Waveform Optimization for MIMO Radar in Colored Noise: Further Results for Estimation-Oriented Criteria

Previous work on multiple-input multiple-output (MIMO) radar waveform design in colored noise based on minimizing minimum mean-square error (MMSE) and normalized mean-square error (NMSE) only considered the optimization of the singular value of the waveform matrix, while the optimization of singular vectors, which forms a basis of singular value optimization, was not stressed enough. In this correspondence, we revisit the waveform design problem for MIMO radar in colored noise based on MMSE and NMSE respectively. Further results for the optimal solutions under both criteria are derived. We prove the optimality of “matching” with the target and colored noise for the singular vectors of the transmitted waveform. Moreover, to obtain minimum MMSE/NMSE, the pairing of the eigenvectors of the target and noise should be carefully designed, where the optimal pairing of the eigenvectors based on MMSE is fixed while the optimal pairing based on NMSE changes according to the transmitted power, the strength of the target, and noise.