Power allocation is one of the fundamental problems in wireless networks and a wide variety of algorithms address this problem from different perspectives. A common element among these algorithms is that they rely on an estimation of the channel state, which may be inaccurate on account of hardware defects, noisy feedback systems, and environmental and adversarial disturbances. Therefore, it is essential that the output power allocation of these algorithms is stable with respect to input perturbations, to the extent that the variations in the output are bounded for bounded variations in the input. In this paper, we focus on UWMMSE -- a modern algorithm leveraging graph neural networks --, and illustrate its stability to additive input perturbations of bounded energy through both theoretical analysis and empirical validation.

翻译：电力分配是无线网络的根本问题之一,而各种算法从不同角度解决这一问题。这些算法的一个共同点是,它们依赖对频道状态的估计,而这种估计可能由于硬件缺陷、噪音反馈系统以及环境和对抗性干扰等原因不准确。因此,这些算法的输出力分配在输入扰动方面必须稳定,只要产出的变化与输入的受约束的变异有关。在本文中,我们侧重于UWMMSE -- -- 一种利用图形神经网络的现代算法 -- -- 并通过理论分析和经验验证来说明其稳定性,即对受约束能源的添加性输入干扰。