Optimal 3-D Deployment Range of RIS in mmWave Communications With Random Blockages

In reconfigurable intelligent surface (RIS)-assisted millimeter-wave (mmWave) communications, the line of sight (LoS) probabilities of the direct base station (BS)-user and reflective BS-RIS-user links are correlated because common obstacles may simultaneously block both links. To reduce the probability that the same obstacles block both links, the RIS should not be deployed close to the BS. However, increasing the BS-RIS distance significantly elevates the path loss along the reflective BS-RIS-user link, thereby degrading the system performance. To compromise the LoS probability and path loss of the reflective link when the direct link is blocked, the three-dimensional (3D) RIS placement problem in a single-cell mmWave system with randomly sized and distributed obstacles is investigated. We derived the integral expressions for the joint blockage probability of both links, the cell coverage probability, and the ergodic spectrum efficiency. With the derived expressions, the optimal RIS 3D deployment range can be obtained by numerical integration and exhaustive grid search. Numerical results validate the theoretical derivations and the fundamental trade-off between the LoS probability and the path loss.