Low-Complexity Time-Invariant Angle-Range Dependent DM Based on Time-Modulated FDA Using Vector Synthesis Method

A low-complexity time-invariant angle-range dependent directional modulation (DM) based on time-modulated frequency diverse array (TM-FDA-DM) is proposed to achieve point-to-point physical layer security communications. The principle of TM-FDA is elaborated and the vector synthesis method is utilized to realize the proposal, TM-FDA-DM, where normalization and orthogonal matrices are designed to modulate the useful baseband symbols and inserted artificial noise, respectively. Since the two designed matrices are time-invariant fixed values, which avoid real-time calculation, the proposed TM-FDA-DM is much easier to implement than time-invariant DMs based on conventional linear FDA or logarithmical FDA, and it also outperforms the time-invariant angle-range dependent DM that utilizes genetic algorithm (GA) to optimize phase shifters on radio frequency (RF) frontend. Additionally, a robust synthesis method for TM-FDA-DM with imperfect angle and range estimations is proposed by optimizing normalization matrix. Simulations demonstrate that the proposed TM-FDA-DM exhibits time-invariant and angle-range dependent characteristics, and the proposed robust TM-FDA-DM can achieve better BER performance than the non-robust method when the maximum range error is larger than 7km and the maximum angle error is larger than 4°.