Beamforming design for secure downlink transmission of MU-MIMO systems with multi-antenna eavesdropper

In this paper we investigate the physical layer security for downlink MU-MIMO systems where the transmitter and the eavesdropper are equipped with multiple antennas, while the legitimate users have single antenna. This is a more challenging topic because the eavesdropper appears to be more powerful than the legitimate users. We propose a transmission scheme able to enhance secure transmission for legitimate users, by intentionally applying different beamforming matrices to pilot signals and data signals. The beamforming matrix for data signals is constructed in a way that legitimate users can derive the channel matrix experienced by data signals based on pilot signals, whereas the eavesdropper fails to obtain the channel matrix experienced by data signals even with the aid of pilot signals. Therefore coherent detection at the eavesdropper is impossible and the signal-plus-interference-to-noise (SINR) of the eavesdropper is significantly degraded. In addition, the proposed beamforming design is formulated as an optimization problem to maximize the minimum SINR. We theoretically prove that with this formulation, the resultant optimal SINR is not affected by the proposed format of beamforming matrix for data signals. Numerical results show that, the proposed beamforming design outperforms the conventional beamforming design in terms of ergodic secrecy sum rate. Furthermore, with suitable beamforming designs, the ergodic secrecy sum rate achieved will not be noticeably affected by the number of antennas at the eavesdropper, although it is significantly degraded with conventional beamforming design.