A Geometry-Inclusive Analysis for Single-Relay Systems

Successful message relay, or the quality of the interuser channel, is critical to fully realize thecooperative benefits promised by the theory. This in turn points out the importance of the geometry ofcooperative system. This paper investigates the impact of the relay's location on the system capacity andoutage probability for both amplify-forward (AF) and decode-forward (DF) schemes. Signal attenuationis modeled using power laws, and capacity is evaluated using the max-flow min-cut theory. A capacitycontour for DF, the more popular mode of the two, is provided to facilitate the derivation of engineeringrules. Finally, a selective single-relay system, which selects the best relay node among a host ofcandidates according to their locations, is analyzed. The average system capacity and outage, averagedover all possible candidates' locations, are evaluated. The result shows that the availability of a smallcandidate pool of 3 to 5 nodes suffices to reap most of the cooperative gains promised by a selectivesingle-relay system