Manifold Optimization for Distributed Phased-MIMO Radar Broad Beampattern Design

This letter investigates the low-variance broad beampattern design method in distributed phased multiple-input multiple-output (phased-MIMO) radar. The constant modulus constraint across multiple subarrays results in a low-rank and nonconvex objective function, which is traditionally addressed by reformulating it into a solvable semidefinite program through convex relaxation. In contrast, we propose a Riemannian manifold-based method to directly address the low-rank problem without relaxation. The low-variance broad beampattern design is first transformed into an unconstrained quadratic form on a complex constant modulus manifold. Then, a Riemannian conjugate gradient descent (RCGD)-based optimization is proposed to solve the nonconvex objective function by deriving the gradient descent direction and adaptive step size. Numerical simulations demonstrate the superior performance in terms of computation speed and accuracy compared to the conventional methods.