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On Signal Peak Power Constraint of Over-the-Air Federated Learning

Lorenz Bielefeld, Paul Zheng, Oner Hanay, Yao Zhu, Yulin Hu, Anke Schmeink

Abstract

Federated learning (FL) has been considered a promising privacy preserving distributed edge learning framework. Over-the-air computation (AirComp) leveraging analog transmission enables the aggregation of local updates directly over-the-air by exploiting the superposition properties of wireless multiple-access channels, thereby alleviating the communication bottleneck issues of FL compared with digital transmission schemes. This work points out that existing AirComp-FL overlooks a key practical constraint, the instantaneous peak-power constraints due to the non-linearity of radio-frequency power amplifiers. Operating directly in non-linear region causes in-band and out-of-band distortions. We present and analyze the effect of the default method that limits the signal's peak power and out-of-band distortions, iterative amplitude clipping combined with filtering. We investigate the effect of imposing instantaneous peak-power constraints in AirComp-FL for both single-carrier and multi-carrier orthogonal frequency-division multiplexing (OFDM) systems. Simulation results demonstrate that, in practical settings, the instantaneous transmit power in AirComp-FL regularly exceeds the power-amplifier linearity limit. As the first work of this line of research, it is essential to evaluate if this is an actual problem that has an impact on FL performance. We therefore apply the classic method of iterative clipping and filtering, and show that the FL performance degrades more or less depending on the scenarios. The degradation becomes pronounced especially in multi-carrier OFDM systems due to the in-band distortions caused by clipping and filtering.

On Signal Peak Power Constraint of Over-the-Air Federated Learning

Abstract

Federated learning (FL) has been considered a promising privacy preserving distributed edge learning framework. Over-the-air computation (AirComp) leveraging analog transmission enables the aggregation of local updates directly over-the-air by exploiting the superposition properties of wireless multiple-access channels, thereby alleviating the communication bottleneck issues of FL compared with digital transmission schemes. This work points out that existing AirComp-FL overlooks a key practical constraint, the instantaneous peak-power constraints due to the non-linearity of radio-frequency power amplifiers. Operating directly in non-linear region causes in-band and out-of-band distortions. We present and analyze the effect of the default method that limits the signal's peak power and out-of-band distortions, iterative amplitude clipping combined with filtering. We investigate the effect of imposing instantaneous peak-power constraints in AirComp-FL for both single-carrier and multi-carrier orthogonal frequency-division multiplexing (OFDM) systems. Simulation results demonstrate that, in practical settings, the instantaneous transmit power in AirComp-FL regularly exceeds the power-amplifier linearity limit. As the first work of this line of research, it is essential to evaluate if this is an actual problem that has an impact on FL performance. We therefore apply the classic method of iterative clipping and filtering, and show that the FL performance degrades more or less depending on the scenarios. The degradation becomes pronounced especially in multi-carrier OFDM systems due to the in-band distortions caused by clipping and filtering.
Paper Structure (24 sections, 1 theorem, 21 equations, 6 figures)

This paper contains 24 sections, 1 theorem, 21 equations, 6 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Federated Learning
  4. Single-Carrier OTA
  5. Transmission of gradient
  6. Power Control
  7. Multi-Carrier OFDM-based OTA
  8. Transmission of gradient
  9. Power Allocation
  10. Instantaneous peak power constraint
  11. Peak-to-Average Power Ratio
  12. Single-carrier transmission
  13. Multi-carrier OFDM transmission
  14. Clipping with Oversampling
  15. Single-carrier
  16. ...and 9 more sections

Key Result

Proposition 1

Assuming $h_1\geq h_2\geq \ldots \geq h_K$. There exists $k^*\in\mathcal{K}$ such that the optimal solution $(\alpha^*, (p_k^*)_{k\in\mathcal{K}})$ to the problem pb: single-carrier satisfies that the corresponding denoising factor is given by and the optimal average transmit power is given by $\blacktriangleleft$$\blacktriangleleft$

Figures (6)

  • Figure 1: Typical input and output power characteristics curve for a power amplifier.
  • Figure 2: Flow Diagram for ICF in multi-carrier OFDM systems.
  • Figure 3: Peak-to-average power ratio (PAPR) w.r.t. CR.
  • Figure 4: Error of the approximated average gradient w.r.t. the actual average gradient. TSE denotes the True Square Error; Estimated MSE is given by \ref{['eq:MSE_TDMA']} and \ref{['eq: MSE_OFDM']}.
  • Figure 5: Test Accuracy w.r.t. CR.
  • ...and 1 more figures

Theorems & Definitions (1)

  • Proposition 1: Cao_2020_OptimizedPowerControlOTAFadingChannelsZhang_Tao_2021_GradientStatPowerContFLOTA