Analytical Design of Directional Modulation in Spatial Frequency Domain

In this paper, we propose a novel, energy-efficient directional modulation scheme to enhance the physical-layer security of wireless communication systems. The proposed analytical method designs a uniform linear array (ULA) in the spatial frequency domain, allowing for arbitrary distortion of the constellation pattern. In the secure directions, the design ensures low bit error rates (BERs), while in unsecure angles, it enforces a threshold BER to disrupt potential eavesdroppers. The proposed scheme is not only simple to design but also provides flexible trade-off between the mainlobe and sidelobes, ensuring efficient energy consumption. Furthermore, we show that the new scheme has low computational complexity when optimizing antenna weightings, and while we only consider 4- and 16-QAM in this paper, the proposed method can be generalized to higher order QAM modulation schemes. Numerical results validate the effectiveness of the design in achieving the desired BER thresholds and energy efficiency, demonstrating its suitability for real-world applications.