We consider a Gaussian multiple-access channel with random user activity where the total number of users ℓn 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.
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机译:我们考虑具有随机用户活动的高斯多路访问信道,其中用户总数为
n inf>
和平均活跃用户数k
n inf>
可能是无限的。对于此信道,我们用ℓ来表征每单位能量可以可靠传输的最大位数。
n inf>
和k
n inf>
。我们证明如果k
n inf>
日志ℓ
n inf>
在n中为亚线性,则每个用户可以实现每单位能量的单用户容量。相反,如果k
n inf>
日志ℓ
n inf>
在n中为超线性,则每单位能量的容量为零。我们进一步证明,当所有用户以概率1活跃时,最优的正交访问方案可能严格地不是最佳选择。
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