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Distributed IRSs Always Benefit Every Mobile Operator

L. Yashvanth, Chandra R. Murthy

TL;DR

This paper examines how multiple distributed IRSs controlled by one mobile operator (MO X) affect the performance of a coexisting out-of-band MO (MO Y) in mmWave systems. Using round-robin scheduling and Jensen-based ergodic-rate analysis, it derives closed-form scaling laws showing MO X's ergodic SE grows as O(2 log2(N)) while MO Y's ergodic SE grows as O(tau log2(N)) with a tau that depends on the OOB path-to-element ratio. It also provides design guidelines to achieve maximum OOB SE almost surely, proves that OOB outage probability decays exponentially with the number of IRSs, and validates the theory with simulations. The findings indicate distributed IRSs benefit all operators, with the strongest gains accruing to the operator that controls the IRSs, while requiring no extra signal processing. Overall, the work highlights the broader, positive impact of distributed IRS deployment in multi-operator environments.

Abstract

We investigate the impact of multiple distributed intelligent reflecting surfaces (IRSs), which are deployed and optimized by a mobile operator (MO), on the performance of user equipments (UEs) served by other co-existing out-of-band (OOB) MOs that do not control the IRSs. We show that, under round-robin scheduling, in mmWave frequencies, the ergodic sum spectral efficiency (SE) of an OOB MO increases logarithmically in the total number of IRS elements with a pre-log factor that increases with the ratio of the number of OOB paths through the IRS to the number of elements at an IRS. We further show that the maximum achievable SE of the OOB MO scales log-linearly with the total IRS elements, with a pre-log factor of $1$. Then, we specify the minimum number of IRSs as a function of the channel parameters and design a distributed IRS system in which an OOB MO almost surely obtains the maximum SE. Finally, we prove that the outage probability at an OOB UE decreases exponentially as the number of IRSs increases, even though they are randomly configured from the OOB UE's viewpoint. We numerically verify our theory and conclude that distributed IRSs always help every MO, but the MO controlling the IRSs benefits the most.

Distributed IRSs Always Benefit Every Mobile Operator

TL;DR

This paper examines how multiple distributed IRSs controlled by one mobile operator (MO X) affect the performance of a coexisting out-of-band MO (MO Y) in mmWave systems. Using round-robin scheduling and Jensen-based ergodic-rate analysis, it derives closed-form scaling laws showing MO X's ergodic SE grows as O(2 log2(N)) while MO Y's ergodic SE grows as O(tau log2(N)) with a tau that depends on the OOB path-to-element ratio. It also provides design guidelines to achieve maximum OOB SE almost surely, proves that OOB outage probability decays exponentially with the number of IRSs, and validates the theory with simulations. The findings indicate distributed IRSs benefit all operators, with the strongest gains accruing to the operator that controls the IRSs, while requiring no extra signal processing. Overall, the work highlights the broader, positive impact of distributed IRS deployment in multi-operator environments.

Abstract

We investigate the impact of multiple distributed intelligent reflecting surfaces (IRSs), which are deployed and optimized by a mobile operator (MO), on the performance of user equipments (UEs) served by other co-existing out-of-band (OOB) MOs that do not control the IRSs. We show that, under round-robin scheduling, in mmWave frequencies, the ergodic sum spectral efficiency (SE) of an OOB MO increases logarithmically in the total number of IRS elements with a pre-log factor that increases with the ratio of the number of OOB paths through the IRS to the number of elements at an IRS. We further show that the maximum achievable SE of the OOB MO scales log-linearly with the total IRS elements, with a pre-log factor of . Then, we specify the minimum number of IRSs as a function of the channel parameters and design a distributed IRS system in which an OOB MO almost surely obtains the maximum SE. Finally, we prove that the outage probability at an OOB UE decreases exponentially as the number of IRSs increases, even though they are randomly configured from the OOB UE's viewpoint. We numerically verify our theory and conclude that distributed IRSs always help every MO, but the MO controlling the IRSs benefits the most.
Paper Structure (9 sections, 3 theorems, 22 equations, 3 figures)

This paper contains 9 sections, 3 theorems, 22 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System Model and Problem Statement
  3. Ergodic Sum Spectral Efficiency Analysis
  4. Ergodic sum-SE of MO-X
  5. Ergodic sum-SE of MO-Y
  6. Design for achieving $\mathcal{O}(\log_2(N))$ growth in the OOB SE
  7. Outage Probability Evaluation
  8. Numerical Results
  9. Conclusions

Key Result

Theorem 1

Consider a distributed IRS-aided mmWave system consisting of $S$ non-colocated IRSs, each with $M$ elements. Then, if the IRSs are optimized (as per eq:opt_IB_mmwave_airtel_multiple_IRS) to serve the UEs of MO X in every time slot, the ergodic sum-SEs of MOs X and Y, $\bar{S}_M^{(X)}$ and $\bar{S}_M

Figures (3)

  • Figure 1: Network scenario of a distributed IRS-aided two-operator system.
  • Figure 2: Schematic of system setup and OOB Performance due to randomly configured distributed IRSs in mmWave frequency bands.
  • Figure 3: Pre-log factor of OOB SE, $\tau$ vs. $S$ as a function of $\delta$ (or $L$).

Theorems & Definitions (6)

  • Theorem 1
  • proof
  • Proposition 1
  • proof
  • Theorem 2
  • proof