Scaling Laws for Gaussian Random Many-Access Channels

This paper considers a Gaussian multiple-access channel with random user activity where the total number of users $\ell _{n}$ and average active notation="LaTeX">$k_{n}$ may grow blocklength notation="LaTeX">$n$ . For this channel, it studies maximum bits that can be transmitted reliably per unit-energy as function When all are probability one, i.e., _{n} = k_{n}$ , is demonstrated that, if an order strictly below notation="LaTeX">$n/\log n$ then each achieve single-user capacity notation="LaTeX">$(\log e)/N_{0}$ (where notation="LaTeX">$N_{0}/ 2$ noise power) by using orthogonal-access scheme. In contrast, above cannot any positive rate unit-energy. Consequently, there sharp transition between orders growth interference-free communication feasible reliable at infeasible. It further schemes in combination orthogonal codebooks, which when bounded, suboptimal. random, different, notation="LaTeX">$k_{n}\log \ell sublinear Conversely, superlinear again infeasible depends on asymptotic behaviors both schemes, optimal suboptimal general.