Beamforming and combining based scheme over κ − μ shadowed fading satellite channels

In this study, the authors address the problem of beamforming and combining based amplify-and-forward relaying in a satellite communication system in which two earth stations (ESs) with multiple antennas communicate via a single antenna based satellite relay. The transparent satellite is used to relay the received signals from one ES to other ES. Both ESs are assumed to be geographically separated by a very large distance, therefore, no direct path exists in between the ESs. The ESs-satellite links are assumed to follow the κ − μ shadowed fading. A closed form expression of moment generating function (MGF) of the instantaneous received signal-to-noise ratio at destination ES is derived. An expression for the symbol error rate of the considered system is obtained by using the expression of MGF. The analytical diversity order of the system is also obtained by using an asymptotic property of the Meijer-G function. It is shown by simulation and analysis that the diversity order of the considered system is min(L 1 μ 1, L 2 μ 2), where L 1 and L 2 are the number of antennas at the ES-1 and ES-2, respectively.