User Capacity Scaling Laws for Fading Multiple-Access Channels

In this paper, the maximum number of simultaneous active transmitters (i.e. user capacity) is obtained in the many user case for fading multiple-access channels in which a minimum rate must be maintained for all active users. The results are presented in the form of scaling laws as the number of transmitters increases and three commonly used fading models, namely, Rayleigh, Rician and Nakagami are considered. It is shown that in all three cases, the user capacity scales double logarithmically with the number of users and differs only by constants depending on the distributions. We also show that the scheduling policy maximizing the number of simultaneous active transmitters can be implemented in a distributed fashion.