Holographic Joint Communications and Sensing With Cramer-Rao Bounds

Joint Communication and Sensing (JCAS) technology facilitates the seamless integration of communication and sensing functionalities within a unified framework, enhancing spectral efficiency, reducing hardware complexity, and enabling simultaneous data transmission and environmental perception. This paper explores the potential of holographic JCAS systems by leveraging reconfigurable holographic surfaces (RHS) to achieve high-resolution hybrid holographic beamforming while simultaneously sensing the environment. As the holographic transceivers are governed by arbitrary antenna spacing, we first derive exact Cram\'er-Rao Bounds (CRBs) for azimuth and elevation angles to rigorously characterize the three-dimensional (3D) sensing accuracy. To optimize the system performance, we propose a novel weighted multi-objective problem formulation that aims to simultaneously maximize the communication rate and minimize the CRBs. However, this formulation is highly non-convex due to the inverse dependence of the CRB on the optimization variables, making the solution extremely challenging. To address this, we propose a novel algorithmic framework based on the Majorization-Maximization (MM) principle, employing alternating optimization to efficiently solve the problem. The proposed method relies on the closed-form surrogate functions that majorize the original objective derived herein, enabling tractable optimization. Simulation results are presented to validate the effectiveness of the proposed framework under diverse system configurations, demonstrating its potential for next-generation holographic JCAS systems.