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NCAirFL: CSI-Free Over-the-Air Federated Learning Based on Non-Coherent Detection

Haifeng Wen, Nicolò Michelusi, Osvaldo Simeone, Hong Xing

TL;DR

NCAirFL, a CSI-free AirFL scheme based on unbiased non-coherent detection at the edge server based on binary dithering and a longterm memory based error-compensation mechanism, achieves a convergence rate of order $\mathcal{O}(1 / \sqrt{T})$ in terms of the average square norm of the gradient for general non-convex and smooth objectives.

Abstract

Over-the-air federated learning (FL), i.e., AirFL, leverages computing primitively over multiple access channels. A long-standing challenge in AirFL is to achieve coherent signal alignment without relying on expensive channel estimation and feedback. This paper proposes NCAirFL, a CSI-free AirFL scheme based on unbiased non-coherent detection at the edge server. By exploiting binary dithering and a long-term memory based error-compensation mechanism, NCAirFL achieves a convergence rate of order $\mathcal{O}(1/\sqrt{T})$ in terms of the average square norm of the gradient for general non-convex and smooth objectives, where $T$ is the number of communication rounds. Experiments demonstrate the competitive performance of NCAirFL compared to vanilla FL with ideal communications and to coherent transmission-based benchmarks.

NCAirFL: CSI-Free Over-the-Air Federated Learning Based on Non-Coherent Detection

TL;DR

NCAirFL, a CSI-free AirFL scheme based on unbiased non-coherent detection at the edge server based on binary dithering and a longterm memory based error-compensation mechanism, achieves a convergence rate of order in terms of the average square norm of the gradient for general non-convex and smooth objectives.

Abstract

Over-the-air federated learning (FL), i.e., AirFL, leverages computing primitively over multiple access channels. A long-standing challenge in AirFL is to achieve coherent signal alignment without relying on expensive channel estimation and feedback. This paper proposes NCAirFL, a CSI-free AirFL scheme based on unbiased non-coherent detection at the edge server. By exploiting binary dithering and a long-term memory based error-compensation mechanism, NCAirFL achieves a convergence rate of order in terms of the average square norm of the gradient for general non-convex and smooth objectives, where is the number of communication rounds. Experiments demonstrate the competitive performance of NCAirFL compared to vanilla FL with ideal communications and to coherent transmission-based benchmarks.

Paper Structure

This paper contains 8 sections, 1 theorem, 32 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Learning Protocol (FedAvg)
  4. Communication Model
  5. Non-coherent AirFL (NCAirFL)
  6. Convergence analysis of NCAirFL
  7. Experiments
  8. Conclusions

Key Result

Lemma 3.1

For any $i\in [n]$ and $t=0,1,\ldots, T-1$, the following inequality holds for the NCAIrFL update eq:sparsified model different-eq:memory update rule where the expectation is taken over the randomness of the dither $\boldsymbol \phi^{(t)}$, and $\lambda=\min(p, 1-p)$. By minimizing the upper bound of eq:contraction on the probability $p$, the optimal choice of $p$ is easily seen to be $1/2$, which

Figures (2)

  • Figure 1: Test accuracy versus communication round index $T$ in the i.i.d. case.
  • Figure 2: Test accuracy versus communication round index $T$ in the non-i.i.d. case.

Theorems & Definitions (1)

  • Lemma 3.1: Contraction