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
翻译:在无线网络边缘进行数据分析的基本算法是分布式主元件分析(DPCA),该算法发现最重要的信息嵌入分布式高维数据集中,通过分布式计算一个叫做主要元件(PCs)的减少dimenion数据子空间(即主要元件),在本文中,为支持无线系统中的一次性DPCA,我们提议了一个模拟MIMO传输框架,其特点是以未经编码的模拟方式传输当地个人电脑来估计全球个人电脑。为了应对频道扭曲和噪音,提供了两个与案件相对应的、不接收频道状态信息(CSI)的最大相似的PC加速测算器。第一个设计,称为统一的PC测算器测量器子子子子子数据集,通过解决Procrustrustrutes问题,揭示常规调节器的正常化通道变换换形式,试图减轻接收器噪音和数据噪音的影响。第二个称为盲点测算器的测算器,根据次空间频道调色器变换特性设计,对收到的本地个人电脑的精确度结果进行校准。使用Scrstrmann Stal-perperde Slation Slation Salide Slader Salidede,Slade Slade 和Slaviews salistral lade Salistral deal lavial labal lade labal lade labal lax sal lade lade labal labal lade lade lade lade lade,Salideal labal labal lade labal ladeal labal labal labal labal lade ladeal labal labal labal 和Sde 和Sdeal 系统的Sde 系统的Sdeal 和Sdealal 系统的Sdealalalalalalalalalalalalalalalalalalalalalalalalalal 系统的Sdeal 系统的Sal 系统的Sdeal 和Salalalalalalalalalalalalalalalalalalalal,Salalalalal