A statistical geometric approach for capacity analysis in two-hop relay communications

In relay communications, the system performances depend heavily on the statistical distances between the source, relay(s) and destination, since the signal strength decays superlinearly with distance. The capacity analysis of relay systems is non-trivial as the relay node(s) is(are) usually randomly located in the network. In this paper, a stochastic geometric approach is presented to analytically study the capacity of two-hop relay communications in both cellular and ad hoc networks. We are interested in the amplify-and-forward (AF) replay scheme, which is easy to implement in reality. Given that the relay is uniformly located inside a hexagonal cell or a circle, we first derive the probability density functions of the stochastic end-to-end path loss, then develop closed-form expressions by adopting series expansion, and finally obtain the explicit distributions of the capacity of two-hop relay communications under AWGN channel. All the theoretic results are validated through Mont-Carlo simulations. Different from previous numerical methods or approximation, the framework presented in this work can easily generate all statistical moments and enable the analysis of outage probability.