Wideband MIMO radar beampattern shaping in spectrally dense environments

Wideband MIMO radar beampattern shaping with Constant Modulus Constraints (CMCs) in spectrally dense environments is critical for future 6G networked sensing technology. Existing methods minimize the weighted function of wideband MIMO radar beampattern matching Mean Square Error (MSE) and the Energy Spectral Density (ESD) of Spatial Spectral Nulling (SSN) region; however, achieving precise ESD control remains a challenge. To address this, we minimize the beampattern matching MSE under CMCs and precise SSN Constraints (SSNCs). The non-convex nature of the CMCs and multiple SSNCs lead to a non-convex Quadratic-Constrained Quadratic Programming (QCQP) problem. To solve the problem, we propose a novel Manifold-Based Exact Penalty (MBEP) method. First, we construct the Complex Circular Manifold (CCM) to satisfy the CMCs and reformulate the SSNCs as an exact penalty function, thereby transforming the problem into an unconstrained optimization problem on the CCM. Subsequently, a Simplified Quasi-Newton (SQN) method is developed to optimize the problem on the CCM. Finally, the penalty factor is adaptively updated to improve the optimization process. Compared with existing methods: 1) the proposed method achieves precise control of the ESD level in the SSN region; and 2) the ESD in the SSN region is reduced by 8.8 dB, while the beampattern matching MSE is decreased by 0.02 dB.