Analog MIMO Communication for One-Shot Distributed Principal Component Analysis

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