Multiple-input multiple-output (MIMO) radar has superior performance to conventional one. It has been introduced to almost every application field of conventional radar in recent years. In practical application, MIMO radar also faces the problem of congested spectrum assignment, which makes it not possible to have a continuous clear band with large bandwidth. Sparse frequency waveform that contains several individual clear bands is a desirable solution to this problem. In this paper, we propose a method to design sparse frequency waveform set with low sidelobes in autocorrelations and cross-correlations by optimizing an objective function constructed based on Power Spectrum Density requirement and sidelobe performances of waveform set. Thus, besides the property of approximate orthogonality, the designed waveforms obtain the ability of avoiding spectrum interference to/from other users. The waveform is phasecoded and thereby has constant modulus. The effectiveness of the proposed method is illustrated by numerical studies. Practical implementation issues such as quantization effect and Doppler effect are also discussed.
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