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Stochastic Geometry Analysis for Distributed RISs-Assisted mmWave Communications

Yuan Xu, Li Wei, Chongwen Huang, Yongxu Zhu, Zhaohui Yang, Jun Yang, Jiguang He, Zhaoyang Zhang, Mérouane Debbah

TL;DR

This work addresses blockage-limited mmWave communications by analyzing distributed RIS deployments using stochastic geometry. It develops a PPP-based model for blockages, users, and RISs, and derives a two-path association framework (direct and RIS-reflected) along with the LoS probability, leading to closed-form expressions for the ergodic coverage probability and the sum rate. The authors show significant performance gains from distributed RISs, with substantial improvements in ergodic coverage and throughput, and provide deployment guidelines based on blockage density. The results offer practical insights for RIS placement and density to achieve target performance in future mmWave cellular networks.

Abstract

Millimeter wave (mmWave) has attracted considerable attention due to its wide bandwidth and high frequency. However, it is highly susceptible to blockages, resulting in significant degradation of the coverage and the sum rate. A promising approach is deploying distributed reconfigurable intelligent surfaces (RISs), which can establish extra communication links. In this paper, we investigate the impact of distributed RISs on the coverage probability and the sum rate in mmWave wireless communication systems. Specifically, we first introduce the system model, which includes the blockage, the RIS and the user distribution models, leveraging the Poisson point process. Then, we define the association criterion and derive the conditional coverage probabilities for the two cases of direct association and reflective association through RISs. Finally, we combine the two cases using Campbell's theorem and the total probability theorem to obtain the closed-form expressions for the ergodic coverage probability and the sum rate. Simulation results validate the effectiveness of the proposed analytical approach, demonstrating that the deployment of distributed RISs significantly improves the ergodic coverage probability by 45.4% and the sum rate by over 1.5 times.

Stochastic Geometry Analysis for Distributed RISs-Assisted mmWave Communications

TL;DR

This work addresses blockage-limited mmWave communications by analyzing distributed RIS deployments using stochastic geometry. It develops a PPP-based model for blockages, users, and RISs, and derives a two-path association framework (direct and RIS-reflected) along with the LoS probability, leading to closed-form expressions for the ergodic coverage probability and the sum rate. The authors show significant performance gains from distributed RISs, with substantial improvements in ergodic coverage and throughput, and provide deployment guidelines based on blockage density. The results offer practical insights for RIS placement and density to achieve target performance in future mmWave cellular networks.

Abstract

Millimeter wave (mmWave) has attracted considerable attention due to its wide bandwidth and high frequency. However, it is highly susceptible to blockages, resulting in significant degradation of the coverage and the sum rate. A promising approach is deploying distributed reconfigurable intelligent surfaces (RISs), which can establish extra communication links. In this paper, we investigate the impact of distributed RISs on the coverage probability and the sum rate in mmWave wireless communication systems. Specifically, we first introduce the system model, which includes the blockage, the RIS and the user distribution models, leveraging the Poisson point process. Then, we define the association criterion and derive the conditional coverage probabilities for the two cases of direct association and reflective association through RISs. Finally, we combine the two cases using Campbell's theorem and the total probability theorem to obtain the closed-form expressions for the ergodic coverage probability and the sum rate. Simulation results validate the effectiveness of the proposed analytical approach, demonstrating that the deployment of distributed RISs significantly improves the ergodic coverage probability by 45.4% and the sum rate by over 1.5 times.
Paper Structure (5 sections, 28 equations, 4 figures)

This paper contains 5 sections, 28 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Performance Analysis
  4. Simulation Results
  5. Conclusion

Figures (4)

  • Figure 1: Downlink distributed RISs-assisted mmWave communications.
  • Figure 2: The cell-wide integration of ${\lambda}^L_R$.
  • Figure 3: Effects of the density of RISs on the ergodic coverage probability of the cell.
  • Figure 4: Effects of the density of RISs on the sum rate for different blockage densities.

Theorems & Definitions (3)

  • Definition 1
  • Definition 2
  • Definition 3