Symbol-Level Precoding for Continuous-Aperture ISAC Systems

Abstract: Continuous-aperture arrays (CAPAs) offer rich electromagnetic degrees of freedom for integrated sensing and communication (ISAC), but optimizing continuous current distributions leads to challenging infinite-dimensional problems. This paper investigates a CAPA-enabled downlink ISAC system with symbol-level precoding and receive polarization combining. The transmit current is optimized to maximize weighted target-illumination power while enforcing constructive-interference constraints for communication users. To address the resulting infinite-dimensional nonconvex problem, we establish that the optimal current distribution lies in a finite-dimensional subspace spanned by the communication and sensing electromagnetic responses. This result yields an exact, structure-preserving reformulation in terms of finite-dimensional coefficients. A penalty projected-gradient algorithm is then developed to jointly optimize the current coefficients and polarization combiners. Simulation results demonstrate that the proposed framework achieves higher sensing utility and improved communication reliability than conventional Fourier-basis CAPA and spatially discrete array baselines.