# Study of NVIS Channel for USN Protocol Definition in Antarctica
## 3 NVIS Channel Analysis
### Postprocessing Analysis  
To analyze all the parameters required to design a new frame protocol based on the NVIS channel we postprocess the received signal frame of Figure 4 in order to obtain key measured parameters. First of all, we obtain the Doppler shift by the 600 Hz tone and we locate the data block by the correlation of the PN sequences of all the frame. Once synchronized, we obtain the BER of each data block depending on its modulation. By the other way, the correlation of the PN sequence of one frame transmitted provides us a lot of information about the evolution of the skywave and groundwave channel impulse response. In Figure 5, we can see an example of a PN sequence correlation where we can see the received groundwave, the reflection at both the E layer and F2 layer.  
The comparison between the correlation and the Livingston Island ionogram provided by Observatori de l'Ebre [33] provides us information about the origin of each path. As we can see in Figure 6, the ionogram shows us the height in the Y-axis for both the E layer and F2 layer for every frequency carrier transmitted in the X-axis. We can see that the E layer reflects a 4.3 MHz signal on a height of 120 km approximately and the F2 layer reflects a 4.3 MHz signal on a height of 310 km. If we analyze Figure 5 for the PN sequence correlation, we can note than the first peak is produced by the groundwave which is the first to be received. The second peak is produced by the ionospheric reflection of the E layer, received 800 microseconds later, equivalent to 240 km approximately. A half of this distance match with the height of the E layer as we can see on the ionogram. The third peak is produced by the ionospheric reflection of the F2 layer, received 2066 microseconds later, equivalent to 620 km approximately. Half of this distance match with the height of the F2 layer as we can see on the ionogram. Furthermore, a multipath of 33 microseconds is produced by the ordinary and extraordinary waves at the F2 layer with an effect produced on the received frame.  
From the PN sequence correlation of Figure 5, we can obtain the delay spread (\(\sigma_{\tau}\)) as the r.m.s. delay value of the signal as a density function S(\(\tau\)):  
\[\overline{\tau}\ =\ \int_{-\infty}^{+\infty}\tau\text{S}(\tau)\text{d}\tau, \tag{3}\]  
Figure 5: Correlation of 150 PN sequences one above the other.  
Figure 6: Ionogram of Livingston Island.  
\[\overline{\tau^{2}}\ =\ \int_{-\infty}^{+\infty}\tau^{2}\mathrm{S}(\tau) \mathrm{d}\tau, \tag{4}\]  
\[\sigma\tau\ =\ \sqrt{\int_{-\infty}^{+\infty}(\tau-\overline{\tau})^{2} \mathrm{S}(\tau)\mathrm{d}\tau}\ =\ \sqrt{\overline{\tau^{2}}-(\overline{\tau})^{2}}, \tag{5}\]  
where \(\tau\) is the time sample and \(\mathrm{S}(\tau)\) the amplitude. For better comprehension, the delay spread of the groundwave by the dispersion of the first peak. Moreover, the delay spread of the skywave is obtained using the distance in time from the second peak (E layer) and the last peak (F2 layer).  
To obtain the scattering function \(\mathrm{S}(\tau;\lambda)\)[27] of the skywave:  
\[\mathrm{S}(\tau;\lambda)\ =\ \int_{-\infty}^{+\infty}\mathrm{Rc}(\tau;\Delta \mathrm{t})\mathrm{e}^{-|2\pi\lambda\Delta\mathrm{t}}\mathrm{d}\Delta\mathrm{t}, \tag{6}\]  
where \(\mathrm{Rc}(\tau;\Delta\mathrm{t})\) gives the average power output as a function of the time delay \(\tau\) and the difference \(\Delta\mathrm{t}\) in observation time We make use of 150 PN sequences of a frame without the groundwave. From the scattering function, we can measure the Doppler spread of the skywave channel. We proceed in the same way for the calculation of the Doppler spread of the groundwave.