On Optimal Sensing and Capacity Trade-off in Cognitive Radio Systems with Directional Antennas

We consider a cognitive radio system, in which the secondary users (SUs) and primary users (PUs) coexist. The SUs are equipped with steerable directional antennas. In our system, the secondary transmitter (SUtx) first senses the spectrum (with errors) for a duration of {\tau}, and, then transmits data to the secondary receiver (SUrx) if spectrum is sensed idle. The sensing time as well as the orientation of SUtx's antenna affect the accuracy of spectrum sensing and yield a trade-off between spectrum sensing and capacity of the secondary network. We formulate the ergodic capacity of secondary network which uses energy detection for spectrum sensing. We obtain optimal SUtx transmit power, the optimal sensing time {\tau} and the optimal directions of SUtx transmit antenna and SUrx receive antenna by maximizing the ergodic capacity, subject to peak transmit power and outage interference probability constraints. Our simulation results show the effectiveness of these optimizations to increase the ergodic capacity of the secondary network.