Outage probability of dual-hop AF opportunistic relaying with directional antennas

An exact expression for the outage probability of opportunistic relaying in a dual-hop amplify-and-forward relay network is derived for general fading environments and the case where the source and destination nodes make use of directional antennas. The relaying nodes are assumed to be distributed according to a homogeneous two-dimensional Poisson point process with fixed density. This assumption is of great practical importance as in a typical practical scenario, the number of relays as well as their distances from the source and destination are random. It is observed that under some circumstances, a directional antenna at the source may permit more efficient deployment of the relay network than the case where an omnidirectional antenna is used.