## 3 Dual-Site Micro-Scale Diversity Scheme
### Emulated Joint Rain Attenuation Statistics  
Although the deployment of actual satellite stations to perform measurements has always been preferred over any simulation methods, it is highly unlikely that one would attempt it without having a reliable set of simulated results to perform a first assessment; this is where the benefit of merely using rain gauges, easier to procure and install than satellite stations becomes apparent. Rain attenuation time series can then be generated  
Figure 3: Cumulative distribution of rain rate for the two locations at NTUA campus and the joint-minimum CCDF (solid line).  
Figure 2: Calculated rain rate time series for the examined period and both locations within the NTUA campus.  
using the Synthetic Storm Technique (SST) with a two-layer model having as input the rain rate time series obtained via the rain gauges [34]. The SST is a physical-mathematical propagation modeling tool based on the Taylor hypothesis in order to translate the rain rate time series into the spatial domain and then calculate the rain attenuation time series on the slant path. Should rainfall rate data be available, the SST must be the preferred choice over any other statistical methodology/theory in order to evaluate the system performance-the application of any of the latter methodologies could yield very questionable results in real applications, especially for low probabilities. To apply the SST, the average storm speed is required along the slant path; for Athens, a value of 10.6 m/s is assumed based on meteorological records. In any case, long-term statistics seem to be insensitive to its precise value [40].  
The two-layer model is defined in the vertical path and is used to capture the melting layer effects. For the conversion of rain rate \(R\) in mm/h to the specific rain attenuation \(A_{0}\) (dB/km), the classic power-law relationship \(A_{0}=kR^{b}\) is used. The parameters \(k\), \(b\) are calculated from the ITU-R. P. 838 [42] for Layer A (raindrops at 20 \({}^{\circ}\)C), while the ones in [37; 40] are used for Layer B (melting hydrometeors at 0 \({}^{\circ}\)C).  
In Figure 4, the 4-year rain attenuation time series emulated using SST are presented for the two station locations operating at a frequency of 19.701 GHz, i.e., a Ka-band downlink. The elevation angle of the links is 45.98\({}^{\circ}\), chosen based on the actual elevation angle (median value) for the geostationary, inclined-orbit satellite Alphasat at 25.0\({}^{\circ}\) E [43] as observed from the particular sites. In Figure 5, the CCDF of rain attenuation is given at Ka-band for the two stations, while the CCDF of the joint-minimum rain attenuation is also presented referring to an idealized site diversity scenario; the joint-minimum rain attenuation across \(N\) links is  
\[A_{joint}(t)=\,\min\left\{A_{1}(t),\ldots,A_{N}(t)\right\} \tag{8}\]  
A gain of almost 2 dB can be achieved for up to 0.01% of the time in this idealized micro-scale site diversity case. In Figures 6 and 7 the rain attenuation time series and CCDFs are shown for a Q-band downlink (39.402 GHz), respectively. A gain of 3 dB for up to 0.1% of the time can be achieved while a gain of 5 dB for up to 0.01% of the time also seems feasible as indicated by the joint-minimum CCDF in Figure 7.