RIS-Enhanced Unimodular Waveform Design for LPI Beampattern Matching in a MIMO Radar System

Transmit beampatterns with high sidelobe levels radiate more energy toward unintended directions, a concern for low-probability-of-intercept (LPI) multiple-input multiple-output (MIMO) radar. To address this challenge, we propose a unimodular waveform design framework for LPI beampattern synthesis in a reconfigurable intelligent surface (RIS)-assisted MIMO radar. Different from conventional RIS-based methods that emphasize direction-of-arrival (DOA) estimation or signal-to-interference-plus-noise ratio (SINR) enhancement, our approach focuses on precise beampattern matching while ensuring constant-modulus constraints on both waveforms and RIS phase shifts. The problem is formulated as the minimization of the mean squared error (MSE) between the desired and synthesized beampatterns, subject to unimodular waveform and RIS phase-shift constraints. This leads to a nonconvex optimization problem with complex coupling between variables. To tackle this, we exploit the geometric structure of the solution space and observe that it resides on a product complex circle manifold (PCCM), which naturally encodes the modulus constraints. Building on this insight, we develop a manifold-based optimization algorithm that operates directly on the PCCM. In the representative single-beam example, the proposed method reduces the peak sidelobe level by more than 14 dB compared with the No-RIS reference. Under matched RIS configurations, it also achieves lower average beampattern MSE and sidelobe levels than the RIS-assisted GP and MM baselines.