Secrecy in MIMOME wiretap channels: Beamforming with imperfect CSI

We propose two beamforming schemes supporting multi-stream transmission in multi-input multi-output multi-antenna eavesdropper wiretap channels with imperfect channel state information of the eavesdropper. We first propose a generalized eigenvalue decomposition (GEVD)-based beamforming scheme by designing the beamforming matrix and determining the power allocation matrix. In particular, we determine a general power allocation matrix for arbitrary signal-to-noise ratio (SNR) and a simplified power allocation matrix for high SNR. We demonstrate that our GEVD-based beamforming scheme delivers a higher achievable secrecy rate than the existing beamforming schemes in the medium and high SNR regime. We also demonstrate that the simplified power allocation matrix delivers the same achievable secrecy rate as the general power allocation matrix at high SNRs. We then propose an easy-to-construct EVD-based beamforming scheme which reduces signal processing cost and eliminates power allocation. We demonstrate that our EVD-based beamforming scheme delivers a higher secrecy rate than the GEVD-based beamforming scheme and the existing beamforming schemes in the low SNR regime.