空中统计估计
Over-the-Air Statistical Estimation
摘要：
在统计估计和无线通信相结合的框架下，研究了高斯多址信道（MAC）下均方误差损失下的分布式极大极小统计估计的方案和下界.首先，我们开发了“模拟”联合估计通信计划，利用高斯MAC的叠加特性，我们的节点数量和参数空间的维度来表征其风险。然后，我们推导出信息理论的最小最大风险的任何估计方案限制在一个给定的使用信道的样本进行通信的下限，并表明我们提出的计划实现的风险是在这些下限的对数因子。我们比较两个可扩展性和下限结果到以前的“数字”下限，其中节点在MAC的香农容量传输无差错比特，表明利用物理层的估计方案提供了依赖于物理层抽象的数字方案的估计误差大幅减少。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
