Performance Analysis of Physical Layer Security for Over-the-Air Computation Using Distributed Null-Steering Beamforming

Over-the-air computation (AirComp) reduces the latency of wireless data aggregation by leveraging the superposition property of the wireless channel to achieve the desired function. This letter proposes a physical layer security (PLS) technique based on cooperative beamforming (CB) and distributed null steering for an AirComp network to effectively prevent eavesdropping. We provide a theoretical framework to combine CB and AirComp with adaptive null steering to degrade the reception of an eavesdropper located near the legitimate receiver. A closed-form expression for the average mean squared error (MSE) is derived, showing that the proposed distributed null-steering beamforming provides significantly better PLS performance than analog cooperative beamforming. Furthermore, a genetic algorithm is employed to jointly optimize the nulling factor and the direction to maximize the average MSE gap.