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We consider a cognitive radio system, in which the secondary users (SUs) andprimary users (PUs) coexist. The SUs are equipped with steerable directionalantennas. In our system, the secondary transmitter (SUtx) first senses thespectrum (with errors) for a duration of {\tau}, and, then transmits data tothe secondary receiver (SUrx) if spectrum is sensed idle. The sensing time aswell as the orientation of SUtx's antenna affect the accuracy of spectrumsensing and yield a trade-off between spectrum sensing and capacity of thesecondary network. We formulate the ergodic capacity of secondary network whichuses energy detection for spectrum sensing. We obtain optimal SUtx transmitpower, the optimal sensing time {\tau} and the optimal directions of SUtxtransmit 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 toincrease the ergodic capacity of the secondary network.

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