Closed-form solution to directly design frequency modulated waveforms for beampatterns

The targets image performance depends on the transmit beampattern and power-spectral-density of the probing signal. To design such probing signals for multiple-input multiple output (MIMO) radar, conventional algorithms are iterative in nature, therefore high computational complexity restricts their use in real time applications. In this paper, to achieve the desired beampattern, a novel closed-form algorithm to design frequency-modulated (FM) waveforms for MIMO radar is proposed. The proposed algorithm has negligible computational complexity and yields unity peak-to-average power ratio constant envelope waveforms. Moreover, in contrast to the narrow band algorithms, it has almost flat main and side lobes. In the proposed algorithm, a relationship between the width of symmetric beampattern and the product of initial frequency and duration of the baseband FM waveforms is developed.