| Summary: | We first review the fundamentals of directional modulation (DM) based on frequency diverse arrays (FDA), which is capable of achieving angle-range dependent point-to-point physical layer secure communications where the phase shifters of the FDA-based DM must be optimized continuously with time by complex algorithms like genetic algorithm (GA). Thereafter, in order to overcome the time-variant drawbacks of conventional FDA-based DM, we propose a time-invariant angle-range dependent DM based on time-modulated logarithmically increasing frequency offset FDA (TDM-log-FDA). Different from the conventional FDA-based DM, where the frequency offsets are linear and determinate, the frequency offsets of TDM-log-FDA are elaborately designed as time-modulated nonlinear logarithmically increasing values guaranteeing the time-invariant characteristic of TDM-log-FDA. Additionally, an improved dot-shaped time-invariant DM based on time-modulated multicarrier frequency offset FDA (DTDM-mc-FDA) is put forward to achieve time-invariant spatial fine focusing point-to-point physical layer secure communications, where multiple carriers instead of a single carrier are transmitted through each antenna element and the corresponding frequency offsets are also time-modulated. Using GA, we obtain the optimized phase shifters for the proposed two time-invariant DMs once and for all, which reduces the realization complexity of phase shifters greatly. Besides, a new metric called secure area is proposed to evaluate the security performance of DM systems. The simulated results demonstrate that the proposed TDM-log-FDA can realize time-invariant angle-range dependent secure communications, while the proposed DTDM-mc-FDA can further enhance the security with more accurately focusing secure area despite a small penalty of complexity.
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