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Resource Allocation for Channel Estimation in Reconfigurable Intelligent Surface-Aided Multi-Cell Networks

Yining Xu, Sheng Zhou

TL;DR

The paper addresses CSI overhead and RIS-reflected interference in RIS-aided multi-cell networks by developing a stochastic-geometry framework to derive coverage probability, ASE, and EE.A general resource-allocation model for channel estimation is proposed, yielding analytical expressions for performance metrics and proving that coverage improves with the unit training overhead beta while identifying conditions for ASE/EE-optimal beta.The work provides detailed distance distributions and association probabilities, and reveals deployment guidelines showing that RIS density should scale with blockage density and balance against base-station density to optimize throughput and energy efficiency.These results offer practical insights into balancing CSI accuracy, reflection-induced interference, and RIS deployment to enhance coverage, rate, and energy efficiency in dense, blockage-prone networks.

Abstract

Reconfigurable intelligent surface (RIS) is a promising solution to deal with the blockage-sensitivity of millimeter wave band and reduce the high energy consumption caused by network densification. However, deploying large scale RISs may not bring expected performance gain due to significant channel estimation overhead and non-negligible reflected interference. In this paper, we derive the analytical expressions of the coverage probability, area spectrum efficiency (ASE) and energy efficiency (EE) of a downlink RIS-aided multi-cell network. In order to optimize the network performance, we investigate the conditions for the optimal number of training symbols of each antenna-to-antenna and antenna-to-element path (referred to as the optimal unit training overhead) in channel estimation. Our study shows that: 1) RIS deployment is not `the more, the better', only when blockage objects are dense should one deploy more RISs; 2) the coverage probability is maximized when the unit training overhead is designed as large as possible; 3) however, the ASE-and-EE-optimal unit training overhead exists. It is a monotonically increasing function of the frame length and a monotonically decreasing function of the average signal-to-noise-ratio (in the high signal-to-noise-ratio region). Additionally, the optimal unit training overhead is smaller when communication ends deploy particularly few or many antennas.

Resource Allocation for Channel Estimation in Reconfigurable Intelligent Surface-Aided Multi-Cell Networks

TL;DR

The paper addresses CSI overhead and RIS-reflected interference in RIS-aided multi-cell networks by developing a stochastic-geometry framework to derive coverage probability, ASE, and EE.A general resource-allocation model for channel estimation is proposed, yielding analytical expressions for performance metrics and proving that coverage improves with the unit training overhead beta while identifying conditions for ASE/EE-optimal beta.The work provides detailed distance distributions and association probabilities, and reveals deployment guidelines showing that RIS density should scale with blockage density and balance against base-station density to optimize throughput and energy efficiency.These results offer practical insights into balancing CSI accuracy, reflection-induced interference, and RIS deployment to enhance coverage, rate, and energy efficiency in dense, blockage-prone networks.

Abstract

Reconfigurable intelligent surface (RIS) is a promising solution to deal with the blockage-sensitivity of millimeter wave band and reduce the high energy consumption caused by network densification. However, deploying large scale RISs may not bring expected performance gain due to significant channel estimation overhead and non-negligible reflected interference. In this paper, we derive the analytical expressions of the coverage probability, area spectrum efficiency (ASE) and energy efficiency (EE) of a downlink RIS-aided multi-cell network. In order to optimize the network performance, we investigate the conditions for the optimal number of training symbols of each antenna-to-antenna and antenna-to-element path (referred to as the optimal unit training overhead) in channel estimation. Our study shows that: 1) RIS deployment is not `the more, the better', only when blockage objects are dense should one deploy more RISs; 2) the coverage probability is maximized when the unit training overhead is designed as large as possible; 3) however, the ASE-and-EE-optimal unit training overhead exists. It is a monotonically increasing function of the frame length and a monotonically decreasing function of the average signal-to-noise-ratio (in the high signal-to-noise-ratio region). Additionally, the optimal unit training overhead is smaller when communication ends deploy particularly few or many antennas.
Paper Structure (26 sections, 3 theorems, 44 equations, 11 figures, 1 table)

This paper contains 26 sections, 3 theorems, 44 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related works
  3. Contributions
  4. Organization
  5. System Model
  6. Network Deployment
  7. Channel Model: Blockage, Path Loss and Small-Scale Fading
  8. Feasibility of Reflection
  9. Beamforming Pattern
  10. User Association
  11. Frame Structure and Resource Allocation
  12. Performance Metrics
  13. Main Results
  14. Link Distance Distribution
  15. The Distribution of the Shortest LoS Direct Link Distance
  16. ...and 11 more sections

Key Result

Theorem 1

The coverage probability of the downlink RIS-aided multi-cell network with directional transmissions is where the functions $\mathcal{L}_{I_\emph{D}}^\emph{d}(\cdot)$, $\mathcal{L}_{I_\emph{R}}^\emph{d}(\cdot)$, $\mathcal{L}_{I_\emph{D}}^\emph{r}(\cdot)$ and $\mathcal{L}_{I_\emph{R}}^\emph{r}(\cdot)$ are given by where the regions $\mathcal{C}_2$ and $\mathcal{C}_3$ consist of two sub-regions $\

Figures (11)

  • Figure 1: An illustration of network deployment, communication links and stochastic geometry models.
  • Figure 2: An illustration of feasible reflection.
  • Figure 3: An illustration of beamforming patterns and beam alignment. In (a) and (b), the beam alignment error is no larger than half beamwidth, therefore the BS and the UE are aligned through a direct link and a reflected link, respectively. In (c) and (d), the beam alignment error exceeds half beamwidth, then the BS and the UE are misaligned in both the direct link and the reflected link, respectively.
  • Figure 4: Frame structure with channel estimation phase and data transmission phase.
  • Figure 5: Coverage probability, ASE and EE scaling with the unit training overhead $\beta$ under different number of BS antennas $M_\text{B}$.
  • ...and 6 more figures

Theorems & Definitions (6)

  • Theorem 1
  • proof
  • Corollary 1
  • proof
  • Corollary 2
  • proof