($k,\alpha$k,α)-Coverage for RIS-Aided mmWave Directional Communication

Reconfigurable intelligent surface (RIS) offers a new way to provide controllable non line-of-sight (NLoS) propagation paths for millimeter-wave (mmWave) directional communication to overcome the performance degradation caused by line-of-sight blockage. However, current coverage models do not consider the impact of path direction difference on path's availability, which is a crucial property of mmWave directional communication network. In the article, we propose a new coverage model called $(k,\alpha)$ -coverage. A receiver is $(k,\alpha)$ -covered if it is covered by at least $k$ RISs to have $k$ different NLoS path directions and the angular separation between any two adjacent path directions is at least $\alpha$ . In this case, when the current communication direction is blocked by an obstacle, other RIS created paths are still likely to be available for transmission, which increases the robustness of mmWave directional communication. To tackle the problem of using the least number of RISs to achieve the $(k,\alpha)$ -coverage, we formally define the $(k,\alpha)$ -coverage models and propose methods to verify if the target area is $(k,\alpha)$ -covered by the given set of RISs. Then, we solve the problem under both deterministic and random RIS deployment schemes. For the deterministic deployment scheme, we derive the optimal $k$ -sided regular polygon deployment patterns and use it to achieve area $(k,\alpha)$ -coverage. An analytical performance bound on the number of RISs needed is also derived. For the random RIS deployment scheme, we derive the $(k,\alpha)$ -coverage probability under uniform and spatial-Poisson RIS distributions. Finally, extensive simulation results are provided to validate our analyses.