ISAC with Co-Prime Arrays: Virtual-Aperture Sensing and Downlink Communications

Abstract

Integrated sensing and communication (ISAC) enables simultaneous wireless communication and environmental sensing in unmanned aerial vehicle (UAV) networks. However, practical joint sensing-communication deployments are fundamentally constrained by limited physical apertures and a finite number of radio-frequency (RF) chains, and shared-aperture operation is further complicated by mutual interference between sensing and communication beams. In this paper, we consider a co-located ISAC transmitter that employs a sparse co-prime array (CPA) for high-resolution sensing while reutilizing the remaining antenna positions within the same aperture for multiuser downlink communication. The sensing precoder is designed via a Cramér-Rao bound (CRB)-oriented metric that exploits the CPA-induced virtual array, and the communication precoder is jointly optimized to satisfy per-UAV SINR targets under a total power budget. The resulting design is reformulated as a tractable semidefinite program via the Schur complement and semidefinite relaxation (SDR) and then efficiently solved using off-the-shelf convex optimization solvers. Simulations demonstrate that the proposed framework significantly reduces the sensing CRB while strictly meeting SINR and power constraints, yielding a favorable sensingcommunication tradeoff.