  Joint activity detection and channel estimation (JADCE) for grant-free random
access is a critical issue that needs to be addressed to support massive
connectivity in IoT networks. However, the existing model-free learning method
can only achieve either activity detection or channel estimation, but not both.
In this paper, we propose a novel model-free learning method based on
generative adversarial network (GAN) to tackle the JADCE problem. We adopt the
U-net architecture to build the generator rather than the standard GAN
architecture, where a pre-estimated value that contains the activity
information is adopted as input to the generator. By leveraging the properties
of the pseudoinverse, the generator is refined by using an affine projection
and a skip connection to ensure the output of the generator is consistent with
the measurement. Moreover, we build a two-layer fully-connected neural network
to design pilot matrix for reducing the impact of receiver noise. Simulation
results show that the proposed method outperforms the existing methods in high
SNR regimes, as both data consistency projection and pilot matrix optimization
improve the learning ability.
