On achievable rates of interference and cognitive channels with a relay

We consider a two-user interference channel assisted by a relay. Treating interference as noise at the receivers, and adopting an amplify and forward (AF) strategy at the relay, we derive achievable rates of both users, for given powers. Next, we solve the optimal power allocation problem maximizing the weighted sum rate of both users with and without relay power optimization. In particular, we propose a simple iterative line search algorithm solving the joint optimization problem over the three transmit powers and show that optimizing the relay power enhances the performance of the system. Then, considering the first user as a primary user, we determine the maximum instantaneous rate that the secondary user can achieve subject to an outage constraint with respect to the primary user and a peak power constraint. We show that, likewise the first part, jointly optimizing the secondary user and the relay transmit powers enhances the secondary user performance.