AbstractConsider a multi‐user underlay cognitive network where multiple cognitive users concurrently share the spectrum with a primary network with multiple users. The channel between the secondary network is assumed to have independent but not identical Nakagami‐m fading. The interference channel between the secondary users (SUs) and the primary users is assumed to have Rayleigh fading. A power allocation based on the instantaneous channel state information is derived when a peak interference power constraint is imposed on the secondary network in addition to the limited peak transmit power of each SU. The uplink scenario is considered where a single SU is selected for transmission. This opportunistic selection depends on the transmission channel power gain and the interference channel power gain as well as the power allocation policy adopted at the users. Exact closed form expressions for the moment‐generating function, outage performance, symbol error rate performance, and the ergodic capacity are derived. Numerical results corroborate the derived analytical results. The performance is also studied in the asymptotic regimes, and the generalized diversity gain of this scheduling scheme is derived. It is shown that when the interference channel is deeply faded and the peak transmit power constraint is relaxed, the scheduling scheme achieves full diversity and that increasing the number of primary users does not impact the diversity order. Copyright © 2014 John Wiley & Sons, Ltd.