A generalized eigenvalue framework for secrecy-rate optimal subspace design

Linear preprocessing for physical-layer security (PLS) often relies on principal component analysis (PCA)-based projections, which enhance variance but do not explicitly suppress eavesdropper leakage. This letter proposes a generalized eigenvalue approach (GEA) that directly maximizes the Gaussian secrecy rate via a log-determinant formulation. The Stiefel-manifold-based closed-form solution has direct dependence on the main and eavesdropper’s channels covariances. The proposed framework is extended to scenarios with a reconfigurable intelligent surface (RIS) with colored or misaligned eigenbasis and consistently outperforms random baselines and PCA techniques.