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Coordinating Multiple Intelligent Reflecting Surfaces without Channel Information

Fan Xu, Jiawei Yao, Wenhai Lai, Kaiming Shen, Xin Li, Xin Chen, Zhi-Quan Luo

TL;DR

This work tackles the CSI burden in coordinating multiple intelligent reflecting surfaces (IRSs) by proposing blind beamforming, a statistics-driven approach that optimizes phase shifts without channel state information. By extending the conditional-sample-mean (CSM) method to sequential configurations across 2 and then general $L$ IRSs, the authors derive provable SNR boost guarantees of $\Theta(N^{2L})$ under relaxed conditions and provide sampling budgets for practical implementation. The method is validated through real-field tests at 2.6 GHz, achieving up to 17 dB SNR improvement, and extensive simulations demonstrate scalability to larger IRS sizes and numbers while comparing favorably to CSI-based benchmarks. Overall, the paper offers a CSI-free, scalable framework for multi-IRS coordination with concrete performance guarantees and actionable deployment insights.

Abstract

Conventional beamforming methods for intelligent reflecting surfaces (IRSs) or reconfigurable intelligent surfaces (RISs) typically entail the full channel state information (CSI). However, the computational cost of channel acquisition soars exponentially with the number of IRSs. To bypass this difficulty, we propose a novel strategy called blind beamforming that coordinates multiple IRSs by means of statistics without knowing CSI. Blind beamforming only requires measuring the received signal power at the user terminal for a sequence of randomly generated phase shifts across all IRSs. The main idea is to extract the key statistical quantity for beamforming by exploring only a small portion of the whole solution space of phase shifts. We show that blind beamforming guarantees a signal-to-noise ratio (SNR) boost of Theta(N^{2L}) under certain conditions, where L is the number of IRSs and N is the number of reflecting elements per IRS. The proposed conditions for achieving the optimal SNR boost of Theta(N^{4}) in a double-IRS system are much easier to satisfy than the existing ones in the literature. Most importantly, the proposed conditions can be extended to a fully general L-IRS system. The above result significantly improves upon the state of the art in the area of multi-IRS-assisted communication. Moreover, blind beamforming is justified via field tests and simulations. In particular, as shown in our field tests at 2.6 GHz, our method yields up to 17 dB SNR boost; to the best of our knowledge, this is the first time that the use of multiple IRSs gets verified in the real world.

Coordinating Multiple Intelligent Reflecting Surfaces without Channel Information

TL;DR

This work tackles the CSI burden in coordinating multiple intelligent reflecting surfaces (IRSs) by proposing blind beamforming, a statistics-driven approach that optimizes phase shifts without channel state information. By extending the conditional-sample-mean (CSM) method to sequential configurations across 2 and then general IRSs, the authors derive provable SNR boost guarantees of under relaxed conditions and provide sampling budgets for practical implementation. The method is validated through real-field tests at 2.6 GHz, achieving up to 17 dB SNR improvement, and extensive simulations demonstrate scalability to larger IRS sizes and numbers while comparing favorably to CSI-based benchmarks. Overall, the paper offers a CSI-free, scalable framework for multi-IRS coordination with concrete performance guarantees and actionable deployment insights.

Abstract

Conventional beamforming methods for intelligent reflecting surfaces (IRSs) or reconfigurable intelligent surfaces (RISs) typically entail the full channel state information (CSI). However, the computational cost of channel acquisition soars exponentially with the number of IRSs. To bypass this difficulty, we propose a novel strategy called blind beamforming that coordinates multiple IRSs by means of statistics without knowing CSI. Blind beamforming only requires measuring the received signal power at the user terminal for a sequence of randomly generated phase shifts across all IRSs. The main idea is to extract the key statistical quantity for beamforming by exploring only a small portion of the whole solution space of phase shifts. We show that blind beamforming guarantees a signal-to-noise ratio (SNR) boost of Theta(N^{2L}) under certain conditions, where L is the number of IRSs and N is the number of reflecting elements per IRS. The proposed conditions for achieving the optimal SNR boost of Theta(N^{4}) in a double-IRS system are much easier to satisfy than the existing ones in the literature. Most importantly, the proposed conditions can be extended to a fully general L-IRS system. The above result significantly improves upon the state of the art in the area of multi-IRS-assisted communication. Moreover, blind beamforming is justified via field tests and simulations. In particular, as shown in our field tests at 2.6 GHz, our method yields up to 17 dB SNR boost; to the best of our knowledge, this is the first time that the use of multiple IRSs gets verified in the real world.
Paper Structure (13 sections, 4 theorems, 58 equations, 15 figures, 2 tables, 2 algorithms)

This paper contains 13 sections, 4 theorems, 58 equations, 15 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Double-IRS Case
  4. Blind Beamforming for a Single IRS
  5. Blind Beamforming for Two IRSs
  6. Comments on Theorem \ref{['coro boost 2']}
  7. General $L$-IRS Case
  8. Experiments
  9. Field Tests
  10. Simulation Tests
  11. Double-IRS System
  12. General $L$-IRS System
  13. Conclusion

Key Result

Proposition 1

The CSM method is equivalent to the CPP method in CPP and yields a quadratic SNR boost in the number of REs in expectation, i.e., so long as $K\ge3$ and $T=\Omega(N^2(\log N)^3)$, where the expectation is taken over random samples of $(\theta_1,\ldots,\theta_N)$.

Figures (15)

  • Figure 1: A double-IRS system with $L=2$, where $h_{0,0}$ is the direct channel, $\{h_{n_1,0},h_{0,n_2}\}$ are the one-hop reflected channels, and $\{h_{n_1,n_2}\}$ are the two-hop reflected channels.
  • Figure 2: Illustration of the second step in \ref{['eqn 2 gamma']}. Let $\bm a=h_{n_1,0}$ and $\bm b=\sum_{n_2=1}^N h_{n_1,n_2}$. According to \ref{['gamma']}, $\bm a$ must lie on a circle with its radius smaller than $(\sin\gamma)\cdot|\bm b|$, so the angle between $\bm b$ and $\bm a+\bm b$ is no greater than $\gamma$ as can be seen from the geometry.
  • Figure 3: Two different paradigms of blind beamforming.
  • Figure 4: Field test with two IRSs deployed in an indoor hallway.
  • Figure 5: Layout drawing of the indoor field test. The two IRSs are placed in two corners for most methods, but are merged into a single larger IRS placed in the middle for "Physical Single-IRS" as indicated by the dashed lines.
  • ...and 10 more figures

Theorems & Definitions (12)

  • Proposition 1: Theorem 2 in blind_beamforming_twc
  • Remark 1
  • Remark 2
  • Theorem 1
  • Example 1: Why is condition C1 needed?
  • Example 2: Why is condition C2 needed?
  • Example 3: Why is condition C3 needed?
  • Theorem 2
  • Lemma 1
  • Remark 3: Same Phase-Shift Resolution
  • ...and 2 more