  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
