We study schemes and lower bounds for distributed minimax statistical estimation over a Gaussian multiple-access channel (MAC) under squared error loss, in a framework combining statistical estimation and wireless communication. First, we develop "analog" joint estimation-communication schemes that exploit the superposition property of the Gaussian MAC and we characterize their risk in terms of the number of nodes and dimension of the parameter space. Then, we derive information-theoretic lower bounds on the minimax risk of any estimation scheme restricted to communicate the samples over a given number of uses of the channel and show that the risk achieved by our proposed schemes is within a logarithmic factor of these lower bounds. We compare both achievability and lower bound results to previous "digital" lower bounds, where nodes transmit errorless bits at the Shannon capacity of the MAC, showing that estimation schemes that leverage the physical layer offer a drastic reduction in estimation error over digital schemes relying on a physical-layer abstraction.

翻译：我们在一个将统计估计和无线通信相结合的框架内,对高山多通频道(高山多通频道)的平差错误损失进行分布式小型统计估计的计划和下限。首先,我们开发“模拟”联合估计通信计划,利用高山多通频道的叠加特性,并用节点的数量和参数空间的维度来描述其风险。然后,我们从任何用于将样品传送到该频道某些用途的微低估计计划的信息-理论下限中得出信息-理论下限,并表明我们提议的计划所实现的风险是在这些较低界限的对数系数之内。我们将可实现性和约束性较低的结果与以前的“数字”下界作比较,在前“数字”低边框中,节点传递出无误点,表明利用物理层的估算计划会大大减少数字计划对物理抽象抽象的误差。