Optimal one-dimensional relay placement in cognitive radio networks

In this work, we find the optimal relay location for a secondary user in a cognitive radio network subject to outage constraints. With selection decode-and-forward relay protocol, we formulate this problem as a nonlinear optimization problem, and then derive an approximation formulation that gives a close-optimal relay location, which means that we can use the approximation instead to solve the relay placement problem in cognitive radio networks. We find that the optimal relay location is determined by the relative locations of the primary destination, the secondary source and the secondary destination. Moreover, we analyze the sensitivity of optimal relay location to other key parameters such as path loss exponent, interference floor and outage constraint of the primary user, and outage constraint of the secondary user.