This paper addresses the simultaneous optimization problem of the multi-objective waveform design for MIMO radar with collocated antennas. Inspired from the idea of alternating projection, a waveform design framework is presented based on the Arbitrary-Dimensional Iterative Spectral Approximation Algorithm (ADISAA). Multi-objective of waveform design such as transmit beampattern match, good correlation, spectrum notch can be controlled by the adjustable weights. Finally, the constant modulus signal is designed. Simulation results show: the proposed algorithm improves the correlation performance of waveform at a specified lag intervals after transmit beampattern matching, the spectrum notch is designed to avoid the spectrum band which is polluted by active jamming and color noise, and it has lower computational complexity.
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