Cognitive radio networks using relays have been introduced to enhance secondary network performance by having secondary users (SUs) transmit in two hops. This paper develops a framework for a random cognitive relay network (RCRN) where the primary, secondary, and relay nodes are randomly distributed according to Poisson point processes (PPPs) to investigate the effect of the random nature of the relays on secondary outage performance.

We first derive the optimal relay location in terms of the outage probability of the secondary network. In addition, we provide the outage probability of the RCRN based on the optimal relay selection strategy that compares the instantaneous channel state information (CSI) of all relays. We then propose an efficient relay selection strategy that reduces the selection complexity and the feedback burden by limiting candidate relays to those located close to the optimal relay location. This paper sheds new light on the design of an efficient RCRN with respect to elements such as the effects of network parameters and the candidate relay set size on the RCRN outage probability.