Synthesis of Sparse Linear Array for Directional Modulation via Convex Optimization

The design of a directional modulation (DM) signal by a phased array is one of the important topics in the field of physical layer security communication. In this paper, we synthesize a sparse array for DM based on convex optimization. The main idea is that a nonconvex optimization problem associated with ℓ
₀
-norm is formulated for synthesizing a sparse array. To solve this nonconvex optimization problem, two different solutions are employed to relax the nonconvex optimization problem in a convex way: one is based on iterative reweighted ℓ
₁
-norm resulting in a superdirective array, the other is based on mixed integer programming resulting in a nonsuperdirective array. Furthermore, multiple important metrics of a DM transmitter, such as power efficiency, information beamwidth, and dynamic DM signal, are also considered in the optimization problem to achieve better performance of the DM signal via a sparse array. Simulation results show that the proposed synthesis method provides greater flexibility of controlling the security performance, power efficiency, and static or dynamic DM signal while the number of excitations is less than the uniformly spaced linear array in the benchmark problems.