# Underwater Communications for Video Surveillance Systems at 2.4 GHz
## 4 Results of Maximum Distances
### Measurements for BPSK at Different Temperatures  
Figure 8 shows the values of maximum distance for 1 Mbps using BPSK modulation for temperatures of 16, 18, 20, 22, and 26 \({}^{\circ}\)C.  
It is important to highlight several relevant aspects. The first and the most significant is the variations obtained as a function of temperature. We can see that smaller distance values are obtained at 26 \({}^{\circ}\)C. Temperatures of 16 \({}^{\circ}\)C and 18 \({}^{\circ}\)C also present low values of distance, whereas for the rest of temperatures are recorded distances above 22 cm. Different working frequencies also offer different values of maximum distance. The longest distance is registered for frequency of 2424 MHz at 22 \({}^{\circ}\)C, followed by the frequencies 2412 MHz and 2427 MHz at 22 \({}^{\circ}\)C.  
To analyze the relationship between the maximum distance, working frequency and the modulation as a function of the temperature, we use a two-way ANOVA where the working frequencies and temperature are the groups to be compared. The variable under study is the maximum distance between antennae when BPSK is used.  
Table 4 shows the calculation of residuals, for BPSK modulation. We can observe that all values match with the hypothesis H1 where all residuals are different to 0. So, we are sure that these parameters cause some effect over maximum distance.  
Figure 8: Maximum distances for BPSK.  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline  & \multicolumn{4}{c}{**Factor 2 (\(\beta\))**} \\ \hline  & **Levels** & **1** & **2** & \(\ldots\) & **J** & **Mean per Row** \\ \hline  & 1 & Y\({}_{11}\) & Y\({}_{12}\) & \(\ldots\) & Y\({}_{1\text{J}}\) & \(\overline{Y}_{1\text{.}}\) \\
**Factor 1 (\(\alpha\))** & 2 & Y\({}_{21}\) & Y\({}_{22}\) & \(\ldots\) & Y\({}_{2\text{J}}\) & \(\overline{Y}_{2\text{.}}\) \\  & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) \\  & 1 & Y\({}_{\text{II}}\) & Y\({}_{\text{I2}}\) & \(\ldots\) & Y\({}_{\text{II}}\) & \(\overline{Y}_{\text{L}}\) \\  & Mean per Column & \(\overline{Y}_{\text{.1}}\) & \(\overline{Y}_{\text{.2}}\) & \(\ldots\) & \(\overline{Y}_{\text{J}}\) & \(\overline{Y}_{\text{.}}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mean values to determine whether factors has some effect over the variable to be analyzed.  
We can now focus our analysis on the dependence of maximum distance with working frequency and temperature. Table 5 shows the analysis of variance measurements at 16 \({}^{\circ}\)C. We see that in the case of rows, the probability value (0.00011845) is lower than the one defined for \(\alpha\). Therefore, the variation of results is significant. On the other hand, the value of F (7.60026754) is higher than the critical value of F (2.60597495). For this reason, we discard the null hypothesis and take the alternative hypothesis. This means that the maximum distance for each frequency depend on the temperature.  
On the other hand, for columns, the value of the probability (1.9998 \(\times\) 10\({}^{-9}\)) is lower than defined for \(\alpha\). Therefore, the variation of the results is also significant. Moreover, the value of F (12.4222303) is higher than the critical value of F (2.07724805). We can discard the null hypotheses for taking the alternative which means that the maximum distance between antennae using BPSK modulation depends on the working frequency.  
These results show that there are significant differences between groups which are due to the increase in the working frequency and temperature and not due to the random effect. With this, we have checked that the maximum distance for BPSK modulation are statistically different and they depend significantly on the working frequency and temperature.