In the context of massive machine-type communications (mMTC) within the Internet of Things (IoT), joint activity detection and channel estimation (JADCE) is a key challenge in enabling massive access due to sporadic device access patterns. In this work, we consider both single-antenna and multiple-antenna base station scenarios and formulate the JADCE problem using the least absolute shrinkage and selection operator (LASSO) framework. To address this problem, we propose a model-driven network that utilizes compressive sensing (CS) and deep learning techniques. Specifically, we first design a prediction-correction alternating direction method of multipliers (PC-ADMM) as the underlying algorithm of the model-driven network. Then, the network is developed based on the PC-ADMM and is designed to be complex-valued. Furthermore, we also model the proximal operator, typically used to generate sparse solutions in LASSO, as a channel attention module within the model-driven network to enhance robustness. Numerical results show that the proposed PC-ADMM framework outperforms existing LASSO-based methods in terms of channel estimation and device activity detection.

Grant-free random access is an effective solution to enable massive access for future Internet of Vehicles (IoV) scenarios based on massive machine-type communication (mMTC). Considering the uplink transmission of grant-free based vehicular networks, vehicular devices sporadically access the base station, the joint active device detection (ADD) and channel estimation (CE) problem can be addressed by compressive sensing (CS) recovery algorithms due to the sparsity of transmitted signals. However, traditional CS-based algorithms present high complexity and low recovery accuracy. In this manuscript, we propose a novel alternating direction method of multipliers (ADMM) algorithm with low complexity to solve this problem by minimizing the$\ell _{2,1}$norm. Furthermore, we design a deep unfolded network with learnable parameters based on the proposed ADMM, which can simultaneously improve convergence rate and recovery accuracy. The experimental results demonstrate that the proposed unfolded network performs better performance than other traditional algorithms in terms of ADD and CE.