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arXiv 2111.02709cs.ITcs.DCmath.IT
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用于单次分布主元分析的模拟MIMO通信

Analog MIMO Communication for One-shot Distributed Principal Component Analysis

Xu Chen, Erik G. Larsson, Kaibin Huang

摘要:

在无线网络边缘进行数据分析的基本算法是分布式主成分分析(DPCA),其通过分布式计算降维数据子空间(称为主成分(PC))来发现嵌入在分布式高维数据集中的最重要信息。在本文中,支持一次性DPCA在无线系统中,我们提出了一个框架的模拟MIMO传输的特点是未编码的模拟传输的本地PC估计的全球PC。为了应对信道失真和噪声,两个最大似然(全局)PC估计器的情况下,相应的接收信道状态信息(CSI)。第一个设计,称为相干PC估计器,是通过解决一个Procrustes问题,并揭示了正规化的信道反演的形式,其中的规定试图减轻接收机噪声和数据噪声的影响。第二个,称为盲PC估计器,设计的基础上的子空间信道旋转不变性的性质和计算的质心接收到的本地PC的格拉斯曼流形。利用流形扰动理论,推导了两种估计的均方子空间距离(MSSD)的严格界,用于性能评估。结果揭示了简单的缩放定律的MSSD有关设备的人口,数据和通道的信噪比(SNR),和阵列的大小。更重要的是,这两个估计被发现有相同的缩放定律,这表明CSI加速DPCA的必要性。仿真结果验证了推导的结果,并证明了所提出的模拟MIMO的有前途的延迟性能

英文摘要:

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

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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