## 5 Conclusions  
This paper investigates a secure beam hybrid precoding algorithm for mmWave communications. Based on [PERSON]'s theorem, an eavesdropping channel model is established along with its secrecy capacity expression. The masking characterization of the sparse mmWave MIMO channel is studied. The sparse beamspace channel \(\mathbf{H}_{b}\) is uniquely determined by the receiver's location. A secure beam digital precoding scheme based on GSVD is analyzed. Building on GSVD-based scheme, a secure beam hybrid precoding algorithm, GSVD-Sparsity, is proposed, which fully exploits the sparsity of \(\mathbf{H}_{b}\). Simulation results validate the security performance and spectral efficiency of digital precoding schemes based on SVD and GSVD, as well as the hybrid precoding algorithm GSVD-Sparsity. The analysis indicates that, in a fully digital system, employing the GSVD-based digital precoding scheme can effectively prevent the eavesdropper from correctly receiving signals at the cost of sacrificing part of the transmission efficiency of the legitimate user, rendering the eavesdropper unable to demodulate the constellation diagram. In a hybrid precoding system, the low-complexity GSVD-Sparsity algorithm can approximate the spectral efficiency of the optimal digital precoding scheme based on GSVD while ensuring transmission security. Massive MIMO and hybrid precoding are key technologies in mmWave communications. Accordingly, the demand for security and privacy protection is also increasing. This work investigates a secure hybrid precoding algorithm based on GSVD and the sparsity of mmWave channels. As a physical layer security technique, it holds promising potential for a wide range of applications.  
Conceptualization, M.W.; methodology, M.W. and B.C.; software, B.C. and L.Y.; validation, M.W., L.Y. and B.C.; formal analysis, L.Y.; investigation, M.W.; resources, B.C.; data curation, L.Y. and B.C.; writing--original draft preparation, M.W., L.Y. and B.C.; writing--review and editing, M.W., L.Y. and B.C.; visualization, M.W.; supervision, L.Y.; project administration, M.W.; funding acquisition, M.W. and L.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Natural Science Foundation of China, grant number 62372244, 62172235; the National Key Research and Development Program of China, grant number 2021 YFB3101100; the Primary Research & Development Plan of Jiangsu Province, grant number BE2023025; the Natural Science Foundation of Nanjing University of Posts and Telecommunications grant number NY222132; the ZTE Industry-university Research Fund, grant number 2023 ZTE08  
Figure 12: The SER of the legitimate user employing 16 QAM under AWGN and multipath channel conditions.  
02; the Postgraduate Research & Practice Innovation Program of Jiangsu Province, grant number 46004 CX17781.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
**Conflicts of Interest:** The authors declare no conflicts of interest.