## 2 Measured Parameters
### HF Channel Parameters  
Our analysis of the channel has been done both in a narrowband and wideband approach. The narrowband analysis focuses on channel availability and SNR computation. The channel availability means the probability of a link to reach a minimum SNR value and hence achieve a certain quality of service. According to [19], a minimum SNR value of 6 dB was specified to estimate the channel availability in a bandwidth of 10 Hz. As the probability of false alarm caused by noise and interferences is quite high when you measure the channel availability, several techniques to improve the reliability of the detection system have been developed [20]. The SNR is computed by comparing the received power measured during the tone intervals to the noise power measured during the idle periods. The wideband analysis focuses in the calculation of the scattering function from the estimated channel impulse response. The composite multipath spread and Doppler spread parameters are also calculated as explained below. Channel estimation was performed through a classical ML (maximum likelihood) based technique sending periodic Pseudo Noise (PN) waveforms with good cyclic cross-correlation characteristics. We used maximum-length shift-register sequences, or m-sequences for short [16]. Let \(PN[n]\) be the transmitted sequence of length \(N_{e}\) (in samples) and \(r[n]\) the received signal during the sounding interval. Then, the correlation of the received signal with a replica of the emitted sequence is carried out:  
\[\phi[n]=\sum_{k=0}^{N_{e}-1}r[n+k]PN[k] \tag{1}\]  
The channel matrix is calculated as:  
\[h[n,\tau]=\phi[nN_{e}+\tau] \tag{2}\]  
where \(\tau\in[0,N_{e}-1]\) is the delay variable. An estimation of the scattering function is calculated from the channel matrix [16] as:  
\[R_{s}[\tau,\
u]=\sum_{\xi}R_{h}[\xi,\tau]e^{-j2\pi\xi\tau} \tag{3}\]  
where \(\
u\) is the Doppler shift variable, \(\xi\) is the time variable and:  
\[R_{h}[\xi,\tau]=\sum_{n}h^{*}[n,\tau]h[n+\xi,\tau] \tag{4}\]  
From the scattering function the multipath power profile is calculated as:  
\[\phi[\tau]=\sum_{\
u=\
u_{1}}^{\
u_{2}}R_{s}[\tau,\
u] \tag{5}\]  
Figure 2: Example of ionogram recorded by the VIS installed at the ASJI. Echoes reflected from particular ionospheric layers are indicated. Similarly, the Doppler power profile is obtained as:  
\[\phi[\
u]=\sum_{\tau=\tau_{1}}^{\tau_{2}}R_{s}[\tau,\
u] \tag{6}\]  
where \([\tau_{1},\tau_{2}]\) and \([\
u_{1},\
u_{2}]\) are the multipath and Doppler shift observation windows, that have been set according to the maximum observed multipath and Doppler spreads. Next, the spread parameters are calculated. The multipath spread is measured from the multipath power profile as the 80% power spread, with a correction applied for the width of the transmitted pulse and the base noise level. This parameter is called composite multipath spread \(\left(\tau_{eff}\right)\)[21]. Analogously the composite Doppler spread \(\left(\
u_{eff}\right)\) is measured from the Doppler power profile as the 80% power spread, applying the same corrections [22]. Then, the area spread factor is defined as the area enclosed by the composite multipath and Doppler spreads in the scattering function [23]. Finally, an estimation of the SNR may be obtained from the scattering function according to the following equation:  
\[SNR=\frac{P|_{Asp}-\rho_{n}A_{sp}}{\rho_{n}A}\ \rho_{n}=\frac{P|_{\overline{ Asp}}}{A_{sp}} \tag{7}\]  
where \(A_{sp}\) is the area spread factor, \(\overline{A_{sp}}\) is the area outside the area spread factor, \(A\) is the total area of the scattering function and \(P\) is the power calculated inside or outside the area spread factor. We have also measured the absolute propagation time as a function of frequency, that is, the time it takes the wave to travel from LIV to Spain. This gives us some ideas about whether the wave has travelled along the standard path or some extraordinary paths are present.