  The multi-user diversity in spectrum sharing cognitive radio systems with
average power constraints over fading channels is investigated. Average power
constraints are imposed for both the transmit power at the secondary
transmitter and the interference power received at the primary receiver in
order to provide optimal power allocation for capacity maximization at the
secondary system and protection at the primary system respectively. Multiple
secondary and primary receivers are considered and the corresponding fading
distributions for the Rayleigh and Nakagami-m fading channels are derived.
Based on the derived formulation of the fading distributions, the average
achievable channel capacity and the outage probability experienced at the
secondary system are obtained, revealing the impact of the average power
constraints on optimal power allocation in multi-user diversity technique in
fading environments with multiple secondary and primary receivers that share
the same channel. The obtained results highlight the advantage of having on one
hand more secondary receivers and on the other hand fewer primary receivers
manifested as an increase in the achievable capacity.
