# Generalized Chirp Spread Spectrum for Underwater Acoustic Communications
## 4 Performance Evaluations
The experiments were conducted in a stable environment under sea state 3 conditions. Table 2 shows the modulation parameters used in the ocean experiments, and approximately 10,000 bits were transmitted and received for each case. In the ocean experiment, the CIR for all slots estimated through the preamble signal included in the transmitted frame was stacked in time order and is shown in Figure 11. As seen in Figure 11, two dominant paths were formed, with the second path's delay measured between approximately 2 to 4 ms, averaging 3 ms. The channel gain of the second path had about \(-3\) dB less power compared to the main path, and the root mean square (RMS) delay spread was measured to be approximately 1.5 ms. The measured SNR was an average  
Figure 8: BER in the West Sea with the modulation order of (**a**) (2, 4), (**b**) (8, 2), (**c**) (2, 16), and (**d**) (4, 8). Figure 9: Sea area near Wangdolcho in the East Sea. of 21 dB, and the average Doppler shift and spread were 5 Hz and 30 Hz, respectively. Despite the calm sea state conditions (sea state 3), subsurface currents resulted in high Doppler spread, leading to performance degradation in BER compared to simulation results across all algorithms. Doppler spread causes temporal dispersion of frequency components, which can lead to inter-symbol interference and signal distortion, even at high SNR. While simulations assume constant and linear Doppler spread, in real ocean environments, the impact is more significant due to time-varying characteristics and multipath interactions. Although G-CSS has a structure robust to Doppler spread, non-linear Doppler effects can still cause performance degradation. The BER measured in this environment is shown in Table 3. The results of the ocean experiments showed that the proposed G-CSS achieved the best BER performance compared with the other methods. When the modulation order of the proposed method was \((8,2)\), the BER was 0.0232, demonstrating that the G-CSS outperformed the conventional up/down-CSS (0.0875) and LoRa-CSS (0.0577) by factors of 3.8 and 2.5, respectively. When the modulation order was \((8,16)\), the BER of the proposed G-CSS was 0.0750, which was approximately 2.5 times and 2.3 times better than the conventional up/down-CSS (0.1904) and LoRa-CSS (0.1739), respectively. The proposed G-CSS maintained relatively stable performance even at higher modulation orders, whereas the performance of the conventional up/down-CSS and LoRa-CSS deteriorated as the modulation order increased. Therefore, the proposed method was shown to provide stable communication performance across \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{3}{c}{**Values**} \\ \cline{2-4}  & **G-CSS (\(M_{l},M_{r}\))** & **Up/Down-CSS** & **LoRa-CSS** \\ \hline Sampling rate & 200 kHz & 200 kHz & 200 kHz \\ \hline Bandwidth & 4.5 kHz & 4.5 kHz & 4.5 kHz \\ \hline Center frequency & 20 kHz & 20 kHz & 20 kHz \\ \hline Code rate & 1/3 & 1/3 & 1/3 \\ \hline \multirow{2}{*}{Modulation order} & (8, 2) & 2 & 16 \\ \cline{2-4}  & (8, 16) & 2 & 128 \\ \hline \multirow{2}{*}{Symbol duration} & 10 msec & 2.5 msec & 10 msec \\ \cline{2-4}  & 10 msec & 1.4 msec & 10 msec \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Modulation parameters for ocean experiments. Figure 10: Measured sound speed profile in the East Sea.