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A single primary user cognitive radio system with multi-user diversity at thesecondary users is considered where there is an interference constraint betweensecondary and primary users. The secondary user with the highest instantaneousSNR is selected for communication from a set of active users which alsosatisfies the interference constraint. The active number of secondary users isshown to be binomial, negative binomial, or Poisson-binomial distributeddepending on various modes of operation. Outage probability in the slow fadingscenario is also studied. This is then followed by a derivation of the scalinglaw of the ergodic capacity and BER averaged across the fading, and userdistribution for a large mean number of users. The ergodic capacity and averageBER under the binomial user distribution is shown to outperform the negativebinomial case with the same mean number of users. Moreover, the Poissondistribution is used to approximate the user distribution under the non-i.i.dinterference scenario, and compared with binomial and negative binomialdistributions in a stochastic ordering sense. Monte-Carlo simulations are usedto supplement our analytical results and compare the performances underdifferent user distributions.

Cognitive Radio with Random Number of Secondary Number of Users