Optimal Joint Fronthaul Compression and Beamforming Design for Networked ISAC Systems

This study investigates a networked integrated sensing and communication (ISAC) system, where multiple base stations (BSs), connected to a central processor (CP) via capacity-limited fronthaul links, cooperatively serve communication users while simultaneously sensing a target. The primary objective is to minimize the total transmit power while meeting the signal-to-interference-plus-noise ratio (SINR) requirements for communication and sensing under fronthaul capacity constraints, resulting in a joint fronthaul compression and beamforming design (J-FCBD) problem. We demonstrate that the optimal fronthaul compression variables can be determined in closed form alongside the beamformers, a novel finding in this field. Leveraging this insight, we show that the remaining beamforming design problem can be solved globally using the semidefinite relaxation (SDR) technique, albeit with considerable complexity. Furthermore, the tightness of its SDR reveals zero duality gap between the considered problem and its Lagrangian dual. Building on this duality result, we exploit the novel UL-DL duality within the ISAC framework to develop an efficient primal-dual (PD)-based algorithm. The algorithm alternates between solving beamforming with a fixed dual variable via fixed-point iteration and updating dual variable via bisection, ensuring global optimality and achieving high efficiency due to the computationally inexpensive iterations. Numerical results confirm the global optimality, effectiveness, and efficiency of the proposed PD-based algorithm.