# An Optical Differential Method for Underwater Wireless Communication in Turbid Environments
## 4 Results
When communicating, we will use two pulse-width modulation pulses with different duty cycles to control the two LEDs separately and mix the two beams of light together. As shown in Table 1, we represent the logical \"on\" and \"off\" by adjusting the duty cycle of the two lights. The beam of light is received by an integrating sphere after passing through a body of water, and its color coordinates and light intensity can be determined by analyzing the spectrum. To compare the performance using light intensity and color, the light sources, noise levels, and coding algorithms in both logic states remain the same. The only difference lies in the extraction of light information. For conventional intensity modulations, the photometric quantity, that is, the luminous flux, is extracted from received optical signals, while the chromaticity quantity, that is, the chromaticity coordinates, is extracted for ODCM. After the receiver obtains the luminous flux and color coordinates, the \(s\) (signal stability) will be calculated. When the \(s\) is greater than 95%, the signal is considered reliable and thus decoded into binary data, and when the \(s\) is less than 95%, the signal is regarded as noisy, and the system will randomly generate binary data instead of the signal. Figure 4 shows decoded images after the light propagates a distance \(l\) in water. As can be clearly seen, the decoded image becomes more and more noisy as \(l\) increases if light intensity modulations are employed. The BER is 27.78%, 78.68%, and 100% when \(l\) is 10 cm, 15 cm, and 20 cm, respectively. In contrast, no bit errors can be found from the first 20 cm of propagating distance if ODCM is used. Similar tests are conducted in 3 NTU Formazin solution, which simulates optical communications in a strongly scattered water environment. Figure 5 shows decoded images at different propagating distances. If light intensity modulations are used, BER increases to 75.29% when \(l\) is only 10 cm. It increases dramatically to almost 100% if \(l\) is larger than 15 cm. However, with respect to ODCM, no bit error can be found if \(l\) is \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**“on” State**} & **“off” State** & **Noise** \\ \hline \(D_{\text{c}}\) = 49\% & \(D_{\text{c}}\) = 24\% & \(s<95\%\) \\ \(D_{\text{w}}\) = 98\% & \(D_{\text{w}}\) = 12\% & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Signal definitions in optical communications. Figure 4: Images collected at the receiving end of underwater optical communication in natural water using light chromaticity and intensity. shorter than 40 cm. When \(l\) increases to 40 cm, a small amount of noise appears at the initial stage (the first 80 min), which might result from the precipitation of Formazin particles. If \(l\) increases from 40 cm to 50 cm, the BER merely increases by 5%, which is, to a large extent, generated at the beginning stage of optical communication. Even when \(l\) is 70 cm, the decoded image can still be identified, the BER of which (70.97%) is very close to that when the level of \(l\) is 10 cm in light intensity modulations. Finally, considering the complexity of natural water bodies, experiments are conducted using the river water collected from the Jing-Hang Grand Canal in Hangzhou to simulate optical communication in natural environments. Instrument measurements show that the turbidity of the collected river water is 4.6 NTU. Figure 6 shows the decoded images at different propagation distances. When optical intensity modulation is adopted, the BER reaches 54.88% when the distance \(l\) is 5 cm, which has already exceeded the forward error correction limit. When the distance \(l\) increases to 20 cm, the signal cannot be recognized at all. In contrast, when using the ODCM, no bit errors are observed when \(l\) is no longer than 30 cm. When \(l\) increases to 35 cm and 40 cm, the BER ascends to 4.30% and 68.5%, respectively. The receiving signals cannot be recognized until \(l\) exceeds 50 cm.