On the Impact of an IRS on the Out-of-Band Performance in Sub-6 GHz & mmWave Frequencies

TL;DR

This work analyzes how an intelligent reflecting surface (IRS) deployed and controlled by one operator affects out-of-band (OOB) performance for another operator operating in a non-overlapping band, across sub-6 GHz and mmWave. It derives ergodic sum spectral efficiencies and outage/CCDF results under round-robin scheduling, showing that the IRS unexpectedly provides instantaneous and average benefits to the OOB operator as the number of IRS elements $N$ increases, due to additional reflection paths and diversity. The study covers sub-6 GHz rich-scattering channels and mmWave directional channels (LoS and (L+)NLoS), establishing that the OOB gains scale as $N$ (or $N^2$ for the in-band user) under various scenarios, with stochastic dominance results confirming non-degradation. Furthermore, the paper proposes opportunistic scheduling (PF and MR) to exploit multi-user diversity, demonstrating substantial extra gains for OOB UEs without IRS coordination. These insights imply that IRS deployment can be beneficial for all operators in a shared environment, while also highlighting practical trade-offs and avenues for future work in more complex, multi-antenna and interference-limited settings.

Abstract

Intelligent reflecting surfaces (IRSs) were introduced to enhance the performance of wireless communication systems. However, from a service provider's viewpoint, a concern with the use of an IRS is its effect on out-of-band (OOB) quality of service. Specifically, if two operators, say X and Y, provide services in a given geographical area using non-overlapping frequency bands, and if operator X uses an IRS to enhance the spectral efficiency (SE) of its users (UEs), does it degrade the performance of UEs served by operator Y? We answer this by analyzing the average and instantaneous performances of the OOB operator considering both sub-6 GHz and mmWave bands. Specifically, we derive the ergodic sum SE achieved by the operators under round-robin scheduling. We also derive the outage probability and analyze the change in the SNR caused by the IRS at an OOB UE using stochastic dominance theory. Surprisingly, even though the IRS is randomly configured from operator Y's point of view, the OOB operator still benefits from the presence of the IRS, witnessing a performance enhancement for free in both sub-6 GHz and mmWave bands. This is because the IRS introduces additional paths between the transmitter and receiver, increasing the overall signal power arriving at the UE and providing diversity benefits. Finally, we show that the use of opportunistic scheduling schemes can further enhance the benefit of the uncontrolled IRS at OOB UEs. We numerically illustrate our findings and conclude that an IRS is always beneficial to every operator, even when the IRS is deployed & controlled by only one operator.

Figures (15)

• Figure 1: Network scenario of an IRS-aided two-operator system.
• Figure 2: Flowchart of the round-robin scheduling based protocol.
• Figure 3: Correlation response of the IRS vector and array steering vectors pointing at different spatial angles, $\nu$, for (a) $N=50$ and (b) $N=500$. When $\nu=\omega^1_{X,k}$, the response attains its maximum value of $1$.
• Figure 4: Normalized Correlation response of the IRS (in (L+)NLoS scenarios) and array vectors at different $\nu$ for $N=500$ with (a) $L=2$, and (b) $L=3$. When $\nu \in \mathcal{L}_2\text{ (or) }\mathcal{L}_3$, the response, $\rho_{\nu,\theta}/N$ peaks and $\approx 1/\sqrt{L}$.
• Figure 5: Ergodic sum-SE vs. transmit SNR.

Theorems & Definitions (19)

• Remark 1
• Theorem 1
• proof
• Theorem 2
• proof
• Proposition 1
• Remark 2
• Theorem 3
• proof
• Remark 3: OOB performance as a function of $L$ for large $N$