An Interpretable Deep-Unfolding Network for Real-Time Simultaneous Multi-Beam Synthesis in Sparse Phased-MIMO Radar

Sparse phased multiple-input multiple-output (phased-MIMO) radar combines wide transmit coverage with high-resolution virtual-aperture reception, but simultaneous multi-beam synthesis requires mainlobe shaping, sidelobe control, and interference nulling to be satisfied jointly. Optimization-based solvers preserve these constraints explicitly, yet their long iterative trajectories limit efficient deployment. This paper presents FastUnfoldNet, a physics-structured deep-unfolding framework that maps the alternating direction method of multipliers (ADMM) beamformer onto a fixed-depth architecture. Each layer retains the closed-form sidelobe, null, and mainlobe projections and the standard dual update, while learnable heavy-ball momentum and relaxation reshape the finite-depth trajectory. Stage-wise penalty sharing further couples adaptive optimization with Cholesky factorization reuse, and phase-aligned teacher-response distillation learns a compact 20-layer trajectory for deployment. Simulations covering focused, flat-top, and simultaneous multi-beam synthesis show that the unfolded models reproduce the beam geometry of the parent solver with a substantially shorter update sequence. Depth, ablation, and in-distribution generalization analyses further identify the roles and boundaries of the learned components. FastUnfoldNet therefore provides an interpretable route from constrained beamforming optimization to fixed-depth inference for the considered sparse phased-MIMO setting.