Robust Synthesis Method for Secure Directional Modulation With Imperfect Direction Angle

Directional modulation (DM) is a secure transmission technology that is able to retain the original constellation of transmitted signals along the desired direction, while distort the constellation in the undesired directions at the same time. In this letter, we develop novel and robust DM synthesis methods for enhancing the transmission performance. Specifically, we first propose a low-complexity dynamic DM synthesis method. In this method, we derive a closed-form expression for the null space of conjugate transpose of the steering vector in the desired direction. Based on the expression derived, we construct a projection matrix in order to form artificial noises to those undesired directions. Then, we focus our attention on more practical scenarios, where there is uncertainty in the estimated direction angle. This uncertainty will cause estimation errors and seriously jeopardize the receiving performance in the desired direction. To mitigate the uncertainty effect, we further propose a robust DM synthesis method based on conditional minimum mean square error. The proposed method aims to minimize the distortion of the constellation points along the desired direction. Simulation results show that our proposed robust DM method is capable of substantially improving the bit error rate performance compared with the state-of-the-art methods.