  Grant-free random access has the potential to support massive connectivity in
Internet of Things (IoT) networks, where joint activity detection and channel
estimation (JADCE) is a key issue that needs to be tackled. The existing
methods for JADCE usually suffer from one of the following limitations: high
computational complexity, ineffective in inducing sparsity, and incapable of
handling complex matrix estimation. To mitigate all the aforementioned
limitations, we in this paper develop an effective unfolding neural network
framework built upon the proximal operator method to tackle the JADCE problem
in IoT networks, where the base station is equipped with multiple antennas.
Specifically, the JADCE problem is formulated as a group-sparse-matrix
estimation problem, which is regularized by non-convex minimax concave penalty
(MCP). This problem can be iteratively solved by using the proximal operator
method, based on which we develop a unfolding neural network structure by
parameterizing the algorithmic iterations. By further exploiting the coupling
structure among the training parameters as well as the analytical computation,
we develop two additional unfolding structures to reduce the training
complexity. We prove that the proposed algorithm achieves a linear convergence
rate. Results show that our proposed three unfolding structures not only
achieve a faster convergence rate but also obtain a higher estimation accuracy
than the baseline methods.
