Asymptotic Analysis of Multi-Antenna Cognitive Radio Systems Using Extreme Value Theory

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. Index Terms Cognitive radio, extreme value theory, mean capacity, outage capacity, rate scaling law, spectrumsharing, transmit antenna selection.