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This study considers the detection problem of multiple-input multiple-output (MIMO) radar in the presence of a compound-Gaussian clutter. Two new detectors based on the Rao and Wald criteria are devised under the known covariance matrix. The theoretical expression for the probability of false alarm is developed and constant false alarm (CFA) rate behaviour is remarked on. Furthermore, the fully adaptive approximated Rao and Wald tests are investigated in place of the exact covariance matrix with a suitable estimator using secondary data. Finally, several numerical simulations with typical parameters are provided and discussed.