Compressive sensing based sparse antenna array design for directional modulation

Directional modulation (DM) can be achieved based on uniform linear arrays where the maximum spacing between adjacent antennas is half-wavelength of the frequency of interest in order to avoid spatial aliasing. To exploit the additional degrees of freedom provided in the spatial domain, sparse antenna arrays can be employed for more effective DM. In this study, the spare array design problem in the context of DM is formulated from the viewpoint of compressive sensing (CS), so that it can be solved using standard convex optimisation toolboxes in the CS area. In detail, a common set of active antennas needs to be found for all modulation symbols generating a response close to the desired one. The key to the solution is to realise that group sparsity has to be employed, as a common antenna set cannot be guaranteed if the antenna locations are optimised for each modulation symbol individually. Moreover, two practical scenarios are considered for the proposed design: robust design with model errors and design with practical non-zero-sized antennas, and corresponding solutions are found by modifying the proposed standard solution.