Power control for cognitive radio systems with unslotted primary users under sensing uncertainty

This paper studies the optimal power control policy and frame duration that maximize the throughput of secondary users operating under transmit power, interference power, and collision constraints in the presence of unslotted primary users. It is assumed that primary user activity follows an ON-OFF alternating renewal process. Secondary users first sense the channel albeit with errors in the form of miss detections and false alarms, and then start the data transmission only if no primary user activity is detected. Under these assumptions, we determine the optimal power control policy subject to peak transmit power and average interference power constraints and propose a lowcomplexity algorithm for the joint optimization of the power level and frame duration under collision constraints.We further analyze some important properties of the collision duration ratio, which is defined as the ratio of average collision duration to transmission duration, and investigate the impact of the probabilities of detection and false alarm on the throughput, optimal transmission power, and the collisions with primary user transmissions.