  In this paper, we propose an antenna selection method in a wireless cognitive
radio (CR) system, namely difference selection, whereby a single transmit
antenna is selected at the secondary transmitter out of $M$ possible antennas
such that the weighted difference between the channel gains of the data link
and the interference link is maximized. We analyze mutual information and
outage probability of the secondary transmission in a CR system with difference
antenna selection, and propose a method of optimizing these performance metrics
of the secondary data link subject to practical constraints on the peak
secondary transmit power and the average interference power as seen by the
primary receiver. The optimization is performed over two parameters: the peak
secondary transmit power and the difference selection weight $\delta\in [0,
1]$. We show that, difference selection using the optimized parameters
determined by the proposed method can be, in many cases of interest, superior
to a so called ratio selection method disclosed in the literature, although
ratio selection has been shown to be optimal, when impractically, the secondary
transmission power constraint is not applied. We address the effects that the
constraints have on mutual information and outage probability, and discuss the
practical implications of the results.
