A Precoding Perturbation Method in Geometric Optimization: Exploring Manifold Structure for Privacy and Efficiency

Inherent broadcast characteristics can raise privacy risks of wireless networks. The specifics of antenna ports, antenna types, orientation, and beamforming configurations of a transmitter can be susceptible to manipulation by any device within range when the signal is transmitted wirelessly. Personal and location information of users connected to the transmitter can be intercepted and exploited by malicious actors to track user movements and profile behaviors or launch targeted attacks, thus compromising user privacy and security. In this paper, we propose a novel precoding perturbation approach for privacy preservation in wireless communications. Our approach perturbs the precoding matrix of the transmitter using a Riemannian manifold (RM) structure that adaptively adjusts the magnitude and direction of perturbation based on the geometric properties of the manifold. The approach ensures robust privacy protection while minimizing the distortion of the transmitted signals, thus balancing privacy preservation and data utility. Privacy can be preserved without relying on additional cryptographic mechanisms, resulting in the computational and communication overhead reduction. Our approach operates directly on the transmission of signals, making them inherently secure against eavesdropping and interception. Simulation results underscore the superiority of the approach, showing a 17.21% improvement in privacy preservation while effectively maintaining data utility.