Integrated Sensing and Communication with Reconfigurable Holographic Surface

Integrated sensing and communication (ISAC) can enhance spectrum and hardware efficiency, but commonly considered phased arrays suffer from high power consumption and hardware cost. This paper presents a novel holographic ISAC system, introducing a reconfigurable holographic surface (RHS) beamforming framework to maximize the sensing mutual information (MI) while satisfying user data rate requirements. The key idea is that we derive an asymptotic lower bound for the MI, and transform it, involving Kronecker products in both the numerator and denominator, into a quadratic objective using the generalized Charnes-Cooper transformation. This enables a tight semidefinite relaxation (SDR) with the guaranteed existence of a rank-one solution, leading to the optimal full-digital (FD) beamformer. Another important aspect is that we prove the optimal FD beamformer directly translates into the globally optimal hybrid RHS beamforming design, when the number of radio frequency (RF) chains matches the RHS elements. When the RF chains are fewer, we develop an alternating optimization algorithm, which employs a tight SDR for digital beamforming design and a Gaussian randomization-based SDR for RHS amplitude control solution in each iteration. Simulations demonstrate that holographic ISAC surpasses phased arrays by 12.4% in sensing MI. Holographic ISAC is highly power-efficient, requiring only 33.3% of the transmit power needed by phased arrays to achieve the same radar detection probability.