Risk-Sensitive Beam-Power Co-Design under Directional Modulation and Mobile Eavesdroppers

Marie Mayer; David N. Hartmann; Laura Lang

Authors

Marie Mayer Mathematics, Engineering Sciences, and Natural Sciences Faculty of Mathematics and Computer Science, Heidelberg University, Heidelberg, Baden-Wurttemberg, Germany Author
David N. Hartmann Mathematics, Engineering Sciences, and Natural Sciences Faculty of Mathematics and Computer Science, Heidelberg University, Heidelberg, Baden-Wurttemberg, Germany Author
Laura Lang Mathematics, Engineering Sciences, and Natural Sciences Faculty of Mathematics and Computer Science, Heidelberg University, Heidelberg, Baden-Wurttemberg, Germany Author

Keywords:

Physical Layer Security, Directional Modulation, Risk-Sensitive Optimization, Mobile Eavesdroppers

Abstract

This paper addresses the challenge of securing wireless communications in the presence of highly dynamic, mobile eavesdroppers using physical layer security. We propose a risk-sensitive joint beamforming and power allocation co-design framework integrated with directional modulation. Unlike traditional physical layer security approaches that focus on maximizing the average secrecy rate, our design incorporates a risk-sensitive exponential utility function that penalizes large fluctuations and worst-case secrecy losses caused by the unpredictable movements of the eavesdropper. By leveraging directional modulation, the transmitter projects information-bearing signals along the spatial path of the legitimate receiver while dynamically emitting artificial noise to scramble the constellation patterns in non-target directions. We formulate a joint optimization problem to determine the optimal beamforming vectors and power division ratio under a total power constraint. Due to the non-convex and mathematically intractable nature of the risk-sensitive objective, we develop an iterative optimization algorithm utilizing successive convex approximation and semidefinite relaxation. Systematic simulation results demonstrate that the proposed risk-sensitive co-design significantly reduces the secrecy outage probability compared to conventional risk-neutral schemes, ensuring robust and reliable secure communication in highly mobile and uncertain wireless environments.

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