Wideband MIMO radar exhibits great potential in achieving the goals of high resolution imaging, but it also suffers from the electromagnetic signal congestion and interference problems, especially for radar that works in Very High Frequency (VHF) and Ultra High Frequency (UHF) band. To solve this problem, a cyclic iterative method for designing orthogonal sparse frequency waveforms is proposed. Firstly, the desired spectrum is used as an auxiliary variable, and a new objective function is constructed based on both the mean square error of the spectrum of transmitting waveform with the desired one and the integration side-lobe levels. The optimization model is established under the constraint that the waveform is constant envelope meanwhile the spectrum magnitude lies between the pre-established upper and lower bounds. Then, under the framework of cyclic iterative algorithm, fast Fourier transform and spectral decomposition techniques are used to improve computational efficiency. Simulation results show that the proposed method has good performance in designing orthogonal sparse frequency waveforms with low auto-correlation and cross-correlation side lobes.
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