Robust Secure Transmission of Using Main-Lobe-Integration-Based Leakage Beamforming in Directional Modulation MU-MIMO Systems

In this paper, we make an investigation of robust beamforming for secure directional modulation in the multiuser multiple-input and multiple-output systems in the presence of direction angle measurement errors. When statistical knowledge of direction angle measurement errors is unavailable, a novel robust beamforming scheme of combining main-lobe-integration and leakage is proposed to simultaneously transmit multiple different independent parallel confidential message streams to the associated multiple distinct desired users. The proposed scheme includes two steps: designing the beamforming vectors of the useful confidential messages and constructing artificial noise (AN) projection matrix. Here, in its first step, the beamforming vectors for the useful confidential messages of desired user $k$ are given by minimizing the useful signal power leakage from the main-lobe of desired user $k$ to the sum of main-lobes of the remaining desired directions plus main-lobes of all eavesdropper directions. In its second step, the AN projection matrix is constructed by simultaneously maximizing the AN power leakage to all eavesdropper directions such that all eavesdroppers are disrupted seriously, where AN is viewed by the transmitter as a useful signal for eavesdroppers. Due to independent beamforming vectors for different desired users, a more secure transmission is achieved. Compared with conventional nonrobust methods, the proposed method can provide a significant improvement in bit error rate along the desired directions and secrecy-sum-rate toward multiple desired users without needing the statistical property or distribution of angle measurement errors.