Robust Beamforming for Physical Layer Security in BDMA Massive MIMO

In this paper, we design robust beamforming to guarantee the physical layer security for a multiuser beam division multiple access (BDMA) massive multiple-input multiple-output (MIMO) system, when the channel estimation errors are taken into consideration. With the aid of artificial noise (AN), the proposed design are formulated as minimizing the transmit power of the base station (BS), while providing legal users and the eavesdropper (Eve) with different signal-to-interference-plus-noise ratio (SINR). It is strictly proved that, under BDMA massive MIMO scheme, the initial non-convex optimization can be equivalently converted to a convex semi-definite programming (SDP) problem and the optimal rank-one beamforming solutions can be guaranteed. In stead of directly resorting to the convex tool, we make one step further by deriving the optimal beamforming direction and the optimal beamforming power allocation in closed-form, which greatly reduces the computational complexity and makes the proposed design practical for real world applications. Simulation results are then provided to verify the efficiency of the proposed algorithm. Index Terms Robust beamforming, massive MIMO, physical layer security, beam division multiple access (BDMA), closed-form. F. Zhu is with High-Tech Institute of Xi’an, Xi’an, Shaanxi 710025, China (e-mail: fengchao [email protected]). F. Gao is with the State Key Laboratory of Intelligent Technology and Systems, Tsinghua National Laboratory for Information Science and Technology, Department of Automation, Tsinghua University, Beijing, 100084, China (e-mail: [email protected]). H. Lin is with the Department of Electrical and Information Systems, Osaka Prefecture University, Sakai, Osaka, Japan (e-mail: [email protected]). S. Jin is with the National Communications Research Laboratory, Southeast University, Nanjing 210096, P. R. China (email: [email protected]). J. Zhao is with School of Information Engineering, East China Jiaotong University, Nanchang, 330013, China, and is also with School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing, 100044, China (email: [email protected]). 2