论文标题
高斯随机多个访问频道的缩放定律
Scaling Laws for Gaussian Random Many-Access Channels
论文作者
论文摘要
本文考虑了一个带有随机用户活动的高斯多访问通道，其中用户总数$ \ ell_n $和平均活性用户数量$ k_n $可能会随着块长$ n $而增长。对于此频道，它研究了可以可靠地传输的最大钻头，该位可以可靠地每单位能量传输，这是$ \ ell_n $和$ k_n $的函数。当所有用户都具有概率1的活动（即$ \ ell_n = k_n $）时，可以证明，如果$ k_n $严格低于$ n/\ log n $的订单，则每个用户可以实现单位能量$（\ log log e e）/n_0 $（where $ n_0/2 $）的单位用户可通过使用噪声电源来实现单位用户的容量。相比之下，如果$ k_n $的订单严格高于$ n/\ log n $，则单位能量的容量为零。因此，在生长的顺序之间存在急剧的过渡，其中无干扰的通信是可行的，而增长顺序是可靠的通信以每单位能量的正率是不可行的。进一步证明，正交访问方案与正交代码簿相结合，在用户数量界限时，可以严格屈服于用户数量时的每单位能量。 当用户活动是随机的，即，当$ \ ell_n $和$ k_n $不同时，可以证明，如果$ k_n \ log \ ell_n $在$ n $中是sublinear，则每个用户可以实现单个单位 - 能量$（\ log log E（\ log e）/n_0 $的单用户容量。相反，如果$ k_n \ log \ ell_n $是$ n $的超级线，则单位能量的容量为零。因此，在增长顺序之间再次发生了急剧的转变，其中无干扰的通信是可行的，增长顺序是不可行的，可靠的沟通依赖于$ \ ell_n $和$ k_n $的渐近行为。进一步证明，当$ \ ell_n = k_n $时，正交访问方案可能是最佳的。
This paper considers a Gaussian multiple-access channel with random user activity where the total number of users $\ell_n$ and the average number of active users $k_n$ may grow with the blocklength $n$. For this channel, it studies the maximum number of bits that can be transmitted reliably per unit-energy as a function of $\ell_n$ and $k_n$. When all users are active with probability one, i.e., $\ell_n = k_n$, it is demonstrated that if $k_n$ is of an order strictly below $n/\log n$, then each user can achieve the single-user capacity per unit-energy $(\log e)/N_0$ (where $N_0/ 2$ is the noise power) by using an orthogonal-access scheme. In contrast, if $k_n$ is of an order strictly above $n/\log n$, then the capacity per unit-energy is zero. Consequently, there is a sharp transition between orders of growth where interference-free communication is feasible and orders of growth where reliable communication at a positive rate per unit-energy is infeasible. It is further demonstrated that orthogonal-access schemes in combination with orthogonal codebooks, which achieve the capacity per unit-energy when the number of users is bounded, can be strictly suboptimal. When the user activity is random, i.e., when $\ell_n$ and $k_n$ are different, it is demonstrated that if $k_n\log \ell_n$ is sublinear in $n$, then each user can achieve the single-user capacity per unit-energy $(\log e)/N_0$. Conversely, if $k_n\log \ell_n$ is superlinear in $n$, then the capacity per unit-energy is zero. Consequently, there is again a sharp transition between orders of growth where interference-free communication is feasible and orders of growth where reliable communication at a positive rate is infeasible that depends on the asymptotic behaviours of both $\ell_n$ and $k_n$. It is further demonstrated that orthogonal-access schemes, which are optimal when $\ell_n = k_n$, can be strictly suboptimal.
