# Generalized Chirp Spread Spectrum for Underwater Acoustic Communications
## 4 Performance Evaluations
Furthermore, G-CSS can be designed according to channel conditions by combining low and high modulation orders, where high modulation orders increase the data transmission rate while maintaining signal orthogonality through adjusted frequency spacing in multipath environments. In Figure 7c, at an SNR of 4 dB, the BERs of the conventional up/down-CSS and LoRa-CSS are \(2\times 10^{-2}\) and \(8\times 10^{-3}\), respectively, while the BER of the proposed G-CSS is \(3\times 10^{-4}\), demonstrating performance improvements by factors of 60 and 27, respectively, over the conventional methods. These results indicate that G-CSS is particularly well-suited for high-speed data transmission environments requiring high modulation orders. In Figure 8, the BER results of the proposed G-CSS for the West Sea channel presented in Figure 6 are shown for modulation orders of \((2,4)\), \((8,2)\), \((2,16)\), and \((4,8)\), respectively, under varying SNR conditions. Compared with the BER results in Figure 7, the performance of all compared methods is generally degraded. This is because the ISI in the West Sea channel is more severe than that in the East Sea channel. As shown in Figure 8a, for low modulation orders like (2, 4), the conventional LoRa-CSS shows a better performance than the proposed G-CSS and up/down-CSS. However, for higher modulation orders, the proposed G-CSS demonstrates a more robust performance. At an SNR of 4 dB, the BER of the conventional up/down-CSS for the East Sea channel (Figure 7b) is \(7\times 10^{-3}\), while the BER for the West Sea channel (Figure 8b) is \(8\times 10^{-2}\), showing an 11.4 fold performance degradation. Similarly, at an SNR of 4 dB, the BER of the conventional LoRa-CSS for the East Sea channel (Figure 7b) is \(9\times 10^{-4}\), whereas for the West Sea channel (Figure 8b), it is \(6\times 10^{-2}\), indicating a 66.7-fold performance degradation. In contrast, the proposed method achieves a BER of \(3\times 10^{-4}\) for the East Sea channel (Figure 7b) and \(1\times 10^{-3}\) for the West Sea channel (Figure 8b) at an SNR of 4 dB, representing only a 3.3-fold performance degradation. This demonstrates that the proposed G-CSS method experiences less performance degradation under adverse conditions and outperforms the conventional methods, particularly at higher modulation orders. The proposed G-CSS achieves this by enabling the configuration of various modulation orders at the start and end points of symbols, allowing for more flexible utilization of frequency resources. Additionally, by assigning chirp signals according to the transmission rate required by the system, the proposed method minimizes the impact of frequency-selective fading in underwater acoustic channels, providing a better communication performance compared with conventional methods. Therefore, the proposed G-CSS offers a promising alternative or complementary approach to existing underwater acoustic communication techniques. In order to analyze the practical applicability of the proposed method, ocean experiments were conducted in August 2024. The ocean experiment took place in the waters off Yeongdeok-Gun in the East Sea of Korea, and the location of the experiment is shown in Figure 9. The experimental environment had a maximum water depth of about 200 m, and the horizontal distance between the transmitter and receiver was approximately 1 km. The transmitter and receiver were located 100 m and 10 m below the surface, respectively. In the ocean experiments, the sound speed profiles (SSPs) were measured using the MiniSVP instrument from Valeport, located in Barnstable, UK, and the results are presented in Figure 10. In Figure 10, the blue diamond markers represent the SSP measured at 11:00, the red circular markers represent the SSP measured at 12:00, and the green square markers represent the SSP measured at 14:00. As shown in Figure 10, the variation in the vertical sound speed profile over time was minimal. Two Neptune D/17/BB were used for transmission and reception.