Robust Covariance-Based Activity Detection for Massive Access

The wireless channel is undergoing continuous changes, and the block-fading assumption, despite its popularity in theoretical contexts, never holds true in practical scenarios. This discrepancy is particularly critical for user activity detection in grant-free random access, where joint processing across multiple resource blocks is usually undesirable. In this paper, we propose employing a low-dimensional approximation of the channel to capture variations over time and frequency and ro-bustify activity detection algorithms. This approximation entails projecting channel fading vectors onto their principal directions to minimize the approximation order. Through numerical examples, we demonstrate a substantial performance improvement achieved by the resulting activity detection algorithm.