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Intelligent Reflecting Surface Aided AirComp: Multi-Timescale Design and Performance Analysis

Guangji Chen, Jun Li, Qingqing Wu, Meng Hua, Kaitao Meng, Zhonghao Lyu

TL;DR

The paper addresses high signaling overhead in IRS-aided AirComp by introducing a multi-timescale protocol that fixes receive beamforming offline using AoA information and optimizes IRS phase shifts from long-term statistics, while adapting transmit powers in each coherence block using a reduced effective I-CSI. This yields a low CSI burden ($\mathcal{O}(K)$) and closed-form, low-complexity solutions for power control, facilitated by a two-step design with discrete phase shifts and majority voting. Theoretical analysis demonstrates an MSE scaling of $\mathcal{O}\left(\dfrac{K}{N^2 M}\right)$ in the large-system limit and proves that channel-inversion power control is asymptotically optimal as $N$ grows, implying energy-efficient operation for devices. Numerical results validate the gains from discrete IRS phase shifts and the proposed protocol, revealing a double benefit: improved computation accuracy and reduced device power consumption in large-scale IRS-aided AirComp systems.

Abstract

The integration of intelligent reflecting surface (IRS) into over-the-air computation (AirComp) is an effective solution for reducing the computational mean squared error (MSE) via its high passive beamforming gain. Prior works on IRS aided AirComp generally rely on the full instantaneous channel state information (I-CSI), which is not applicable to large-scale systems due to its heavy signalling overhead. To address this issue, we propose a novel multi-timescale transmission protocol. In particular, the receive beamforming at the access point (AP) is pre-determined based on the static angle information and the IRS phase-shifts are optimized relying on the long-term statistical CSI. With the obtained AP receive beamforming and IRS phase-shifts, the effective low-dimensional I-CSI is exploited to determine devices' transmit power in each coherence block, thus substantially reducing the signalling overhead. Theoretical analysis unveils that the achievable MSE scales on the order of ${\cal O}\left( {K/\left( {{N^2}M} \right)} \right)$, where $M$, $N$, and $K$ are the number of AP antennas, IRS elements, and devices, respectively. We also prove that the channel-inversion power control is asymptotically optimal for large $N$, which reveals that the full power transmission policy is not needed for lowering the power consumption of energy-limited devices.

Intelligent Reflecting Surface Aided AirComp: Multi-Timescale Design and Performance Analysis

TL;DR

The paper addresses high signaling overhead in IRS-aided AirComp by introducing a multi-timescale protocol that fixes receive beamforming offline using AoA information and optimizes IRS phase shifts from long-term statistics, while adapting transmit powers in each coherence block using a reduced effective I-CSI. This yields a low CSI burden () and closed-form, low-complexity solutions for power control, facilitated by a two-step design with discrete phase shifts and majority voting. Theoretical analysis demonstrates an MSE scaling of in the large-system limit and proves that channel-inversion power control is asymptotically optimal as grows, implying energy-efficient operation for devices. Numerical results validate the gains from discrete IRS phase shifts and the proposed protocol, revealing a double benefit: improved computation accuracy and reduced device power consumption in large-scale IRS-aided AirComp systems.

Abstract

The integration of intelligent reflecting surface (IRS) into over-the-air computation (AirComp) is an effective solution for reducing the computational mean squared error (MSE) via its high passive beamforming gain. Prior works on IRS aided AirComp generally rely on the full instantaneous channel state information (I-CSI), which is not applicable to large-scale systems due to its heavy signalling overhead. To address this issue, we propose a novel multi-timescale transmission protocol. In particular, the receive beamforming at the access point (AP) is pre-determined based on the static angle information and the IRS phase-shifts are optimized relying on the long-term statistical CSI. With the obtained AP receive beamforming and IRS phase-shifts, the effective low-dimensional I-CSI is exploited to determine devices' transmit power in each coherence block, thus substantially reducing the signalling overhead. Theoretical analysis unveils that the achievable MSE scales on the order of , where , , and are the number of AP antennas, IRS elements, and devices, respectively. We also prove that the channel-inversion power control is asymptotically optimal for large , which reveals that the full power transmission policy is not needed for lowering the power consumption of energy-limited devices.
Paper Structure (11 sections, 4 theorems, 32 equations, 4 figures)

This paper contains 11 sections, 4 theorems, 32 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System model and Protocol Design
  3. System Model
  4. Protocol Design
  5. Optimization of ${\bf{\Theta }}$
  6. Optimization of $\left\{ {{b_k},\eta } \right\}$
  7. Theoretical Analysis
  8. Scaling Law Analysis
  9. Is Full Power Transmission Needed?
  10. Numerical results
  11. Conclusion

Key Result

Proposition 1

When ${{\bf{h}}_{d,k}} = {\bf{0}}$, the optimal ${\bf{v}}$ to minimize the MSE is given by

Figures (4)

  • Figure 1: Multi-timescale protocol for IRS aided AirComp.
  • Figure 2: Evaluation of MSE scaling law.
  • Figure 3: MSE versus $N$ with $K = 20$.
  • Figure 4: Critical number versus $N$ with $K = 20$.

Theorems & Definitions (8)

  • Proposition 1
  • proof 1
  • Proposition 2
  • Remark 1
  • Theorem 1
  • proof 2
  • Theorem 2
  • proof 3