Outage probability of underlay cognitive relay networks with spatially random nodes

We consider an underlay cognitive relay network coexisting with a primary multicast network (e.g. digital television (TV) broadcasting network), in which secondary user (SU) transmissions are power constrained to limit the interference on any primary receiver in the network. The primary receivers and SU relays are randomly located due to irregular deployments and/or mobility and thus, their spatial distributions are modeled by two independent Poisson point processes (PPPs). In this paper, we analyze an opportunistic relaying scenario and develop a relay-selection scheme by considering the interference constraints on all the primary receivers in the network. We then analytically evaluate the relaying performance in terms of outage probability by using tools from stochastic geometry and point process theory, and finally compare the performance against that of direct communication. Closed-form expressions are derived for the outage probabilities of both the relay and direct links, along with their high-signal-to-noise ratio (SNR) asymptotics.