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Federated Learning for Terahertz Wireless Communication

O. Tansel Baydas, Ozgur B. Akan

TL;DR

This work develops a multicarrier stochastic framework to analyze federated learning over wideband THz channels, explicitly linking local SGD updates to THz impairments such as beam squint, molecular absorption, jitter, and compression. It uncovers a harmonic-mean SNR bottleneck and a fundamental bandwidth limit that can degrade convergence, and it shows that SNR-weighted aggregation can recover convergence in high-squint regimes at the cost of a controlled bias. Theoretical results include a non-convex convergence bound and design inequalities that map physical-layer parameters to learning accuracy, complemented by experimental validation. The findings offer practical guidance for deploying THz-enabled FL, emphasizing channel estimation, equalization, and adaptive, distortion-aware aggregation to ensure reliable edge learning over challenging wideband links.

Abstract

The convergence of Terahertz (THz) communications and Federated Learning (FL) promises ultra-fast distributed learning, yet the impact of realistic wideband impairments on optimization dynamics remains theoretically uncharacterized. This paper bridges this gap by developing a multicarrier stochastic framework that explicitly couples local gradient updates with frequency-selective THz effects, including beam squint, molecular absorption, and jitter. Our analysis uncovers a critical diversity trap: under standard unbiased aggregation, the convergence error floor is driven by the harmonic mean of subcarrier SNRs. Consequently, a single spectral hole caused by severe beam squint can render the entire bandwidth useless for reliable model updates. We further identify a fundamental bandwidth limit, revealing that expanding the spectrum beyond a critical point degrades convergence due to the integration of thermal noise and gain collapse at band edges. Finally, we demonstrate that an SNR-weighted aggregation strategy is necessary to suppress the variance singularity at these spectral holes, effectively recovering convergence in high-squint regimes where standard averaging fails. Numerical results validate the expected impact of the discussed physical layer parameters' on performance of THz-FL systems.

Federated Learning for Terahertz Wireless Communication

TL;DR

This work develops a multicarrier stochastic framework to analyze federated learning over wideband THz channels, explicitly linking local SGD updates to THz impairments such as beam squint, molecular absorption, jitter, and compression. It uncovers a harmonic-mean SNR bottleneck and a fundamental bandwidth limit that can degrade convergence, and it shows that SNR-weighted aggregation can recover convergence in high-squint regimes at the cost of a controlled bias. Theoretical results include a non-convex convergence bound and design inequalities that map physical-layer parameters to learning accuracy, complemented by experimental validation. The findings offer practical guidance for deploying THz-enabled FL, emphasizing channel estimation, equalization, and adaptive, distortion-aware aggregation to ensure reliable edge learning over challenging wideband links.

Abstract

The convergence of Terahertz (THz) communications and Federated Learning (FL) promises ultra-fast distributed learning, yet the impact of realistic wideband impairments on optimization dynamics remains theoretically uncharacterized. This paper bridges this gap by developing a multicarrier stochastic framework that explicitly couples local gradient updates with frequency-selective THz effects, including beam squint, molecular absorption, and jitter. Our analysis uncovers a critical diversity trap: under standard unbiased aggregation, the convergence error floor is driven by the harmonic mean of subcarrier SNRs. Consequently, a single spectral hole caused by severe beam squint can render the entire bandwidth useless for reliable model updates. We further identify a fundamental bandwidth limit, revealing that expanding the spectrum beyond a critical point degrades convergence due to the integration of thermal noise and gain collapse at band edges. Finally, we demonstrate that an SNR-weighted aggregation strategy is necessary to suppress the variance singularity at these spectral holes, effectively recovering convergence in high-squint regimes where standard averaging fails. Numerical results validate the expected impact of the discussed physical layer parameters' on performance of THz-FL systems.

Paper Structure

This paper contains 36 sections, 4 theorems, 59 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Federated Learning Topology
  4. Probability Space and Filtration
  5. THz Channel Model and Communication Impairments
  6. Deterministic Path Loss and Molecular Absorption
  7. Stochastic Gain Variations: Jitter, Fading, and Squint
  8. Compression Noise, Additive Distortion, and Erasures
  9. Received Update Model
  10. Mean-Gain Estimation and Compensation
  11. Validity of the OFDM Model
  12. Statistical Abstraction of the Channel
  13. Error Decomposition and Statistical Structure
  14. Bias
  15. Frequency-Selective Second-order Error
  16. ...and 21 more sections

Key Result

Lemma 3.1

Let the estimator for subcarrier $n$ be $\widehat{\theta}_{i,t}^{(n)}=\frac{1}{M}\sum_{s=t-M+1}^{t} z_{i,s}^{(n)}$, where $z_{i,s}^{(n)}$ are unbiased instantaneous pilot statistics. Assume the pilot noise is conditionally sub-Gaussian with proxy variance $\nu_i^2$. Then for any $\epsilon>0$: In particular, $\widehat{\theta}_{i,t}^{(n)} \xrightarrow{p} \bar{d}_i\mu_{H,i}^{(n)}$ as $M\to\infty$.

Figures (4)

  • Figure 1: Topology and Challanges of FL in THz bands
  • Figure 2: Impact of transmit power on convergence. Low power leads to signal erasure.
  • Figure 3: (a) Performance degradation due to beam squint; high severity destroys the link. (b) Jitter stability test showing a cliff effect beyond. (c) Comparison of compensated vs. uncompensated reception, proving equalization is required for convergence.
  • Figure 4: (a) Client Distance on Convergence; the severe path loss and absorption at high distance degrade the SNR below the erasure threshold, preventing model training. (b) Bandwidth expansion; increasing bandwidth without power scaling raises the noise floor, degrading SNR. (c) Weighted Aggregation vs. FedAvg under severe channel stress.

Theorems & Definitions (7)

  • Lemma 3.1: Concentration of the gain estimator
  • Lemma 5.1: Explicit bound on the local update energy
  • Theorem 5.2: Non-convex convergence under Multicarrier THz impairments
  • Proposition 6.1: Multicarrier Stability Conditions
  • proof
  • proof
  • proof