  This paper investigates the transmission design in the
reconfigurable-intelligent-surface (RIS)-assisted downlink system. The channel
state information (CSI) is usually difficult to be estimated at the base
station (BS) when the RIS is not equipped with radio frequency chains. In this
paper, we propose a downlink transmission framework with unknown CSI via
Bayesian optimization. Since the CSI is not available at the BS, we treat the
unknown objective function as the black-box function and take the beamformer,
the phase shift, and the receiving filter as the input. Then the objective
function is decomposed as the sum of low-dimension subfunctions to reduce the
complexity. By re-expressing the power constraint of the BS in spherical
coordinates, the original constraint problem is converted into an equivalent
unconstrained problem. The users estimate the sum MSE of the training symbols
as the objective value and feed it back to the BS. We assume a Gaussian prior
of the feedback samples and the next query point is updated by minimizing the
constructed acquisition function. Furthermore, this framework can also be
applied to the power transfer system and fairness problems. Simulation results
validate the effectiveness of the proposed transmission scheme in the downlink
data transmission and power transfer.
