We study the problem of decentralized power allocation in a multi-access channel (MAC) with non-cooperative users, additive noise of arbitrary distribution and a generalized power constraint, i.e., the transmit power constraint is modeled by an upper bound on $\mathbb{E}[\phi(|S|)]$, where $S$ is the transmit signal and $\phi(.)$ is some non-negative, increasing and bounded function. The generalized power constraint captures the notion of power for different wireless signals such as RF, optical, acoustic, etc. We derive the optimal power allocation policy when there a large number of non-cooperative users in the MAC. Further, we show that, once the number of users in the MAC crosses a finite threshold, the proposed power allocation policy of all users is optimal and remains invariant irrespective of the actual number of users. We derive the above results under the condition that the entropy power of the MAC, $e^{2h(S)+c}$, is strictly convex, where $h(S)$ is the maximum achievable entropy of the transmit signal and $c$ is a finite constant corresponding to the entropy of the additive noise.

翻译：本文研究多址信道中非协作用户的分散式功率分配问题，其中包含任意分布的加性噪声和广义功率约束。该约束通过$\mathbb{E}[\phi(|S|)]$的上界建模发射功率，其中$S$为发射信号，$\phi(·)$为非负、递增且有界函数。广义功率约束能表征射频、光学、声学等不同无线信号的功率概念。当多址信道中存在大量非协作用户时，我们推导出最优功率分配策略。进一步研究表明，一旦多址信道中的用户数量超过有限阈值，本文提出的所有用户功率分配策略均为最优，且不随实际用户数量变化。上述结果在加性噪声熵$e^{2h(S)+c}$严格凸的条件下成立，其中$h(S)$为发射信号可达最大熵，$c$为与加性噪声熵对应的有限常数。