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

We consider the identifiability issue of maximum- likelihood based activity detection in massive MIMO-based grant- free random access. An intriguing observation by (Chen et al., 2022) indicates that the identifiability undergoes a phase transition for commonly-used random user signatures as L-2 , N and K tend to infinity with fixed ratios, where L , N and K denote the user signature length, the total number of users, and the number of active users, respectively. In this letter, we provide a precise analytical characterization of the phase transition based on a spectral universality conjecture. Numerical results demonstrate excellent agreement between our theoretical predictions and the empirical phase transitions.