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.
Over-the-air (OTA) learning aggregates distributed statistics in the air. In federated distillation (FD), exchanging soft labels instead of model parameters slashes communication costs. Most OTA-FD designs are coherent, requiring per-round CSI and phase alignment with nontrivial pilot/feedback overhead and sensitivity to CFO/phase noise. This represents one point in a broader design space. We analyze the opposite point: a fully noncoherent approach that discards instantaneous CSI altogether. The geometry of soft labels makes noncoherent energy aggregation a natural fit: energies are nonnegative and additive; the target lies on the probability simplex. Our thesis is not that noncoherent is universally superior, but that under short coherence or strict device simplicity, the cost of even imperfect phase H. Chen (haochen@boisestate.edu) and Z. Bozorgasl (zavarehbozorgasl@u.boisestate.edu) are with the Department of Electrical and Computer Engineering, Boise State University, Boise, ID 83712 USA. acquisition outweighs its benefits. We therefore prioritize an unbiased estimator and hardware-friendly constantenvelope signaling, accepting a well-quantified variance as the trade-off. This paper develops SCENE (Self-CEntering Noncoherent Estimator), a pilot-free OTA-FD estimator built on mean-centering of received energies. SCENE eliminates noise-energy bias and yields an unbiased estimate of the weighted soft-label average under coarse pathloss inversion, with variance O(1/(SM )). Lightweight renormalization makes the per-round output a valid soft label. Constant-envelope signaling enables efficient non-linear PAs and materially lowers device energy per round versus coherent high-PAPR schemes.
• A truly noncoherent OTA mapping from soft labels to energy.
• SCENE: a simple, unbiased, pilot-free noncoherent estimator for soft-label aggregation with variance O(1/(SM )).
• A constant-power transmission scheme by design, making it highly suitable for power-efficient amplifiers and simpler hardware compared to high-PAPR coherent schemes.
• An analysis framework for comparing the MSE against coherent baselines to identify the regimes (e.g., high mobility) where our scheme is superior.
Soft-label-based federated distillation (FD) exchanges predictions/logits instead of parameters, typically evaluated on a public (unlabeled) dataset, enabling model heterogeneity and reducing communication cost compared to parameter sharing. Foundational frameworks include FedMD [1], which introduced public-data logit sharing for heterogeneous models, and FedDF [2], which performs server-side ensemble distillation on unlabeled or generated data to fuse heterogeneous clients. DS-FL [3] formalized public-data distillation with the entropy reduction averaging (ERA) rule that deliberately sharpens aggregated logits for faster convergence under non-IID data. A parallel line explores server capacity and split-style training via FedGKT [4], which alternates client-side small models with a large server model using bidirectional KD; this highlights that distillation can decouple edge compute from server capacity. When public data are unavailable, FedGen [5] and related data-free KD approaches learn a generator at the server to synthesize queries for distillation, trading sample fidelity for privacy portability. Robust fusion under heterogeneity has been studied by FedBE [6], which casts aggregation as Bayesian model ensemble followed by distillation. Given that soft labels can still be large when K or the public batch is large, recent work targets communication shaping. CFD [7,8] quantizes soft labels and applies delta coding with active query selection, showing orders-of-magnitude savings versus vanilla FD. Very recent extensions like SCARLET [9] add soft-label caching across rounds combined with an enhanced ERA rule to avoid redundant retransmissions. These techniques are complementary to our transport-layer contribution: SCENE can aggregate soft labels over the air under any of
OTA Type Pilots/CSI Aggregand Estimator
Hu et al. [22] Coherent OTA-FD Per-round CSI logits beamforming + scaling Hu et al. [23] Coherent DP OTA-FD Per-round CSI logits DP + co-design Transceiver opt. [24] Coherent OTA-FD Per-round CSI logits MMSE transceiver NCAirFL [15] Noncoh. AirFL No pilots gradients unbiased noncoh. detector FSK/PPM MV [16,17] the above FD protocols. Surveys provide taxonomies and practical guidance. We follow the organization of [10] (FD survey) and [11] (practical guide to KD in FL), as well as broader KD-in-FL surveys [12,13]. For completeness, we note emerging security analyses showing that logit poisoning is a meaningful threat model in FD [14], which our self-centering estimator mitigates partly via its explicit renormalization and projection options.
B. Noncoherent OTA for AirFL (gradients) vs. SCENE for FD (soft labels)
There is a growing body of noncoherent over-the-air learning for FL gradients/parameters: (i) CSI-free noncoherent
This content is AI-processed based on open access ArXiv data.