Riemannian Manifold Optimization for Amplitude-Constrained Beampattern Synthesis

Beampattern synthesis is essential in modern communication, radar, and electronic warfare systems as it enables the design of customized radiation patterns. This letter introduces a method that employs Riemannian manifold optimization to effectively handle both the constant modulus constraint and dynamic range ratio (DRR) control in array beampattern synthesis. A multiobjective optimization function is developed to ensure uniform mainlobe response, ensure smooth beam transitions, concentrate energy at the beam center, and effectively suppress sidelobes. In addition, log-sum-exp smoothing techniques are utilized to convert nonsmooth problems into differentiable forms, precise control of the beam direction is achieved through exponential transformations, and a smoothing term based on the Laplacian matrix is introduced to minimize power deviation between beams. In addition, a DRR constraint is constructed using complex circles, ensuring that the constraint remains rigorously maintained throughout the optimization process. This letter demonstrates the effectiveness of the proposed method through examples of array pattern optimization under amplitude constraints. The results indicate that the proposed method not only achieves precise main lobe performance but also provides effective sidelobe suppression, all while strictly adhering to the amplitude constraints.