Source Enumeration Using the Distribution of Angles: A Parameter-Free Approach for Grant-Free Access in Massive MIMO Uplink

Source enumeration, the task of estimating the number of sources from the signal received by the array of antennas, is a critical problem in wireless communication. Numerous methods have been proposed to estimate the number of sources under white or colored Gaussian noise. However, their performance degrades significantly in the presence of a limited number of observations and/or a large number of sources. We propose a method that performs well a) under both i.i.d. Gaussian and heavy-tailed ℓ2-norm noise, b) when the number of sources is large, and c) with fewer observations than antennas. We establish a condition on the eigenvalues of the observation covariance that ensures accurate source enumeration. We further highlight the superiority of our algorithm over state-of-the-art methods with extensive simulation results and validate its effectiveness in estimating the active user count in grant-free massive MIMO.