Impact of the number of antennas and distances among users on cognitive radio networks

In this paper, we study the impact of the number of antennas and distances among users on the performance of a spectrum sharing system. In particular, we assume that a secondary transmitter is equipped with a single antenna while both secondary receiver and primary receiver have multiple antennas. Also, it is assumed that the secondary users are subject to the peak interference power constraint. On this basis, the cumulative distribution function and probability density function for the signal-to-noise ratio are derived for Rayleigh fading channels. Moreover, using these results, we obtain closed-form expressions for the outage probability, ergodic capacity and an exact expression for symbol error probability. These formulas allow us to examine the impact of the number of antennas of the SU-Rx, the PU-Rx and distance among users on the system performance. Finally, Monte-Carlo simulations are provided to verify our analytical results.