Low-complexity and high-performance receive beamforming for secure directional modulation networks against an eavesdropping-enabled full-duplex attacker

In this paper, we present a novel scenario for directional modulation (DM) networks with a full-duplex (FD) malicious attacker (Mallory), where Mallory can eavesdrop the confidential message from Alice to Bob and simultaneously interfere Bob by sending a jamming signal. Considering that the jamming plus noise at Bob is colored, an enhanced receive beamforming (RBF), whitening-filter-based maximum ratio combining (MRC) (WFMRC), is proposed. Subsequently, two RBFs of maximizing the secrecy rate (Max-SR) and minimum mean square error (MMSE) are presented to show the same performance as WFMRC. To reduce the computational complexity of conventional MMSE, a low-complexity MMSE is also proposed. Eventually, to completely remove the jamming signal from Mallory and transform the residual interference plus noise to a white one, a new RBF, null-space projection (NSP) based maximizing WF receive power, called NSP-based Max-WFRP, is also proposed. From simulation results, we find that the proposed Max-SR, WFMRC, and low-complexity MMSE have the same SR performance as conventional MMSE, and achieve the best performance while the proposed NSP-based Max-WFRP performs better than MRC in the medium and high signal-to-noise ratio regions. Due to its low-complexity,the proposed low-complexity MMSE is very attractive. More important, the proposed methods are robust to the change in malicious jamming power compared to conventional MRC.