On Minimizing Symbol Error Probability for Antipodal Beamforming in MIMO Gaussian Wiretap Channels

This paper investigates a beamforming scheme designed to minimize the symbol error probability (SEP) for a legitimate user while guaranteeing that the likelihood of an eavesdropper correctly recovering symbols remains below a predefined threshold. The focus is on finding an optimal beamforming vector for binary antipodal signal detection in multiple-input multiple-output (MIMO) Gaussian wiretap channels. Finding the optimal beamforming vector is a non-convex problem, and thus conventional computationally efficient algorithms for convex problems cannot be applied in this context. To that end, our proposed algorithm relies on Karush–Kuhn–Tucker (KKT) conditions and the generalized eigen-decomposition method to find an exact solution. The numerical results are presented to assess the performance of the proposed method for various scenarios.