Beamforming Design for Cell-Free ISAC MIMO Systems with Capacity-Limited Backhaul

In the cell-free integrated sensing and communication (ISAC) system, distributed access points (APs) collaborate to simultaneously serve users and sense targets, which reduces the impact of signal blockage and enhances sensing accuracy. However, the cooperation among APs depends on backhaul links to exchange information with a central processing unit (CPU), which is often limited in practice. Therefore, this paper investigates beamforming design for cell-free ISAC multiple-input-multipleoutput (MIMO) systems with capacity-limited backhaul, aiming to minimize transmit power while ensuring both sensing and communication performance. Two algorithms are proposed: the global optimization algorithm and the low-complexity algorithm. The global optimization algorithm leverages the equivalence between backhaul capacity and AP-UE service pair selection, decomposing the original problem into multiple sub-problems. Each sub-problem is converted into a semidefinite programming (SDP). By selecting the best solution from all sub-problems, the globally optimal solution can be achieved. In the low-complexity algorithm, the backhaul capacity constraint is approximated by a smooth function. Successive convex approximation (SCA) is then applied to address the resulting non-convex constraint iteratively. Simulation results validate the effectiveness of the proposed algorithms.