Computationally efficient waveform design in spectrally dense environment

The problem of unimodular radar waveform design with similarity constraint in spectrally dense environment is considered. The corresponding optimization problem is nonconvex and additionally large-scale. Indeed, the waveform length can be of several thousands and the waveform has to be designed in every coherent processing interval. Since the problem is nonconvex, the majorization-minimization (MaMi) method is used for addressing it, and since it is large-scale, the alternating direction method of multipliers (ADMM) is adopted. Thus, we develop a computationally efficient approach for solving the problem by using MaMi with proper design of majorization function together with alternating ADMM with newly proposed computationally efficient proximal projections. We evaluate the computational cost of the proposed algorithm and show its fast convergence unmatched by existing approaches in terms of simulations.