Unified Performance Analysis of Stochastic Clustered Cooperative Systems With Distance-Based Relay Selection

In this paper, we present a unified performance analysis of stochastic clustered cooperative systems with distance-based relay selection, where the destination is located at the cluster center, the locations of the source and the candidate relays follow an independent and identical distribution, and there exists a Poisson field of interferers. As the distance-based relay selection leads to spatial correlation between cooperative transmission distances in a cluster, we first derive a general joint probability distribution function of cooperative transmission distances based on
$\psi $
-order statistics. Then, the transmission success probability of the stochastic clustered cooperative systems with decode-and-forward (DF) scheme is derived. In order to reduce computational complexity, we offer an approximate expression of the transmission success probability. Furthermore, we provide an asymptotic transmission success probability in the interference-limited scenario, when the number of candidate relays in a cluster is sufficiently large. Besides, the performance analysis framework is extended into the clustered cooperative systems with finite relay distribution regions. Taking the cluster member distributions of Thomas cluster process (TCP) and Matérn cluster process (MCP) as examples, we verify our theoretical analysis via Monte-Carlo simulations. With the theoretical results, the optimization of relay selection parameter is also demonstrated.