# Study of NVIS Channel for USN Protocol Definition in Antarctica
## 3 NVIS Channel Analysis
### Results Obtained
a time symbol of 0.42 ms as the standards STANAAG and MIL-STD-188 110, we can observe that the received frame will present strong ISI among symbols. On the other hand, the minimum delay spread for the groundwave when the reflection by NVIS channel is not available is approximately 0.05 ms, which corresponds to a coherence bandwidth of 20 kHz. The Doppler spread gives us information about the variability of the channel and it has to be analyzed when designing a new communications frame protocol. In Figure 11 we can analyze the Doppler spread of the NVIS channel received at Rockie Glacier without the groundwave. The figure shown is a boxplot for the different hours during the day where the red line is the mean Doppler spread  
Figure 10: NVIS with groundwave Total Delay Spread vs. Time. Figure 9: NVIS Total Delay Spread vs. Time. received, the blue square the 50% of the Doppler spread received, the black line is the 25% upper and down Doppler spread received and the red crosses are outliers of the percentages. As we can see, the maximum Doppler spread of the channel is about 0.1 Hz (10 s) and the minimum near 0.05 Hz (20 s). This value is a key issue to determine the maximum time of the data block. Despite the measured value, the data block set will be the same as the HF standards to allow for an easier comparison. On the other hand, we can analyze the Doppler spread of the groundwave in Figure 12. In this case, the maximum Doppler spread is about 0.088 Hz (11.36 s) and the minimum near 0.062 Hz (16.12 s), so the channel can be considered quasi-stationary since the variations are only caused by the changes of the dielectric constant of the earth. These variations at Livingston Island are produced by the terrain snow and ice changes [29]. Furthermore, the groundwave of Argentina Cove can be received by the sea instead of the signal crossing the mountain as we can see in Figure 1. The Doppler spread variations can be also produced by the daily changes of the sea surges. Figure 11: NVIS Total Doppler Spread vs. Time. Figure 12: Groundwave Total Doppler Spread vs. Time. In Figure 13 we can analyze the Doppler shift produced by the clocks of the Red Pitaya platform. The Doppler shift in this case is directly related to the temperature of the platform, which will affect the stability of the clock. The Doppler shift caused by the ionosphere will be negligible compared to the variation of the clocks, especially in low cost platforms. As we can see, the maximum Doppler shift received is \(-17.5\) Hz and the minimum \(-12.5\) Hz. Finally, we can study the probability to receive a BER value under the skywave channel effects for both nodes. For that purpose, we will analyze the Cumulative Distribution Function (CDF) of the BER demodulated for the transmitted modulations of order 4 at 24 W and 2.3 kHz of bandwidth. The CDF shows us the probability of achieving a BER lower than a given value. In Figure 14, the Y-axis shows us the probability of receiving a BER less or equal than a value Xo of X-axis in Rockie Glacier. As we can see, the probability of receiving a BER lower than \(2\times 10^{-3}\) is about 84.2% for the QPSK and a 57.2% for the 4 FSK. As we can see the QPSK is most robust in front of the NVIS channel effects. It is important to note that the QPSK modulation has been equalized, while the 4 FSK was demodulated without equalization. The 4 FSK do not need an equalization because the phase shift does not affect the received frequency. Figure 14: NVIS CDF NVIS QPSK and 4 FSK. Figure 13: Nodes Total Doppler Shift vs. Time. Finally, we can analyze in Figure 15 the CDF of both groundwave and skywave received data at Argentina Cove. In this case, as we have seen, the delay spread is higher than the skywave delay spread received at Rockie Glacier. As we can see, the probability to achieve a BER lower than \(2\times 10^{-3}\) is about 81.1% for the QPSK and a 53.8% for the 4 FSK. Despite the fact that the received data present a delay spread higher than the skywave channel, the ISI effect is the same.