  Massive access is a critical design challenge of Internet of Things (IoT)
networks. In this paper, we consider the grant-free uplink transmission of an
IoT network with a multiple-antenna base station (BS) and a large number of
single-antenna IoT devices. Taking into account the sporadic nature of IoT
devices, we formulate the joint activity detection and channel estimation
(JADCE) problem as a group-sparse matrix estimation problem. This problem can
be solved by applying the existing compressed sensing techniques, which however
either suffer from high computational complexities or lack of algorithm
robustness. To this end, we propose a novel algorithm unrolling framework based
on the deep neural network to simultaneously achieve low computational
complexity and high robustness for solving the JADCE problem. Specifically, we
map the original iterative shrinkage thresholding algorithm (ISTA) into an
unrolled recurrent neural network (RNN), thereby improving the convergence rate
and computational efficiency through end-to-end training. Moreover, the
proposed algorithm unrolling approach inherits the structure and domain
knowledge of the ISTA, thereby maintaining the algorithm robustness, which can
handle non-Gaussian preamble sequence matrix in massive access. With rigorous
theoretical analysis, we further simplify the unrolled network structure by
reducing the redundant training parameters. Furthermore, we prove that the
simplified unrolled deep neural network structures enjoy a linear convergence
rate. Extensive simulations based on various preamble signatures show that the
proposed unrolled networks outperform the existing methods in terms of the
convergence rate, robustness and estimation accuracy.
