Joint HBF and AN Design for Secure mmWave Communications: An MSE Minimization Approach

Transmitting artificial noise (AN) signals with information-bearing signals is a widely adopted technique to enhance physical layer security for multiple-input multiple-output (MIMO) wireless communications. Existing AN-aided MIMO precoding schemes exhibit critical limitations: their strong dependence on the availability of the null-space of user equipment (UE) channels, and suboptimal secrecy performance caused by decoupled precoder-AN optimization. To address these issues, a joint hybrid beamforming (HBF) and AN design framework through mean square error (MSE) minimization is investigated for secure millimeter wave (mmWave) MIMO communications. The proposed method decomposes the sum-MSE minimization problem into coupled transmitter-receiver sub-problems solved via alternating optimization. A manifold optimization technique handles analog beamformer design under constant modulus constraints, while closed-form solutions for digital precoders and AN beamformer are derived for the transmitter sub-problem. This coordinated approach enables simultaneous updates of the digital precoders and the AN beamformer within each iteration. Simulations demonstrate superior secrecy performance compared to conventional null-space-dependent methods. Particularly, in cases where the null-space does not exist, the proposed method is still applicable.