Over-the-Air Statistical Estimation of Sparse Models
Over-the-Air Statistical Estimation of Sparse Models
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DOI：
10.1109/globecom46510.2021.9685768
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发表时间：
2021-12
期刊：
影响因子：
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通讯作者：
Chuan-Zheng Lee;L. P. Barnes;Wenhao Zhan;Ayfer Özgür
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文献类型：
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作者：
Chuan-Zheng Lee;L. P. Barnes;Wenhao Zhan;Ayfer Özgür
我们提出了使用统计、压缩感知和无线通信技术，在平方误差损失下对高斯多址信道（MAC）上的稀疏参数或观测向量进行极小极大统计估计的方案。这些“模拟”方案利用高斯 MAC 固有的叠加，使用压缩感知来减少所需的信道使用数量。对于稀疏高斯位置和稀疏乘积伯努利模型，我们根据节点数量、参数、通道使用和非零条目（稀疏性）推导出风险表达式。我们表明，它们比“数字”方案中现有的风险下限提供了指数级的改进，这些方案假设节点以香农容量无差错地传输比特。这表明，联合设计估计和通信的模拟方案可以有效地利用高维模型和观测中固有的稀疏性，并在这种情况下比分离源编码和信道编码的数字方案提供巨大的改进。
We propose schemes for minimax statistical estimation of sparse parameter or observation vectors over a Gaussian multiple-access channel (MAC) under squared error loss, using techniques from statistics, compressed sensing and wireless communication. These “analog” schemes exploit the superposition inherent in the Gaussian MAC, using compressed sensing to reduce the number of channel uses needed. For the sparse Gaussian location and sparse product Bernoulli models, we derive expressions for risk in terms of the numbers of nodes, parameters, channel uses and nonzero entries (sparsity). We show that they offer exponential improvements over existing lower bounds for risk in “digital” schemes that assume nodes to transmit bits errorlessly at the Shannon capacity. This shows that analog schemes that design estimation and communication jointly can efficiently exploit the inherent sparsity in high-dimensional models and observations, and provide drastic improvements over digital schemes that separate source and channel coding in this context.