# Time Series Irradiance Synthesizer for Optical GEO Satellite Downlinks in 5G Networks
## 4 Validation and Numerical Results  
### Validation with Experimental Data  
In this section, the accuracy, performance and capability of the proposed synthesizer to reproduce the received irradiance statistics will be evaluated. Therefore, good agreement in terms of first and second order irradiance statistics between the numerical and the experimental results is necessary. The validation procedure is the following:  
* Computation of the first order statistics, that is, normalized probability density function (PDF), cumulative distribution function (CDF) of the available data from ARTEMIS optical experiments. For every session the SI is also calculated. * Computation of the second order statistics, that is, power spectral density (PSD) of the available experimental data. * Generation of received irradiance time-series using the proposed methodology. The model inputs are the ARTEMIS coordinates and transmitting settings given by Tables 1 and 2, the refractive index structure parameter at ground level \(A_{0}\) which was kept fixed at a value of \(10^{-15}\big{(}m^{-2/3}\big{)}\) due to the fact that the sessions took place at night, the session's ground wind speed \(Vg\) which was provided by the nearby installed weather station and the aperture averaging factor \(A(D_{r})\) where \(D_{r}\) is the LUCE's diameter. The \(A(D_{r})\) is estimated close to 0.1 using (9). * Computation of normalized PDF, CDF and PSD of the synthesized data and the corresponding SIs. * Comparison of the derived numerical results with the respective experimental results and examination of possible discrepancies. The first experimental session examined took place on 13/09/2003 during 23:30-23:50. In Table 3 the recorded ground wind speed, the derived SI from the synthesized data and the measured SI are given. In Figure 4 the numerical first order statistics, that is, normalized PDF and CDF for this session are presented and compared to the experimental results. In Figure 5 the numerical second order statistics, that is, PSD are shown and tested against the experimental results. The next experimental session took place on 16/09/2003 during 21:10--21:30. In Table 3 the recorded ground wind speed, the derived SI from the synthesized data and the measured SI is given. In Figure 6 the numerical first order statistics, that is, normalized PDF and CDF for this session are presented and compared to the experimental results. In Figure 7 the numerical second order statistics, that is, PSD are shown and tested against the experimental results. The following experimental session took place on 10/09/2003 during 20:10-20:30. In Table 3 the recorded ground wind speed, the derived SI from the synthesized data and the measured SI is given. In Figure 8 the numerical first order statistics, that is, normalized PDF and CDF for this session are presented and compared to the experimental results. In Figure 9 the numerical second order statistics, that is, PSD are shown and tested against the experimental results. Figure 4: First order irradiance statistics validation for session on 13/09/2003 23:30. (**a**) Normalized probability density function (PDF) of measured data vs. Normalized PDF of generated data; (**b**) cumulative distribution function (CDF) of measured data vs. CDF of generated data. Figure 5: Second order irradiance statistics validation for session on 13/09/2003 23:30. PSD of measured data vs. PSD of generated data. Figure 8: First order irradiance statistics validation for session on 10/09/2003 20:10. (**a**) Normalized PDF of measured data vs. Normalized PDF of generated data; (**b**) CDF of measured data vs. CDF of generated data. Figure 6: First order irradiance statistics validation for session on 16/09/2003 21:10. (**a**) Normalized PDF of measured data vs. Normalized PDF of generated data; (**b**) CDF of measured data vs. CDF of generated data. Figure 7: Second order irradiance statistics validation for session on 16/09/2003 21:10. PSD of measured data vs. PSD of generated data.