frac{1}{N-1} \sum_{k=2}^{N}\left(\left|X_{k}^{j}\right|-\left|Y_{k}^{j}\right|\right)^{2} \right)\, \tag{7}\]  
where \(N_{frame}\) represents the total number of frames, and \(N\) is the number of samples per frame (corresponding to the FFT size). The term \(\left|X_{k}^{j}\right|\) refers to the amplitude spectrum of the original signal at frequency index \(k\) for frame \(j\), while \(\left|Y_{k}^{j}\right|\) denotes the amplitude spectrum of the reconstructed signal at the same frequency and frame. The summation starts from \(k=2\) to exclude the DC component, focusing only on the non-DC frequency components. Table 4 presents the results of this quantitative evaluation, including a comparison with the existing DIFAR sonobuoy-based neural codec [6]. Furthermore, the proposed method incorporates the results of encoder optimization achieved through parameter pruning, which is known as Proposed-Pruned. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Signal Type** & **Spectrogram MSE** & **LSD (dB)** & **SNR (dB)** \\ \hline \multirow{2}{*}{Conventional [6]} & CW & 0.00277 & 1.19 & 25.93 \\  & LFM & 0.01428 & 1.19 & 17.66 \\ \multirow{2}{*}{Proposed} & CW & 0.00109 & 1.13 & 29.19 \\  & LFM & 0.00639 & 1.10 & 21.56 \\ \multirow{2}{*}{Proposed–Pruned} & CW & 0.00128 & 1.15 & 28.59 \\  & LFM & 0.00719 & 1.12 & 21.08 \\ \hline \hline \end{tabular}
\end{table}