  Millimeter-Wave Massive MIMO is important for beyond 5G or 6G wireless
communication networks. The goal of this paper is to establish successful
communication between the cellular base stations and devices, focusing on the
problem of joint user activity detection and channel estimation. Different from
traditional compressed sensing (CS) methods that only use the sparsity of user
activities, we develop several Approximate Message Passing (AMP) based CS
algorithms by exploiting the sparsity of user activities and mmWave channels.
First, a group soft-thresholding AMP is presented to utilize only the user
activity sparsity. Second, a hard-thresholding AMP is proposed based on the
on-grid CS approach. Third, a super-resolution AMP algorithm is proposed based
on atomic norm, in which a greedy method is proposed as a super-resolution
denoiser. And we smooth the denoiser based on Monte Carlo sampling to have
Lipschitz continuity and present state evolution results. Extensive simulation
results show that the proposed method outperforms the previous state-of-the-art
methods.
