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.
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