Statistical Framework for Clustering MU-MIMO Wireless via Second Order Statistics

TL;DR

This paper introduces a statistical framework for clustering MU-MIMO wireless users based on the distances between their channel covariance matrices, providing theoretical insights into the estimator's performance.

Contribution

It develops a new estimator for the Log-Euclidean distance between covariance matrices and proves its asymptotic Gaussianity in MU-MIMO systems.

Findings

Estimator is consistent as samples grow large.

Central limit theorem established for the distance estimator.

Framework enables accurate performance prediction of clustering algorithms.

Abstract

This work explores the clustering of wireless users by examining the distances between their channel covariance matrices, which reside on the Riemannian manifold of positive definite matrices. Specifically, we consider an estimator of the Log-Euclidean distance between multiple sample covariance matrices (SCMs) consistent when the number of samples and the observation size grow unbounded at the same rate. Within the context of multi-user MIMO (MU-MIMO) wireless communication systems, we develop a statistical framework that allows to accurate predictions of the clustering algorithm's performance under realistic conditions. Specifically, we present a central limit theorem that establishes the asymptotic Gaussianity of the consistent estimator of the log-Euclidean distance computed over two sample covariance matrices.