## 4 Multi-Site Micro-Scale Diversity Scheme
### Numerical Results  
Using the multi-dimensional synthesizer proposed in the previous subsection, capacity time series can be generated for SIMO and MISO satellite communication systems. In Figure 13 time series of downlink capacity for a single link and a SIMO system with three ground stations are shown. The use of such a methodology to create capacity time series bears the advantage that the cumulative statistics of rain attenuation from either measurements, emulated time series or any other prediction method can be utilized, including numerical techniques, such as the prediction by ITU-R. P. 618 [44] or any other well-established distribution used for the modeling the rain attenuation such as the Weibull, the log-normal, etc. [45; 46; 47]. In this paper, the cumulative distribution of rain attenuation derived from the SST was used directly; the frequency was assumed equal to 19.701 GHz and the elevation angle equal to 45.98\({}^{\circ}\) as in the previous section. Figure 11: Simulated rain attenuation time series using the proposed copula synthesizer for three ground stations in Athens at 19.701 GHz, i.e., Ka-band downlink. Figure 12: Joint CCDF of rain attenuation from the multi-dimensional synthesizer vs. the emulated time series for systems operating at Ka- and Q-band. The outage capacity statistics for the downlink SISO and SIMO cases for 2, 3 and 4 receiving antennas are shown in Figure 14. Regarding the two station scenario, the stations are placed 386 m apart while in the three station case, the stations form an equilateral triangle comprising of 386 m sides. Finally, the four stations corresponding to the last scenario are placed in a square grid with 386 m sides. It is apparent that the gain introduced in the system compared to the single-link case is quite pronounced and as such, micro-scale site diversity systems may provide a considerable diversity gain for both clear-sky and rainy conditions. More presicely, a capacity gain of about 40% can be observed for \(M_{R}=2\) and 82% for \(M_{R}=4\) at 0.01% of the time (i.e., \(10^{-4}\) probability). In Figure 15, the outage capacity for 1% of the time is shown for the Ka-band downlink SISO and SIMO cases considering various clear-sky SNR values; a gain in the order of 50% for four stations is observed. Figure 14: Ka-band (19.701 GHz) downlink outage capacity statistics for the SISO and the SIMO case with 2, 3 and 4 stations using the copula synthesizer. Figure 13: Capacity time series for SISO and SIMO with three stations for the Ka-band downlink at 19.701 GHz using the copula synthesizer. For the case of a MISO system, the uplink from a user terminal with multiple antennas is examined. In order to have a fair comparison with the SISO system, the uplink power transmitted through each of the MISO system's antennas is divided by their number as also explained in Section III. Using the multi-dimensional synthesizer proposed in the previous subsection, capacity time series are generated for MISO satellite communication systems using again 2, 3 and 4 ground stations (\(M_{T}\)) and geometries similar to the ones used in the SIMO system. Since MISO techniques refer to the uplink/return-link of a user's terminal, the operating frequency has been chosen at 29.881 GHz. As in the previous numerical results, the CDF of rain attenuation calculated from the SST is used for the generation of rain attenuation time series. The uplink outage capacity is shown in Figure 16 for the three MISO cases and the corresponding SISO links; as in the case of downlink, a gain is also observed in the micro-scale site diversity system when the MISO technique is employed. At 0.01% of the time (i.e., \(10^{-4}\) probability), the achievable capacity gain almost reaches 100% for \(M_{T}=2\) and up to 190% for \(M_{T}=4\), respectively. The diversity gain is further increased with increasing the number of antennas.