On cognitive radio systems with directional antennas and imperfect spectrum sensing

In this paper, we consider a cognitive radio system, consisting of a primary user (PU), a secondary user (SU) transmitter, and a SU receiver. The SUs are equipped with directional antennas. The SU transmitter first performs spectrum sensing (with errors) and then transmits data. We assume the SU and PU can coexist and the SU transmits at two power levels, according to the result of spectrum sensing (i.e., whether the spectrum is sensed idle or busy). We establish a lower bound on the ergodic capacity of the channel between SU transmitter and receiver, and study how spectrum sensing errors affect the bound. Furthermore, we explore the optimal SU transmit power levels and the optimal directions of SU transmit and receive antennas, such that the lower bound is maximized, subject to average transmit power and average interference power constraints. Through numerical simulations, we show that (compared with the case when the SUs use omni-directional antennas) directional antennas can significantly improve the lower bound in the presence of spectrum sensing errors, subject to the constraints.