Secure Wireless Transmission via Continuous-Aperture Arrays (CAPA)

This paper investigates the performance gains of a continuous aperture array (CAPA)-based downlink secure transmission system with multiple legitimate user terminals (LUTs) and eavesdroppers (Eves). The secure transmission problem is formulated as a weighted secrecy sum-rate (WSSR) maximization problem under a power constraint, which presents a challenging non-convex functional optimization problem. To address this, we propose a fractional programming (FP)-based optimization algorithm. By treating continuous function differentiation as an extension of infinite-dimensional vector differentiation, we first derive the fundamental structure of the optimal current distribution on the transmitting surface. Then, a continuous-function inversion theory, analogous to matrix inversion in the discrete domain, is introduced to derive a closed-form expression for the optimal source current pattern. Simulation results demonstrate that (i) CAPA-based systems achieve higher WSSR compared to spatially discrete array-based systems and (ii) the proposed method outperforms Fourier-based discretization methods while significantly reducing computational complexity.