Waveform Design for Clutter Suppression With Adaptive Spectrum and Sidelobe via Riemannian Manifold Optimization

This paper studies clutter suppression from the frequency-domain perspective while considering the control of sidelobes. To achieve this purpose, we construct a bi-objective optimization model for signal-to-interference-plus-noise ratio and sidelobes under the constant modulus constraint. Furthermore, we generalize the model to multi-channel scenarios. Through this modeling approach, adaptive adjustment of the spectrum and sidelobes can be achieved. To solve the resulting high-order bi-objective non-convex optimization problem, we propose a manifold-based optimization algorithm. This algorithm transforms the constrained problem into an unconstrained optimization problem on the manifold space, thus avoiding approximation loss. In addition, it achieves efficient convergence by using an approximate Hessian matrix with a cautious update rule. We accelerate this algorithm using fast Fourier transform and analyze its computational complexity. Simulation results demonstrate the advantages of the proposed algorithm in clutter suppression, sidelobe control, and computational complexity.