Hybrid Beamforming Design for Near-Field ISAC with Modular XL-MIMO

A novel modular extremely large-scale multiple-input-multiple-output (XL-MIMO) integrated sensing and communication (ISAC) framework is proposed in this paper. We consider a downlink ISAC scenario and exploit the modular array architecture to enhance the communication spectral efficiency and sensing resolution while reducing the channel modeling complexity by employing the hybrid spherical and planar wavefront model. Considering the hybrid digital-analog structure inherent to modular arrays, we formulate a joint analog-digital beamforming design problem based on the communication spectral efficiency and sensing signal-to-clutter-plus-noise ratio (SCNR). By exploring the structural similarity of the communication and sensing channels, it is proved that the optimal transmit covariance matrix lies in the subspace spanned by the subarray response vectors, yielding a closed-form solution for the optimal analog beamformer. Consequently, the joint design problem is transformed into a low-dimensional rank-constrained digital beamformer optimization. We first propose a manifold optimization method that directly optimizes the digital beamformer on the rank-constrained Stiefel manifold. Additionally, we develop an semidefinite relaxation (SDR)-based approach that relaxes the rank constraint and employ the randomization technique to obtain a near-optimal solution. Simulation results demonstrate the effectiveness of the proposed modular XL-MIMO ISAC framework and algorithms.