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Waveform design for target identification and classification in multiple-input multiple-output (MIMO) radar systems has been studied in several recent works. In previous works, optimal signals for an estimation algorithm are found assuming that only signal- independent noise exists. This work extends previous research by studying the case where clutter is also present. We develop a procedure to design the optimal waveform which minimizes estimation error at the output of the minimum mean squared error (MMSE) estimators in two scenarios. In the first one different transmit antennas see uncorrelated aspects of the target, and we consider the correlated target aspects in the second one. Estimation error in the first case will not zero even if the transmit power tends to infinity. This value of this error is referred to as the lower estimation error bound εOUND. It can be shown that since the MIMO radar receiver can null out the clutter subspace, εOUND is zero in the second scenario. Waveform design for MMSE estimator under the uncorrelated target aspects assumption, leads to the semi-definite programming (SDP) problem, a convex optimization problem which can be efficiently solved through numerical methods. An explicit solution is developed for this SDP problem in two cases. In the first case target and clutter covariance matrices are jointly diagonalizable, and in the second one the signal-to-noise ratio (SNR) is sufficiently high. Finding optimal transmit signals for the correlated target aspects scenario also results in an SDP problem.