Performance Analysis of Opportunistic Relaying in a Poisson Field of Amplify-and-Forward Relays

The performance of opportunistic relaying in a dual-hop amplify-and-forward relay network where the relaying nodes are distributed according to a homogeneous two-dimensional Poisson point process with fixed density is analyzed. Largely ignored in the literature, this assumption leads to more realistic results, as in a typical practical scenario neither the number of relays nor their distances from the source and destination are known. An exact expression for the outage probability of this cooperative system for general fading environments and different types of relaying is derived. The expression is then {simplified under an assumption that the radius of the relay deployment region is sufficiently large}, and specialized to additive white Gaussian noise (no fading), Rayleigh fading and severe (half-Gaussian) fading environments. Simple and tight upper and lower bounds on the outage probability are also derived. Simulation results validate the theoretical analyses and verify the accuracies of the proposed bounds.