Multi-user diversity with random number of users

Multi-user diversity (MUD) is considered when the number of users in the system is random. Average throughput of a MUD system is shown to have a completely monotone derivative with respect to (deterministic) number of users. Following this, randomization of number of users is shown to give degraded throughput averaged across the number of users distribution. Using stochastic ordering theory, a framework for comparison of performance for different user distributions is provided. For Poisson distributed number of users communicating over Rayleigh faded channels, long-term average throughput is shown to scale as a double logarithmic function of average number of users.