Frequency diverse array beamforming for physical-layer security with directionally-aligned legitimate user and eavesdropper

The conventional physical-layer (PHY) security approaches, e.g., transmit beamforming and artificial noise (AN)-based design, may fail when the channels of legitimate user (LU) and eavesdropper (Eve) are close correlated. Due to the highly directional transmission feature of millimeter-wave (mmWave), this may occur in mmWave transmissions as the transmitter, Eve and LU are aligned in the same direction exactly. To handle the PHY security problem with directionally-aligned LU and Eve, we propose a novel frequency diverse array (FDA) beamforming approach to differentiating the LU and Eve. By intentionally introducing some frequency offsets across the antennas, the FDA beamforming generates an angle-range dependent beampattern. As a consequence, it can degrade the Eve's reception and thus achieve PHY security. In this paper, we maximize the secrecy rate by jointly optimizing the frequency offsets and the beamformer. This secrecy rate maximization (SRM) problem is hard to solve due to the tightly coupled variables. Nevertheless, we show that it can be reformulated into a form depending only on the frequency offsets. Building upon this reformulation, we identify some cases where the SRM problem can be optimally solved in closed form. Numerical results demonstrate the efficacy of FDA beamforming in achieving PHY security, even for aligned LU and Eve.