LPI Radar Waveform Design With Desired Cyclic Spectrum and Pulse Compression Properties

This paper considers the practical LPI radar waveform design problem for jointly achieving a desired cyclic spectrum and pulse compression properties. In this work, the weighted cyclic frequency sidelobe (WCFS) level is minimized to achieve the LPI purpose while the similarity constraint regarding a known radar waveform that occupies the desired detection properties is considered. The waveform design problem is then formulated as a quartic optimization problem with heterogeneous quadratic inequality constraints. These properties make the problem NP-hard in general. To solve this problem efficiently, by introducing necessary auxiliary variables, the original problem is converted into several quadratic optimization problems with respect to each independent variable under a separated linear inequality constraint, which can be efficiently solved by leveraging the alternation direction method of multipliers (ADMM) framework. Finally, the performance of the proposed method is demonstrated via numerical examples.