Cognitive Radio with Random Number of Secondary Number of Users

A single primary user cognitive radio system with multi-user diversity at the secondary users is considered where there is an interference constraint between secondary and primary users. The secondary user with the highest instantaneous SNR is selected for communication from a set of active users which also satisfies the interference constraint. The active number of secondary users is shown to be binomial, negative binomial, or Poisson-binomial distributed depending on various modes of operation. 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 BER averaged across the fading, and user distribution for a large mean number of users. The ergodic capacity and average BER under the binomial user distribution is 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-i.i.d 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. Index Terms Cognitive radio, multi-user diversity, stochastic ordering, interference constraint