Convex sensing-reporting optimization for cooperative spectrum sensing

We consider the cooperative spectrum sensing problem in cognitive radio with energy detection. Secondary users with non-identical, independent sensing channels make 1-bit sensing decisions and report their decisions to the secondary base station over orthogonal fading channels. The base station acts as a fusion center by combining the decisions with OR-rule. We allow the secondary users to trade sensing time slots for additional reporting time slots. We derive the corresponding false alarm and missed detection probabilities, which are functions of the secondary sensor decision thresholds and the durations for sensing and reporting. Furthermore, we bound these probabilities and impose a practical convex region that enables convex optimization to minimize the false alarm probability for a target missed detection probability. Allowing secondary users to trade sensing time slots for additional reporting time slots is shown to significantly improve sensing performance, even with poor sensing channels and a small number of secondary users.