Variational Inference-Based Channel Estimation for Reconfigurable Intelligent Surface-Aided Wireless Systems

We propose a variational inference-based channel estimation method in fully passive reconfigurable intelligent surface (RIS)-aided mmWave single-user single-input multiple-output (SIMO) communication systems. The main goal is to jointly estimate the user equipment (UE)-to-RIS (UE-RIS) and RIS-to-base station (RIS-BS) channels using uplink training signals in a passive RIS setup. Specifically, by using a variational inference framework, we approximate the posterior of the channels with convenient distributions given the received uplink training signals. The parameters of the approximated distributions are generated by deep neural networks trained using variational loss functions derived using a lower bound on the log-likelihood of the received signal. Then, the learned distributions, which are close to the true posterior distributions in terms of Kullback Leibler divergence, are leveraged to obtain the maximum a posteriori (MAP) estimation of the UE-RIS and RIS-BS channels. We evaluate the proposed channel estimation solution under two channel priors. The first channel prior models Rayleigh fading channels with Gaussian prior, whereas the second one represents sparse channels in the angular domain with Laplace prior. The simulation results demonstrate that MAP channel estimates using the approximated posteriors yield a capacity which is close to the one achieved with the true posteriors, thus demonstrating the effectiveness of the proposed method.