## 4 Ionospheric Channels Analysis
The results are clearly better, achieving a result of 86% of the data frames detected from 7 UTC to 16 UTC. The usage of both ionospheric channels at the same time resulted in the reception of simultaneous signals. If these signals are decorrelated (two channels are considered as not correlated when their cross-correlation coefficient value is lower than 0.7 [30]), an increase of SNR (signal-to-noise ratio) can be achieved. MIMO and single-input multiple-output (SIMO) links can benefit directly from this SNR gain, enabling link enhancement by the application of diversity techniques. Figure 10 displays the cross-correlation coefficient between the ordinary wave's channel and the extraordinary wave's channel throughout the day. This value was computed by correlating the impulse responses of both channels. Before calculating the coefficient, the impulse responses were previously synchronized, so the delay between the received waves was not taken into account. A probability graph was exhibited in order to evaluate if both received signals were decorrelated enough, depending on the hour of the day. Analyzing the results, it can be stated that there is a probability of nearly 40% to achieve a correlation coefficient below 0.7 in the happy hour intervals. The SNR of the received signals in these intervals could be improved by the usage of diversity techniques. In Figure 11, the delay spread of the ordinary and extraordinary waves can be analyzed, respectively. The multipath of the NVIS link between Barcelona and Cambrils was studied throughout the day. All the undesired paths limited our channel's coherence bandwidth, thus affecting the data frame design and the link's performance. The figure displayed below only takes into account the well-demodulated data frames. If a data frame did not present enough SNR and the PN sequences were not correctly found, no multipath was computed. Therefore, the following graph was analyzed together with the channel's availability, presented above (Figure 9). Only the hours where both channels were active (7 UTC to 16 UTC) were taken into account for the delay spread study in order to have accurate results. Figure 9: Availability of the Barcelona—Cambrils NVIS ionospheric channels. After carefully analyzing the delay spread of both channels, the highest value of the link was found to be 2.89 ms, corresponding to a coherence bandwidth of 346 Hz, and was provided by the extraordinary wave. On the other hand, the ordinary wave presented a peak value of 2.71 ms, corresponding to 369 Hz of coherence bandwidth. Both values implied receiving strong ISI among symbols in our system if we considered a time symbol of 0.42 ms (standards STANAG and MIL-STD-188 110, 2.38 kHz bandwidth). The coherence bandwidth of the ionospheric channel was thus defined as follows:  
\[\text{CB}=1/\sigma, \tag{1}\]  
where \(\sigma\) corresponds to the delay spread. If we now study the less restrictive values, it can be observed that both waves often presented no multipath at all, as was observed in the mean values of the delay spread received (very low delay spread values). Therefore, the study of the mean value of the delay spread is key in our system design. The overall mean values of the delay spread of both channels were similar, presenting some differences if the graph was analyzed hour by hour. The differences in the multipath detected could only be observed if we compared all data frames individually, resulting in different instantaneous values. The mean value received of the ordinary wave was 0.33 ms, and the mean value received of the extraordinary wave was 0.31 ms. Taking into account the most-restrictive mean value (0.33 ms), which corresponds to a coherence bandwidth of 3 kHz (higher  
Figure 11: NVIS delay spread vs. time of the NVIS channels. Figure 10: Probability (in %) of finding a cross-correlation coefficient below 0.7 between both channels. than our used bandwidth; thus, our system overcame the ISI of the channel in almost all transmissions).