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SCENE OTA-FD: Self-Centering Noncoherent Estimator for Over-the-Air Federated Distillation

Hao Chen, Zavareh Bozorgasl

TL;DR

SCENE targets short-coherence and hardware-constrained regimes, where avoiding per-round CSI is essential, and trades a modest noncoherent variance constant for zero uplink pilots, unbiased aggregation, and hardware-friendly transmission and can outperform coherent designs when pilot overhead is non-negligible.

Abstract

We propose SCENE (Self-Centering Noncoherent Estimator), a pilot-free and phase-invariant aggregation primitive for over-the-air federated distillation (OTA-FD). Each device maps its soft-label (class-probability) vector to nonnegative transmit energies under constant per-round power and constant-envelope signaling (PAPR near 1). At the server, a self-centering energy estimator removes the noise-energy offset and yields an unbiased estimate of the weighted soft-label average, with variance decaying on the order of 1/(SM) in the number of receive antennas M and repetition factor S. We also develop a pilot-free ratio-normalized variant that cancels unknown large-scale gains, provide a convergence bound consistent with coherent OTA-FD analyses, and present an overhead-based crossover comparison. SCENE targets short-coherence and hardware-constrained regimes, where avoiding per-round CSI is essential: it trades a modest noncoherent variance constant for zero uplink pilots, unbiased aggregation, and hardware-friendly transmission, and can outperform coherent designs when pilot overhead is non-negligible.

SCENE OTA-FD: Self-Centering Noncoherent Estimator for Over-the-Air Federated Distillation

TL;DR

SCENE targets short-coherence and hardware-constrained regimes, where avoiding per-round CSI is essential, and trades a modest noncoherent variance constant for zero uplink pilots, unbiased aggregation, and hardware-friendly transmission and can outperform coherent designs when pilot overhead is non-negligible.

Abstract

We propose SCENE (Self-Centering Noncoherent Estimator), a pilot-free and phase-invariant aggregation primitive for over-the-air federated distillation (OTA-FD). Each device maps its soft-label (class-probability) vector to nonnegative transmit energies under constant per-round power and constant-envelope signaling (PAPR near 1). At the server, a self-centering energy estimator removes the noise-energy offset and yields an unbiased estimate of the weighted soft-label average, with variance decaying on the order of 1/(SM) in the number of receive antennas M and repetition factor S. We also develop a pilot-free ratio-normalized variant that cancels unknown large-scale gains, provide a convergence bound consistent with coherent OTA-FD analyses, and present an overhead-based crossover comparison. SCENE targets short-coherence and hardware-constrained regimes, where avoiding per-round CSI is essential: it trades a modest noncoherent variance constant for zero uplink pilots, unbiased aggregation, and hardware-friendly transmission, and can outperform coherent designs when pilot overhead is non-negligible.
Paper Structure (30 sections, 3 theorems, 19 equations, 3 figures, 2 tables, 1 algorithm)

This paper contains 30 sections, 3 theorems, 19 equations, 3 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contributions.
  3. Related Work
  4. Soft-Label Federated Distillation
  5. Noncoherent OTA for AirFL (gradients) vs. SCENE for FD (soft labels)
  6. Notation and Assumptions
  7. Noncoherent Energy Aggregation and SCENE
  8. Measurement Model
  9. Received signal and noncoherent aggregation.
  10. Determining $\rho$ for SCENE
  11. Feasibility with a per-trial cap.
  12. Min-$\rho$ protocol (per round $t$)
  13. Why the minimum?
  14. SCENE: Self-CEntering Noncoherent Estimator
  15. Remark 1 (What "pilot-free" means).
  16. ...and 15 more sections

Key Result

Theorem 1

Assume: (A1) small-scale fading $h_{i,m,s}\sim \mathcal{CN}(0,\beta_i)$ i.i.d. across devices $i$, antennas $m=1,\dots,M$, and repetitions $s=1,\dots,S$; (A2) AWGN with per-RE noise-energy mean $\sigma_N^2$ and finite variance $v_N$; (A3) devices use $\eta_i=\rho\,\omega_i/\beta_i$ with $\sum_i \ome Moreover, with $E_{i,c}=\eta_i q_{i,c}$ and $V_{\rm sig}(c)\triangleq \sum_i \beta_i^2 E_{i,c}^2$,

Figures (3)

  • Figure 1: S versus server/global test accuracy (percent) at SNR = 5 dB.
  • Figure 2: S versus server/global test accuracy (percent) at SNR = 10 dB.
  • Figure 3: different combinations of (S,M)=(1,16),(16,1),(2,8),(8,2),(4,4) for 100 clients, one-shot, average of 20 trials at SNR = 5 dB.

Theorems & Definitions (5)

  • Theorem 1: Unbiasedness and variance
  • proof : Proof sketch
  • Proposition 1: Bias under large-scale mismatch
  • proof
  • Lemma 1: Bias-Induced Fixed-Point Shift