Two Efficient Beamformers for Secure Precise Jamming and Communication With Phase Alignment

To cause effective interference on eavesdropper with an enhanced security, a secure precise jamming and communication (SPJC) is proposed to radiate the transmit energy of artificial noise (AN) and confidential message (CM) into the neighborhoods of Eve and Bob by using random subcarrier selection, directional modulation, and beamforming under phase alignment constraint (PAC). Here, we propose two good-performance beamforming schemes: minimum transmit power (Min-TP) and minimum regularized transmit power (Min-RTP) to achieve SPJC under PAC and orthogonal constraint (OC), where AN and CM are projected onto the null-spaces of the desired and eavesdropping channels, respectively. Simulation results show that the proposed Min-TP and Min-RTP methods perform much better than existing equal amplitude (EA) and null-space projection (NSP) methods in terms of secrecy rate (SR) at medium and high signal-to-noise ratio regions. The SR performance difference between the proposed two methods becomes trivial as the number of transmit antennas approaches large. More importantly, they form two main peaks of AN and CM around Eve and Bob, respectively.