Capacity per Unit-Energy of Gaussian Many-Access Channels
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We consider a Gaussian multiple-access channel where the number of transmitters grows with the blocklength n. For this setup, the maximum number of bits that can be transmitted reliably per unit-energy is analyzed. We show that if the number of users is of an order strictly above n/ n, then the users cannot achieve any positive rate per unit-energy. In contrast, if the number of users is of order strictly below n/ n, then each user can achieve the single-user capacity per unit-energy ( e)/N_0 (where N_0/ 2 is the noise power) by using an orthogonal access scheme such as time division multiple access. We further demonstrate that orthogonal codebooks, which achieve the capacity per unit-energy when the number of users is bounded, can be strictly suboptimal.
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