Resource-Element Energy Difference for Noncoherent Over-the-Air Federated Learning

TL;DR

This paper proposes REED, a noncoherent physical-layer primitive for signed aggregation in OTA-FL, avoiding the need for instantaneous CSI and synchronization, and analyzes its statistical properties under Rayleigh fading.

Contribution

It introduces REED, a novel noncoherent energy-based primitive for signed model updates in OTA-FL, with a detailed analysis of its statistical behavior and diversity-resource tradeoff.

Findings

Derived exact first- and second-moment expressions for REED.

Revealed the variance laws separating different noise sources.

Established an explicit diversity-resource tradeoff for REED.

Abstract

Over-the-air federated learning (OTA-FL) reduces uplink latency by aggregating client updates directly over the wireless multiple-access channel. Coherent analog aggregation realizes this idea by aligning the phases and amplitudes of simultaneously transmitted waveforms, which typically requires synchronization, instantaneous channel-state information (CSI), phase compensation, and power control. Noncoherent energy detection removes the need for phase-coherent combining, but a single energy measurement is nonnegative and, therefore, cannot represent signed model updates. This paper introduces resource-element energy difference (REED), a noncoherent physical-layer primitive for continuous signed aggregation. REED maps the positive and negative parts of each real-valued update to transmit energies on paired orthogonal resource elements and estimates the signed sum by subtracting the corresponding received energies. The construction uses slow-timescale calibration of average channel powers, but does not require instantaneous transmitter- or receiver-side CSI or channel inversion. For independent Rayleigh fading, we derive exact first- and second-moment expressions for single-shot REED and for a chip-diverse extension that spreads each coordinate over multiple independently faded paired chips. The resulting variance laws separate fading-induced self-noise, signal-noise interaction, and receiver-noise fluctuation, giving an explicit diversity-resource tradeoff. More->The rest of abstract is in the paper.