# Cooperative Reception of Multiple Satellite Downlinks
## 2 System Description and Design
### SIMO System  
The next step was to design the receive diversity system which involves the collection of multiple copies of the same signal by multiple receive antennas through multiple independent channels as illustrated in Figure 5.  
As Figure 5 demonstrates, the same message signal (\(m\)) is transmitted by the transmitter's antenna and received by \(N\) receive antennas to collect \(N\) versions of the received signals (\(r_{1}\), \(r_{2}\)... \(r_{N}\)) after being propagated through different and independent channels (\(h_{1}\), \(h_{2}\)... \(h_{N}\)). These different paths would reflect different and independent impairment impacts on the same transmitted signal. Therefore, processing multiple copies of the same  
Figure 4: SISO BER versus data rate (at \(E_{b}\)/\(N_{o}\) = 10 dB). Figure 5: Multiple downlinks reception system. signal would help in case that one or more of these paths severely degrade the signal strength by constructing the message signal from the other good quality copies received by such a system. The received versions are processed and combined in a virtual ground station (VGS) to exploit the diversity gain, significantly improve the radio link quality, and decrease the outages probability. The aimed diversity gain can offer the opportunity to deploy the affordable omnidirectional antennas at the involved ground stations instead of the directional antennas with their expensive steering equipment. The lesser receiving antenna gain in this replacement would cause more detection errors which can be later compensated by the diversity gain. The proposed collaborative omnidirectional ground stations along with the virtual combining platform is modeled in Figure 6. This model shows how such network may track more than one satellite simultaneously, utilize omnidirectional receiving antennas, receive uncorrelated downlink replicas propagated through different independent paths, and provide resistance to outages. In terms of system outages as a statistical quantity, (1, 2,..., _N_) earth stations operating in a single mode would have attenuations of (\(A_{1}(t)\), \(A_{2}(t)\),..., \(A_{N}(t)\)), correspondingly. However, for these Earth stations to cooperatively work in a diversity mode, the cooperative receiving system would have a joint attenuation of \(A_{S}(t)\) = _min_ {\(A_{1}(t)\), \(A_{2}(t)\),... \(A_{N}(t)\)}. Therefore, the attenuation of the system in a receiving diversity mode would be the minimum among all the cooperative Earth stations. Consequently, if one or two stations are deeply faded with high attenuation level, the receive diversity scheme would still be able to receive a good quality signal from other sites and share it with those attenuated stations [39]. Hence, the outage probability of the diversity mode versus single mode is framed as follows:  
Assuming that the probability of outage in a single receiving site is \(P_{out}\), the probability of successful reception is (\(1-P_{out}\)). Suppose we engage _two_ ground stations in the receive diversity system, then the system reception probability is:  
* Success probability of (\(1-P_{out}\))\({}^{2}\), when both sites are receiving good quality signal;  
Figure 6: System model: cooperative omnidirectional ground stations (GS_1, GS_2,..., GS_N) along with the VGS in a network to receive data from multiple satellites simultaneously. * Success probability of \((1-P_{out})\)-\((P_{out})\), when only one site is receiving good quality signal; and
* Outage probability of \((P_{out}\cdot P_{out})\) = \(P_{out}\)2, when both sites fail to receive good quality signal. Accordingly, when engaging \(N\) Earth stations in the receive diversity system, the outage probability becomes \((P^{N})\) which represents significant outages reduction compared to the conventional single-site systems.