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arXiv · 2609.10207

Covariance-Aware MM-PGD for Mixed Near-/Far-Field Activity Detection

Xinjue Wang·Zhi-Yong Wang·Sergiy A. Vorobyov·Esa Ollila·Gayan Amarasuriya Aruma Baduge·Mojtaba Vaezi
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Abstract

Grant-free activity detection with mixed near-field (NF) and far-field (FF) devices is an important problem that can be addressed via covariance-based detectors. The difficulty is that NF users induce device-specific structured spatial covariances, whereas FF users are well approximated by isotropic covariances. Under a unified Rician model, we first formulate activity detection as a relaxed maximum-likelihood problem in the full LM-dimensional vectorized observation space. We then develop a covariance-aware majorization-minimization projected gradient descent (MM-PGD) detector. It updates the full activity vector jointly and avoids the per-coordinate high-rank subproblems that arise in the NF regime. Numerical results over SNR, antenna-count, and NF-ratio sweeps show that MM-PGD achieves up to 20x lower miss-detection probability than the strongest coordinate-wise baseline. The advantage is most pronounced at high NF ratios, while in the all-FF case MM-PGD performs on par with the strongest coordinate-wise baseline.

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Xinjue Wang, Zhi-Yong Wang, Sergiy A. Vorobyov, Esa Ollila, Gayan Amarasuriya Aruma Baduge, Mojtaba Vaezi. 2026-09-09. Covariance-Aware MM-PGD for Mixed Near-/Far-Field Activity Detection. https://arxiv.org/abs/2609.10207

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