## 5 Conclusions  
In this work we present the single-frequency study of the two ionospheric characteristic waves as different communication channels. We analyzed the cross-correlation coefficient and the availability of both waves using nearly orthogonal polarized antennas. Similarly, we also studied the delay spread of both channels. We measured the frequency offset caused by the use of low-stability clocks on a low-cost system. Finally, we studied the BER and \(\mathrm{E_{b}/N_{0}}\) improvement of the system with the application of polarization diversity techniques, using selection combining and equal-gain combining. The research carried out in this work focused on two main objectives: the exploration of the feasibility of using polarization diversity techniques thanks to the decorrelation between the ordinary and extraordinary waves, and the study of the properties of each ionospheric channel for the optimization of the data frames in future studies and further channel characterization. From 17 UTC to 6 UTC, the lowest cross-correlation coefficient was found. This work presents the comparison between all the parameters studied. Table 3 is exhibited below for a better understanding of these parameters. The availability results showed that the extraordinary wave presented better results. Two \"happy hour\" [13] intervals were identified (sunrise and evening beginning), where the number of data frames detected by each ionospheric channel differed more. Another study realized in this work analyzed the usage of both signals simultaneously and the data frame detection between them both working together. The mean value of this new availability (from 7 UTC to 16 UTC) was 86%, increasing the results obtained by a singular  
Figure 15: Cumulative distribution function (CDF) of the bit error rate for fourth-order modulations at 50 W. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{3}{c}{**Ordinary Wave**} & \multicolumn{3}{c}{**Extraordinary Wave**} \\ \cline{2-7}  & **Max** & **Min** & **Mean** & **Max** & **Min** & **Mean** \\ \hline Availability (7 UTC to & \multirow{2}{*}{74\%} & \multirow{2}{*}{30\%} & \multirow{2}{*}{57.6\%} & \multirow{2}{*}{94\%} & \multirow{2}{*}{56.67\%} & \multirow{2}{*}{72.2\%} \\
16 UTC) & & & & & & \\ Delay Spread & 2.71 ms & \(\sim\)0 ms & 0.33 ms & 2.89 ms & \(\sim\)0 ms & 0.31 ms \\ SDR Frequency offset & \(-19.5\,\mathrm{Hz}\) & \(-14.5\,\mathrm{Hz}\) & \(-17.7\,\mathrm{Hz}\) & \(-19.5\,\mathrm{Hz}\) & \(-14.5\,\mathrm{Hz}\) & \(-17.7\,\mathrm{Hz}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Channel study summary. characteristic wave by more than 13%. These results encourage the study and application of diversity techniques and their combining at the receiver to increase the SNR of this NVIS link. The delay spread (directly related to the multipath) of both channels was almost identical, a fact that allowed us to use the same coherence bandwidth for both channels. Having a huge value difference between both channels would imply the usage of the most restrictive data frames for the channel with the lower delay spread, not taking full advantage of the parameters of one channel. The study of the Doppler shift was not performed properly because the system used a low-cost platform (higher frequency offset from the Red Pitaya clocks than the ionosphere's Doppler shift). Thus, well-designed data frame working together with a powerful post-processing of the signal are key to mitigate the channel's negative effect (up to \(\pm\)20 Hz in this work's infrastructure). After analyzing the results obtained in the BER and \(\mathrm{E_{b}}/\mathrm{N_{0}}\) studies, we can conclude that the application of polarization diversity implies an improvement in the robustness of the link. A higher \(\mathrm{E_{b}}/\mathrm{N_{0}}\) and a lower BER were received using both selection combining and equal-gain combining.