Precise Analysis of Covariance Identifiability for Activity Detection in Grant-Free Random Access

TL;DR

This paper analytically characterizes the phase transition boundary for covariance-based activity detection in grant-free random access with massive MIMO, providing insights into when activity detection is theoretically identifiable.

Contribution

It offers a precise analytical description of the phase transition boundary for covariance identifiability in activity detection, advancing understanding beyond prior empirical observations.

Findings

The phase transition boundary for covariance identifiability is analytically characterized.

Theoretical results align closely with numerical experiments.

Provides a deeper understanding of activity detection limits in massive MIMO systems.

Abstract

We consider the identifiability issue of maximum likelihood based activity detection in massive MIMO based grant-free random access. A prior work by Chen et al. indicates that the identifiability undergoes a phase transition for commonly-used random signatures. In this paper, we provide an analytical characterization of the boundary of the phase transition curve. Our theoretical results agree well with the numerical experiments.