Directional modulation (DM) as a physical layer security technique has been studied from many different aspects recently. Normally all existing designs based on antenna arrays lead to varying weight coefficients for different antennas and for different signal symbols, which poses a particular challenge for feed circuits design in analogue implementation. In this paper, to reduce the implementation complexity, a constant magnitude constraint is proposed for the first time, and the resultant non-convex constraint can be modified to a convex form so that the problem can be solved conveniently by existing convex optimisation toolboxes. Design examples are provided to show the effectiveness of the proposed design.

Introduction

With the fast development of the Fifth Generation (5G) network, communication has been more important than ever [1], [2]. As physical layer security technique to keep known constellation mappings in a desired direction or directions, while scrambling them for the remaining ones, directional modulation (DM) has been studied widely [3]. In [4], a four-element reconfigurable antenna array was designed, where the DM design was achieved by changing elements for each symbol. In [5], phased antenna array was employed for DM, with an individual tailor-made feed circuit (including phase shift and amplitude change) prepared for each antenna. Compared with a given antenna array design, to further reduce the number of antennas, DM design was extended to sparse antenna arrays [6]. To overcome the inherent limitation of DM, where eavesdroppers and the desired users share the same received signal when they are in the same spatial direction of the antenna array, two positional modulation (PD) designs were proposed, with one based on a reflecting surface [7], and the other employing multiple antenna arrays [8]. Both designs are based on the idea that if the received signal is a combination of signals from different paths with different directions, then signals at these locations can be distinguished. To increase the channel capacity of DM, two antenna array structures were proposed recently.