## 2 System Model  
In this section, the system model used for the evaluation of micro-scale site diversity systems is presented. Both dual- and multi-site micro-scale diversity systems are examined. Figure 1 presents the system geometries consisting of a conventional single station scheme (Figure 1a) as well as three micro-scale site diversity systems for two, three and four ground stations, respectively, in Figure 1b-d. The system is assumed to operate at Ka-band and above with highly directive antennas; the multiple links do not interfere with each other, there is always Line-of-Sight (LOS) and any attenuation is caused due to the signal propagating through the atmosphere with rain being the dominant fading mechanism. In the system examined herein, perfect knowledge of the channel conditions at both the transmitting and the receiving end of the stations is assumed (i.e., the induced rain attenuation at the slant paths); the stations are considered to be identical and interconnected with one another. As already mentioned in the introduction, in order to acquire the channel state the ground stations are either equipped with beacon receivers at the  
Figure 1: System configurations for (**a**) single-link systems, (**b**) dual-site micro-scale diversity systems, (c) triple-site micro-scale diversity systems and (**d**) quad-site micro-scale diversity systems. operating frequency (or close enough) or estimate the channel using the pilot symbols of the frame. Considering that the links operate at Ka-band frequencies and above, the channel conditions shall remain constant within the Round-Trip Time (RTT) delay, i.e., approximately 500 ms for a GEO link. A highly appreciated metric used in the design of satellite communication systems is the outage capacity, i.e., the percentage of time during which the system capacity falls below a certain threshold, \(P(C\leq C_{th})\). In this study, the Shannon-Hartley formula is used for the calculation:  
\[C=B\log_{2}(1+SNR) \tag{1}\]  
where \(B\) is the system bandwidth and \(SNR\) represents the Signal to Noise Ratio in linear terms; Equation (1) refers to single links. In the case of multiple stations in SIMO configuration and taking into account that the receiver has perfect knowledge of the channel, the Maximal Ratio Combining (MRC) scheme can be employed yielding the following capacity [39]:  
\[C_{SIMO}=B\log_{2}(1+\mathbf{h}\mathbf{h}^{H}) \tag{2}\]  
where \(\mathbf{h}=[h_{1},\ldots,h_{M_{R}}]\) is the \(M_{R}\times 1\) vector of the SIMO channel for the \(M_{R}\) receiving antennas. The superscript \(H\) refers to the transpose conjugate of the channel vector. The squared measure of the elements in vector \(\mathbf{h}\) is given by:  
\[|h_{i}|^{2}=SNR_{CS,i}10^{-A_{i}/10} \tag{3}\]  
where \(SNR_{CS,i}\) is the SNR in clear-sky conditions for the link between the satellite and the \(i\) receiver's antenna and \(A_{i}\) is the rain attenuation induced in the same link. Therefore, (2) becomes:  
\[C_{SIMO}=B\log_{2}(1+\sum_{i=1}^{M_{R}}SNR_{CS,i}10^{-A_{i}/10}) \tag{4}\]  
Regarding the MISO scheme, it is well-known that capacity cannot be enhanced unless the transmitter has knowledge of the channel conditions [17]; when the channel conditions are known or can be acquired, the signal can be preprocessed before being transmitted. The precoding vector to be used shall then be equal to [39; 40]:  
\[\mathbf{w}=\sqrt{M_{T}}\frac{\mathbf{h}^{H}}{\sqrt{\sum_{i=1}^{M_{T}}|h_{i}|^ {2}}} \tag{5}\]  
where \(\mathbf{h}=[h_{1},\ldots,h_{M_{T}}]\) is the channel vector for the \(M_{T}\) transmitting antennas and the squared measure of every element vector, i.e., \(|h_{i}|^{2}\) is given by:  
\[|h_{i}|^{2}=\frac{SNR_{CS,i}}{M_{T}}10^{-A_{i}/10} \tag{6}\]  
where the clear-sky SNR is divided by \(M_{T}\) in order to keep the total transmitted power at the same level as in the SISO case. The signal is multiplied with the vector \(\mathbf{w}\) before being transmitted and according to (5) the highest power ratio shall occur at the link experiencing the least attenuation.