Optimal Elevation and Azimuth Rotation for RIS-Assisted Wireless Transmission

In this letter, we propose to optimize the rotation of reconfigurable intelligent surface (RIS) in both elevation and azimuth dimensions for further improving the RIS-assisted wireless transmission performance. Considering a mobile multi-user scenario, we first derive the upper bound of the ergodic sum-rate and the normalized radiation intensity of RIS after rotation in both elevation and azimuth dimensions. On this basis, we formulate the optimization problem with respect to the two rotation angles for the sake of maximizing the cascaded path gain, and derive the optimal solutions in closed form. Furthermore, we extend the optimal two-dimensional rotation (2DR) scheme to the scenario where multi-hop RISs assist wireless communication. Our simulation results verify the correctness of our derivation and show that our proposed 2DR scheme leads to a significantly higher ergodic sum-rate as compared to the single-elevation rotation (SER) scheme and no rotation (NR) scheme.