Transmit Beamforming Design for ISAC With Stacked Intelligent Metasurfaces

Abstract

This paper proposes a transmit beamforming strategy for the integrated sensing and communication (ISAC) systems enabled by the novel stacked intelligent metasurface (SIM) architecture, different from conventional single-layer reconfigurable intelligent surface (RIS) by cascading multiple transmissive metasurface layers, where the base station (BS) simultaneously performs downlink communication and radar target detection via fully passive wave domain beamforming, result in the significant reduction in hardware cost and power consumption. To ensure superior dual-function performance simultaneously, we design the multi-layer cascading beamformer by maximizing the sum rate of the users while optimally shaping the normalized beam pattern for detection. A dual-normalized differential gradient descent (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{D}^{3}$</tex-math></inline-formula>) algorithm is further proposed to solve the resulting non-convex multi-objective problem (MOP), where gradient differences and dual normalization are employed to ensure a flexible trade-off between communication and sensing objectives at the gradient level, providing finer control over the optimization process. Numerical results demonstrate the superiority of the proposed beamforming design in terms of balancing communication and sensing performance.