Distributed Riemannian Manifold Optimization for Unimodular Waveform Set Design Toward AAF/CAF Shaping

The unimodular waveform set with desired autoambiguity functions (AAFs) and cross-ambiguity functions (CAFs) have extensive applications in assessing interference suppression performance across range and Doppler dimensions. In this article, we focus on designing low computational complexity but theoretically-guaranteed algorithms to achieve these kinds of waveforms. Specifically, we first formulate the waveforms set designing problem as a quartic polynomial minimization problem under constant modulus constraint, aiming at minimizing the response values within the interested areas of the AAFs and CAFs. Then, the established optimization problem is equivalently transformed into a series of constrained subproblems by introducing auxiliary variables. To reach its good approximate solution efficiently, we further convert the constrained subproblem into an unconstrained one over manifold space, which is further addressed by employing the Riemannian conjugate gradient method. In addition, we also theoretically prove that the proposed approach can converge to the stationary point of the original nonconvex problem. Experiments based on the numerical simulations and hardware systems are conducted to demonstrate the effectiveness and superiority of the proposed method and explore the influence of the nonlinear instruments.