Physical-Layer Security for Proximal Legitimate User and Eavesdropper: A Frequency Diverse Array Beamforming Approach

Transmit beamforming and artificial noise-based methods have been widely employed to achieve physical-layer (PHY) security. However, these approaches may fail to provide satisfactory secure performance if the channels of legitimate user (LU) and eavesdropper (Eve) are highly correlated, which usually occurs in the case of close-located LU and Eve. The goal of this paper is to address the PHY security problem for proximal LU and Eve in millimeter-wave transmissions. To this end, we propose a novel frequency diverse array (FDA) beamforming approach, which intentionally introduces some frequency offsets across array antennas to decouple the highly correlated channels of LU and Eve. By exploiting this decoupling capability, the FDA beamforming can degrade Eve's reception and thus enhance PHY security. Leveraging FDA beamforming, we aim to maximize the secrecy rate by jointly optimizing the frequency offsets and the transmit beamformer. This secrecy rate maximization problem is difficult due to the tightly coupled variables. However, we show that it can be reformulated into a form only depending on the frequency offsets. Building upon this reformulation, we further employ the block successive upper-bound minimization method to iteratively obtain a solution with stationary convergence guarantee. Numerical results demonstrate that FDA beamforming can provide higher secrecy rate than conventional beamforming, especially for proximal LU and Eve.