Optimal and robust waveform design for MIMO radars in the presence of clutter

Waveform design for target identification and classification in MIMO radar systems has been studied in several recent works. While the previous works assumed that the noise was independent of the transmission signals, here we extend the results to the signal dependent noise (clutter). We consider two scenarios. In the first scenario it is assumed that different transmit antennas see uncorrelated aspects of the target. In the second scenario, we consider the correlated target. As clutter is dependent to signal, target estimation error cannot vanish only by increasing the transmission power. It can be shown that in the second scenario, MIMO radar receiver can nullify the clutter subspace. Thus, in the second scenario, target estimation error tends to zero if the transmission power tends to infinity. We consider waveform design problem for these scenarios based on MMSE and MI criteria. Like previous works, we find that these criteria lead to the same solution. Our problems lead to the convex optimization problems, which can be efficiently solved through tractable numerical methods. Closed-form solutions are also developed for this SDP problem in two cases. In the first case, target and clutter covariance matrices are jointly diagonalizable and in the second, signal to noise ratio (SNR) is assumed to be sufficiently high. We also present two suboptimal formulations which require less knowledge of the statistical model of the target. In the first one the robust waveforms are computed by minimizing the estimation error of the worst-case target realization and in the second, target estimation error of the scaled least square (SLS) estimator is minimized.