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Coherence-Aware Over-the-Air Distributed Learning under Heterogeneous Link Impairments

Mehdi Karbalayghareh, David J. Love, Christopher G. Brinton

TL;DR

A coherence-aware federated learning (FL) framework that jointly addresses impairments on downlink and uplink with communication-efficient strategies and establishes convergence guarantees under heterogeneous link impairments, imperfect CSI, and aggregation noise is proposed.

Abstract

Distributed machine learning (ML) over wireless networks hinges on accurate channel state information (CSI) and efficient exchange of high-dimensional model updates. These demands are governed by channel coherence time and bandwidth, which vary across devices (links) due to heterogeneous mobility and scattering, causing degraded downlink delivery and distorted uplink over-the-air (OTA) aggregation. We propose a coherence-aware federated learning (FL) framework that jointly addresses impairments on downlink and uplink with communication-efficient strategies. In the downlink, we employ product superposition to multiplex global model symbols for long-coherence (static) devices onto the pilot tones required by short-coherence (dynamic) devices for channel estimation, turning pilot overhead into payload while preserving estimation fidelity. In the proposed scheme, an orthogonal frequency-division multiplexing (OFDM) super-block is partitioned into sub-blocks aligned with the smallest coherence time and bandwidth, enabling consistent channel estimation and stabilizing OTA aggregation across heterogeneous devices. Partial model reception at dynamic devices is mitigated via previous local model filling (PLMF), which reuses prior updates. We establish convergence guarantees under heterogeneous link impairments, imperfect CSI, and aggregation noise. The proposed framework enables efficient scheduling under coherence heterogeneity; analysis and experiments demonstrate notable gains in communication efficiency, latency, and learning accuracy over conventional FL baselines.

Coherence-Aware Over-the-Air Distributed Learning under Heterogeneous Link Impairments

TL;DR

A coherence-aware federated learning (FL) framework that jointly addresses impairments on downlink and uplink with communication-efficient strategies and establishes convergence guarantees under heterogeneous link impairments, imperfect CSI, and aggregation noise is proposed.

Abstract

Distributed machine learning (ML) over wireless networks hinges on accurate channel state information (CSI) and efficient exchange of high-dimensional model updates. These demands are governed by channel coherence time and bandwidth, which vary across devices (links) due to heterogeneous mobility and scattering, causing degraded downlink delivery and distorted uplink over-the-air (OTA) aggregation. We propose a coherence-aware federated learning (FL) framework that jointly addresses impairments on downlink and uplink with communication-efficient strategies. In the downlink, we employ product superposition to multiplex global model symbols for long-coherence (static) devices onto the pilot tones required by short-coherence (dynamic) devices for channel estimation, turning pilot overhead into payload while preserving estimation fidelity. In the proposed scheme, an orthogonal frequency-division multiplexing (OFDM) super-block is partitioned into sub-blocks aligned with the smallest coherence time and bandwidth, enabling consistent channel estimation and stabilizing OTA aggregation across heterogeneous devices. Partial model reception at dynamic devices is mitigated via previous local model filling (PLMF), which reuses prior updates. We establish convergence guarantees under heterogeneous link impairments, imperfect CSI, and aggregation noise. The proposed framework enables efficient scheduling under coherence heterogeneity; analysis and experiments demonstrate notable gains in communication efficiency, latency, and learning accuracy over conventional FL baselines.
Paper Structure (38 sections, 2 theorems, 89 equations, 5 figures)

This paper contains 38 sections, 2 theorems, 89 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contributions
  4. System Model
  5. Channel Model
  6. Pilot Assignment
  7. Baseline Transmission Scheme
  8. Coherence-Aware Device Scheduling and Communication Protocol
  9. Device Scheduling
  10. Downlink Signaling: Integrated Pilot--Parameter Broadcast
  11. Downlink Impact on the Local Model
  12. Deterministic coverage and received indices
  13. Per-entry distortion on received coordinates
  14. PLMF for missing parameters
  15. Limits for the Downlink
  16. ...and 23 more sections

Key Result

Theorem 1

Assume each local loss function $F_k$ is L-smooth and the global loss function $F$ is convex. Let $\boldsymbol{\theta}^*$ be a minimizer of $F$, and $F^* = F(\boldsymbol{\theta}^*)$. Under assumptions (A1)–(A4):

Figures (5)

  • Figure 1: (a) The OTA-FL scenario with heterogeneous devices. (b) Unequal coherence blocks (time--frequency frames) for dynamic devices; different colors denote distinct fading states within each block. Green squares denote the pilot placement within each coherence block to estimate the channel, where pilot--parameter superposition is employed.
  • Figure 2: Training loss versus communication rounds on the MNIST dataset for the proposed product superposition-based FL scheme.
  • Figure 3: Test accuracy versus normalized communication cost on the MNIST dataset for the proposed scheme and conventional baselines, under different pilot overhead values: (a) $\lambda = 0.2$, (b) $\lambda = 0.3$, and (c) $\lambda = 0.4$.
  • Figure 4: Test accuracy versus training overhead at fixed communication rounds $T = 20$ (MNIST dataset).
  • Figure 5: Test accuracy versus normalized communication cost on the CIFAR-10 dataset for the proposed scheme, and the conventional FL with ordinary pilots. Shaded regions indicate standard deviation.

Theorems & Definitions (15)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6
  • Remark 7
  • Remark 8
  • Remark 9
  • Remark 10
  • ...and 5 more