Robust Covariance-Based Activity Detection for Massive Access
Jianan Bai, Erik G. Larsson
TL;DR
This work addresses activity detection for grant-free massive access under time-frequency channel variations that violate the traditional block-fading assumption. It introduces a PCA-based, low-rank channel model that represents the fading vector as $\boldsymbol{h} \approx \boldsymbol{G}\boldsymbol{\theta}$ with $\boldsymbol{G}=\boldsymbol{U}\boldsymbol{D}_{\boldsymbol{\rho}}^{1/2}$, extending the notion of coherence blocks to a prediction horizon. Activity detection is cast as a covariance-matching ML problem updated by a coordinate-descent algorithm that accounts for rank-$N$ channel updates, yielding robust performance even under rapid variations. The key result is that a small approximation order $N$ (roughly $3$–$5$) suffices to capture time-frequency variations and dramatically improve detection accuracy compared with traditional block-fading or frequency-only models, enabling more reliable GFRA in wideband and high-mobility scenarios.
Abstract
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 robustify 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.