Capacity per Unit-Energy of Gaussian Random Many-Access Channels

Abstract

We consider a Gaussian multiple-access channel with random user activity where the total number of userslₙ and the average number of active users kₙ may be unbounded. For this channel, we characterize the maximum number of bits that can be transmitted reliably per unit-energy in terms of lₙ and kₙ . We show that if kₙ log lₙ is sublinear in n, then each user can achieve the single-user capacity per unit-energy. Conversely, if kₙ log lₙ is superlinear in n, then the capacity per unit-energy is zero. We further demonstrate that orthogonal-access schemes, which are optimal when all users are active with probability one, can be strictly suboptimal.