Continuous-Aperture Array for Integrated Sensing and Communication: Rate-CRB Tradeoff

An analytical and optimization framework on rate-Cramér-Rao bound (CRB) tradeoff is proposed in this paper for the continuous-aperture array (CAPA)-based integrated sensing and communication (ISAC) system. To evaluate the dual-functional performance, the sensing CRB and communication rate are analyzed concerning the induced electromagnetic (EM) waves of CAPAs. For rate-CRB region characterization, the spatially continuous beamforming of transmit CAPA is optimized under three cases: i) A novel closed-form expression for the optimal CAPA beamformer is derived under the single-user single-target scenario, proven to be aligned within the space spanned by the EM-based sensing and communication channels; ii) A general subspace-based beamforming design approach is proposed to address the intractable continuity, converting the continuous beamforming design in spatial domain to discrete weight design in subspace domain and resorting to the semidefinite relaxation for the globally optimal solution; iii) Moreover, the general beamforming design is specialized to both the low-complexity zero-forcing (ZF) and the conventional spatially discrete array (SPDA)-based designs. Numerical results demonstrate that: i) The proposed subspace-based approach can realize efficient and effective beamforming design for reduced mutual interference, enhanced sensing performance, and guaranteed communication rate; ii) The general CAPA beamforming design achieves broader rate-CRB region than the ZF-oriented design and reaches the ultimate performance of the SPDA-based system.