The downlink channel estimation requires a huge pilot overhead in the reconfigurable intelligent surface (RIS) assisted communication system. By exploiting the powerful learning ability of the neural network, the machine learning (ML) technique can be used to estimate the high-dimensional channel from a few received pilot signals at the user. However, since the training dataset collected by the single user only contains the information of part of the channel scenarios of a cell, the neural network trained by the single user is not able to work when the user moves from one channel scenario to another. To solve this challenge, we propose to leverage the distributed machine learning (DML) technique to enable the reliable downlink channel estimation. Specifically, we firstly build a downlink channel estimation neural network shared by all users, which can be collaboratively trained by the BS and the users with the help of the DML technique. Then, we further propose a hierarchical neural network architecture to improve the channel estimation accuracy, which can extract different channel features for different channel scenarios. Simulation results show that compared with the neural network trained by the single user, the proposed DML based neural networks can achieve better estimation performance with the reduced pilot overhead for all users from different scenarios.

Millimeter-wave massive multiple-input multiple-output (MIMO) can use a lens antenna array to considerably reduce the number of radio frequency (RF) chains, but channel estimation is challenging due to the number of RF chains is much smaller than that of antennas. By exploiting the sparsity of beamspace channels, the beamspace channel estimation can be formulated as a sparse signal recovery problem, which can be solved by the classical iterative algorithm named approximate message passing (AMP), and its corresponding version learned AMP (LAMP) realized by a deep neural network (DNN). However, these existing schemes cannot achieve satisfactory estimation accuracy. To improve the channel estimation performance, we propose a prior-aided Gaussian mixture LAMP (GM-LAMP) based beamspace channel estimation scheme in this paper. Specifically, based on the prior information that beamspace channel elements can be modeled by the Gaussian mixture distribution, we first derive a new shrinkage function to refine the AMP algorithm. Then, by replacing the original shrinkage function in the LAMP network with the derived Gaussian mixture shrinkage function, a prior-aided GM-LAMP network is developed to estimate the beamspace channel more accurately. Simulation results by using both the theoretical channel model and the ray-tracing based channel dataset show that, the proposed GM-LAMP network can achieve better channel estimation accuracy than existing schemes.