Sparse frequency waveform design based on PSD fitting

New method for designing sparse frequency waveform with sidelobe constraint is proposed in this paper. First, optimal power spectrum density (PSD) corresponding to minimum integrated sidelobe energy (ISE) is derived for sparse frequency waveform. Then, based on this optimal condition, the original problem dealing with both PSD requirement and sidelobe requirement is reformulated into a problem focusing only on PSD. In this way, the proposed method has a simpler optimization objective function and enjoys more efficiency than current methods focusing on both two requirements. Several optimization techniques are applied to this simpler design concept and numerical studies are provided to illustrate the effectiveness of it.