Phase-Only Artificial Noise for Secure Communication with Multiple Antennas Using Simultaneous Orthogonalization

The security of a wireless channel between a transmitter and legitimate user(s) in the presence of eavesdroppers can be improved by the addition of artificial noise (AN) transmission. In the case where the channel state information of the eavesdroppers is not known, some AN schemes transmit multiple uncorrelated noise signals via distinct orthogonal beamforming vectors. The vectors are designed to avoid affecting the legitimate links, and mutual orthogonality increases the likelihood that the AN signals are received at the eavesdroppers with high power. Applications in massive-MIMO, where hardware is constrained, motivate us to design vectors whose elements have arbitrary phases but equal magnitudes [1].This work proposes an algorithm that generates multiple such phase-only beamforming vectors via a single optimization problem and significantly increases the number of vectors which can be found compared to the previous work [2]. Consequently, our results demonstrate substantially higher lower-bounds on maximum achievable secrecy rate via this approach compared to the previous work [2] for similar scenarios.