Specific order and bisection search aided joint 3D beamforming and RIS reflecting optimization

In this paper, a three-node transmission model is conceived, where the base station (BS) node leverages 3D beamforming, the reconfigurable intelligent surface (RIS) node can constructively reconfigure the wireless channel, the user node only has a single antenna due to a limited price. Maximization of its downlink spectral efficiency is a joint optimization problem of three variables, namely phase-shift matrix Φ of RIS, tilt angle θ and beamforming vector w used in BS 3D beamforming. We solve this problem by employing the alternating optimization (AO) algorithm. But, in each iteration, a specific optimization order of firstly Φ, secondly θ and finally w is proposed, which facilitates the search of optimal θ in the way of narrowing its trust region and enabling unimodal property over the narrowed trust region. It finally results in a better combination of {Φ, θ, w}.