# Proximal Gradient-Based Unfolding for Massive Random Access in IoT Networks

arXiv: https://arxiv.org/abs/2212.01839 · HTML: https://mlsanity.com/paper/2212.01839/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2022.

## Built on by (most cited first, 1 of 1)

- [Mixture of Experts-augmented Deep Unfolding for Activity Detection in IRS-aided Systems](https://mlsanity.com/paper/2502.20183/) (2025)

## Abstract (arXiv)

Grant-free random access is an effective technology for enabling low-overhead and low-latency massive access, where joint activity detection and channel estimation (JADCE) is a critical issue. Although existing compressive sensing algorithms can be applied for JADCE, they usually fail to simultaneously harvest the following properties: effective sparsity inducing, fast convergence, robust to different pilot sequences, and adaptive to time-varying networks. To this end, we propose an unfolding framework for JADCE based on the proximal gradient method. Specifically, we formulate the JADCE problem as a group-row-sparse matrix recovery problem and leverage a minimax concave penalty rather than the widely-used ℓ1-norm to induce sparsity. We then develop a proximal gradient-based unfolding neural network that parameterizes the algorithmic iterations. To improve convergence rate, we incorporate momentum into the unfolding neural network, and prove the accelerated convergence theoretically. Based on the convergence analysis, we further develop an adaptive-tuning algorithm, which adjusts its parameters to different signal-to-noise ratio settings. Simulations show that the proposed unfolding neural network achieves better recovery performance, convergence rate, and adaptivity than current baselines.