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Over-the-Air Computation via Broadband Channels

Tianrui Qin, Wanchun Liu, Branka Vucetic, Yonghui Li

TL;DR

This letter proposes an M -frequency AirComp system, where each sensor selects a subset of the M frequencies and broadcasts its signal over these channels under a certain power constraint, and develops an algorithm for joint design to achieve the best AirComp performance.

Abstract

Over-the-air computation (AirComp) has been recognized as a low-latency solution for wireless sensor data fusion, where multiple sensors send their measurement signals to a receiver simultaneously for computation. Most existing work only considered performing AirComp over a single frequency channel. However, for a sensor network with a massive number of nodes, a single frequency channel may not be sufficient to accommodate the large number of sensors, and the AirComp performance will be very limited. So it is highly desirable to have more frequency channels for large-scale AirComp systems to benefit from multi-channel diversity. In this letter, we propose an $M$-frequency AirComp system, where each sensor selects a subset of the $M$ frequencies and broadcasts its signal over these channels under a certain power constraint. We derive the optimal sensors' transmission and receiver's signal processing methods separately, and develop an algorithm for joint design to achieve the best AirComp performance. Numerical results show that increasing one frequency channel can improve the AirComp performance by threefold compared to the single-frequency case.

Over-the-Air Computation via Broadband Channels

TL;DR

This letter proposes an M -frequency AirComp system, where each sensor selects a subset of the M frequencies and broadcasts its signal over these channels under a certain power constraint, and develops an algorithm for joint design to achieve the best AirComp performance.

Abstract

Over-the-air computation (AirComp) has been recognized as a low-latency solution for wireless sensor data fusion, where multiple sensors send their measurement signals to a receiver simultaneously for computation. Most existing work only considered performing AirComp over a single frequency channel. However, for a sensor network with a massive number of nodes, a single frequency channel may not be sufficient to accommodate the large number of sensors, and the AirComp performance will be very limited. So it is highly desirable to have more frequency channels for large-scale AirComp systems to benefit from multi-channel diversity. In this letter, we propose an -frequency AirComp system, where each sensor selects a subset of the frequencies and broadcasts its signal over these channels under a certain power constraint. We derive the optimal sensors' transmission and receiver's signal processing methods separately, and develop an algorithm for joint design to achieve the best AirComp performance. Numerical results show that increasing one frequency channel can improve the AirComp performance by threefold compared to the single-frequency case.

Paper Structure

This paper contains 9 sections, 2 theorems, 30 equations, 4 figures.

Table of Contents

  1. Introduction
  2. AirComp System over Multiple Frequency Channels
  3. AirComp Optimization
  4. Optimal Design of the Rx Scaling Factor
  5. Optimal Design of the Tx-Scaling Factors
  6. Computational Complexity Reduction
  7. AirComp with Real or Complex Number Operations?
  8. Numerical Results
  9. Conclusions

Key Result

Proposition 1

Given the Tx scaling factors $\{\textbf{b}_{km}\}$, the optimized Rx scaling factor is where $\textbf{S}$ is defined in eq:S.

Figures (4)

  • Figure 1: A $K$-sensor-$M$-frequency AirComp system.
  • Figure 2: Performance comparison between the proposed algorithm and the optimal one with $M=1$.
  • Figure 3: $\mathsf{CMSE}$ versus $M$.
  • Figure 4: Channel coefficients and Tx scaling factors at different frequencies.

Theorems & Definitions (4)

  • Proposition 1
  • Proposition 2
  • Remark 1
  • Remark 2