Phase Transition Analysis for Covariance Based Massive Random Access with Massive MIMO

Abstract

This paper studies the massive random access problem in which a large number of sporadically active devices wish to communicate to a base-station (BS) equipped with a large number of antennas. The devices are pre-assigned unique pilot sequences for random access. It has been shown previously that the device activity detection problem at the BS can be formulated as a maximum likelihood estimation (MLE) problem, whose solution depends on the sample covariance matrix of the received signal. This paper adopts the MLE formulation, and proposes an approach to analyze the covariance based detection by studying the asymptotic properties of the MLE via its associated Fisher information matrix. This paper proposes a necessary condition on the Fisher information matrix such that the estimation error tends to zero in the massive multiple-input multiple-output (MIMO) regime. A phase transition analysis is carried out based on the necessary condition. This paper also analyzes the distribution of the estimation error for the case with a large but finite number of antennas at the BS. Numerical experiments validate the analysis.