A fundamental algorithm for data analytics at the edge of wireless networks is distributed principal component analysis (DPCA), which finds the most important information embedded in a distributed high-dimensional dataset by distributed computation of a reduced-dimension data subspace, called principal components (PCs). In this paper, to support one-shot DPCA in wireless systems, we propose a framework of analog MIMO transmission featuring the uncoded analog transmission of local PCs for estimating the global PCs. To cope with channel distortion and noise, two maximum-likelihood (global) PC estimators are presented corresponding to the cases with and without receive channel state information (CSI). The first design, termed coherent PC estimator, is derived by solving a Procrustes problem and reveals the form of regularized channel inversion where the regulation attempts to alleviate the effects of both receiver noise and data noise. The second one, termed blind PC estimator, is designed based on the subspace channel-rotation-invariance property and computes a centroid of received local PCs on a Grassmann manifold. Using the manifold-perturbation theory, tight bounds on the mean square subspace distance (MSSD) of both estimators are derived for performance evaluation. The results reveal simple scaling laws of MSSD concerning device population, data and channel signal-to-noise ratios (SNRs), and array sizes. More importantly, both estimators are found to have identical scaling laws, suggesting the dispensability of CSI to accelerate DPCA. Simulation results validate the derived results and demonstrate the promising latency performance of the proposed analog MIMO.

中文翻译：

---

用于一次性分布式主成分分析的模拟 MIMO 通信

无线网络边缘数据分析的基本算法是分布式主成分分析( DPCA )，它通过对称为主成分的降维数据子空间的分布式计算，找到嵌入分布式高维数据集中的最重要信息。件）。在本文中，为了支持无线系统中的 one-shot DPCA，我们提出了一个模拟 MIMO 传输框架，该框架具有本地 PC 的未编码模拟传输，用于估计全局 PC。为了应对信道失真和噪声，提出了两个最大似然（全局）PC估计器，分别对应于有和没有接收信道状态信息的情况（CSI）。第一个设计，称为相干 PC 估计器，是通过解决 Procrustes 问题得出的，并揭示了正则化通道反转的形式，其中调节试图减轻接收器噪声和数据噪声的影响。第二个称为盲 PC 估计器，它是基于子空间通道旋转不变性属性设计的，并计算接收到的在 Grassmann 流形上的本地 PC 的质心。使用流形微扰理论，推导出两个估计器的均方子空间距离(MSSD) 的紧密界限以进行性能评估。结果揭示了关于设备数量、数据和通道信噪比的 MSSD 的简单缩放定律(SNR) 和阵列大小。更重要的是，发现两个估计量具有相同的比例定律，这表明 CSI 对加速 DPCA 的可有性。仿真结果验证了推导出的结果，并证明了所提出的模拟 MIMO 的潜在延迟性能。