  In this paper, an underlay cognitive radio (CR) system is considered with
multiple cognitive or secondary users contending to transmit their information
to the cognitive destination (e.g., eNodeB) using the spectral resource of a
primary user. The novel closed-form expressions are derived for the selection
probabilities of cognitive users with opportunistic scheduling wherein an
optimal metric is employed for opportunistic transmission. The analytical
results corroborated by the Monte Carlo simulations, can be used to demonstrate
the fairness achieved in opportunistic scheduling. It is shown that the
fairness in terms of equal chance for transmission amongst all cognitive users
can only be seen for the scenarios when the fraction of distances between the
cognitive transmitter and cognitive receiver, and cognitive transmitter and
primary receiver is identical for each of the cognitive transmitters.
