Capacity per Unit-Energy of Gaussian Random Many-Access Channels
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We consider a Gaussian multiple-access channel with random user activities where the total number of users ℓ_n and the average number of active users k_n may be unbounded. For this channel, we characterize the maximum number of bits that can be transmitted reliably per unit-energy in terms of ℓ_n and k_n. We show that if k_nlogℓ_n is sublinear in n, then each user can achieve the single-user capacity per unit-energy. Conversely, if k_nlogℓ_n 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.
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