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Directional modulation (DM) has become a new research hotspot of physical layer security (PLS) communication at the transmitter side. In this paper, we propose a robust synthesis algorithm for DM signal under the condition of the array manifold vectors perturbation. This algorithm optimizes the constraints of sidelobe level and Euclidean distance of constellation points by considering the worst case performance of array manifold vectors. Furthermore, we also design an active constellation extension (ACE) method to relax the equality constraint of desired modulation symbols into a robust inequality constraint at the desired direction. These constraints can be reformulated in a convex form with  and  regularization, which are computationally tractable. Simulation results show better performance of the proposed robust algorithm compared with the benchmark synthesis algorithms in the presence of array manifold vectors uncertainty.

Robust Synthesis Algorithm for Directional Modulation Signal with Array Manifold Vectors Uncertainty