# Underwater Communications for Video Surveillance Systems at 2.4 GHz
## 4 Results of Maximum Distances
### Measurements for QPSK at Different Temperatures  
Figure 9 shows the values of maximum distance for 2 Mbps which uses QPSK modulation at 16 \({}^{\circ}\)C, 18 \({}^{\circ}\)C, 20 \({}^{\circ}\)C, 22 \({}^{\circ}\)C, and 26 \({}^{\circ}\)C. This modulation also presents effects as a function of the temperature. The smaller distances are obtained for the temperature of 26 \({}^{\circ}\)C. Temperatures of 16 \({}^{\circ}\)C and 18 \({}^{\circ}\)C have maximum distances below 22 cm, while the frequencies that come from 2412 MHz to 2427 MHz at 20 \({}^{\circ}\)C achieve distances between 23 and 25 cm. Finally, we can see that the greatest distances are achieved for 2412 MHz at 22 \({}^{\circ}\)C.  
The ANOVA for QPSK uses the frequency and each temperature as a group to be compared and in this case, the variable to be studied is the maximum distance between antennae using QPSK modulation. Table 6 shows the calculation of residuals, for QPSK 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.  
Table 7 shows de ANOVA results of dependency between QPSK modulation, working frequency and temperature. We see that in the case of rows, the probability value (0.00031136) is lower than the one defined for \(\alpha\). Therefore, the variation of results is significant. On the other hand, the value of F (6.71606994) is higher than the critical value of F (2.60597495). For this reason, we discard the null  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Data Transfer** & **2412** & **2417** & **2422** & **2427** & **2432** & **2437** & **2442** & **2447** & **2452** & **2457** & **2462** \\
**Rates** & **MHz** & **MHz** & **MHz** & **MHz** & **MHz** & **MHz** & **MHz** & **MHz** & **MHz** & **MHz** \\ \hline
1 Mbps at 16 \({}^{\circ}\)C & 2.50 & 1.80 & 0.70 & 0.80 & 2.20 & 1.10 & 1.30 & 1.75 & 2.00 & - & - \\
1 Mbps at 18 \({}^{\circ}\)C & 1.00 & 0.30 & 0.80 & 1.20 & 0.20 & 1.10 & 0.70 & 0.25 & 0.01 & - & - \\
1 Mbps at 20 \({}^{\circ}\)C & 3.50 & 2.70 & 2.70 & 3.80 & 1.80 & 1.40 & 0.80 & 1.75 & 1.00 & 0.1 & 0.2 \\
1 Mbps at 22 \({}^{\circ}\)C & 4.50 & 3.70 & 1.20 & 0.80 & 2.20 & 2.10 & 3.70 & 3.25 & 3.00 & - & - \\
1 Mbps at 26 \({}^{\circ}\)C & 4.50 & 4.30 & 3.80 & 4.20 & 2.80 & 2.90 & 2.30 & - & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 4: Calculation of residuals for BPSK.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Origin of** & **Sum of** & **Degree of** & **Average** & **F** & **Probability** & **Critical Value for F** \\
**Variations** & **Squares** & **Freedom** & **Squares** & **F** & **Probability** & **Critical Value for F** \\ \hline Temperatures & 568.154545 & 4 & 142.038636 & 7.60026754 & 0.00011845 & 2.60597495 \\ Frequency & 2321.54545 & 10 & 232.154545 & 12.4222303 & 1.9998 \(\times\) 10\({}^{-9}\) & 2.07724805 \\ Error & 747.545455 & 40 & 18.6886364 & & & \\ Total & 3637.24545 & 54 & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 5: ANOVA for BPSK.  
hypothesis and consider 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 (\(5.3453\times 10^{-11}\)) is lower than defined for \(\alpha\). Therefore, the variation of the results is also significant. Moreover, the value of F (\(15.8849444\)) 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 QPSK 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 QPSK modulation are statistically different and they depend significantly on the working frequency and temperature.