Underlay Cognitive Multiuser Diversity With Random Number of Secondary Users

A single primary user cognitive radio system with multiuser diversity at the secondary users (SUs) is considered, where there is an interference constraint between SUs and the primary receiver. The SU with the highest instantaneous signal-to-noise ratio is selected for communication from a set of active users, which also satisfies the interference constraint. The active number of SUs is shown to be binomial, negative binomial, or Poisson-binomial distributed depending on various modes of operation. The outage probability in the slow-fading scenario is also studied. This is then followed by a derivation of the scaling law of the ergodic capacity and bit error rate (BER) averaged across the fading and the user distribution for a large mean number of users. The ergodic capacity and average BER under the binomial user distribution are shown to outperform the negative binomial case with the same mean number of users. Moreover, the Poisson distribution is used to approximate the user distribution under the non-independent and identically distributed interference scenario and compared with binomial and negative binomial distributions in a stochastic ordering sense. Monte Carlo simulations are used to supplement our analytical results and compare the performances under different user distributions.