  We consider a spectrum-sharing cognitive radio system with antenna selection
applied at the secondary transmitter (ST). Based on the extreme value theory,
we deduce a simple and accurate expression for the asymptotic distribution of
the signal to interference plus noise ratio at the secondary receiver. Using
this result, the asymptotic mean capacity and the outage capacity for the
secondary user (SU) are derived. The obtained asymptotic capacities approach
the exact results as the number of transmit antennas $N$ increases. Results
indicate that the rate of the SU scales as $\log(N)$ when the transmit power of
the ST is limited by the maximum allowable interference level, while rate
scales as $\log(\log(N))$ if ST is limited by the maximum transmit power.
