Wireless channels can be inherently privacy-preserving by distorting the
received signals due to channel noise, and superpositioning multiple signals
over-the-air. By harnessing these natural distortions and superpositions by
wireless channels, we propose a novel privacy-preserving machine learning (ML)
framework at the network edge, coined over-the-air mixup ML (AirMixML). In
AirMixML, multiple workers transmit analog-modulated signals of their private
data samples to an edge server who trains an ML model using the received
noisy-and superpositioned samples. AirMixML coincides with model training using
mixup data augmentation achieving comparable accuracy to that with raw data
samples. From a privacy perspective, AirMixML is a differentially private (DP)
mechanism limiting the disclosure of each worker’s private sample information
at the server, while the worker’s transmit power determines the privacy
disclosure level. To this end, we develop a fractional channel-inversion power
control (PC) method, {alpha}-Dirichlet mixup PC (DirMix({alpha})-PC), wherein
for a given global power scaling factor after channel inversion, each worker’s
local power contribution to the superpositioned signal is controlled by the
Dirichlet dispersion ratio {alpha}. Mathematically, we derive a closed-form
expression clarifying the relationship between the local and global PC factors
to guarantee a target DP level. By simulations, we provide DirMix({alpha})-PC
design guidelines to improve accuracy, privacy, and energy-efficiency. Finally,
AirMixML with DirMix({alpha})-PC is shown to achieve reasonable accuracy
compared to a privacy-violating baseline with neither superposition nor PC.

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