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In high-resolution radars or at low gazing angles, the clutter is more satisfied in the compound-Gaussian model. Meanwhile, the polarisation diversity can be exploited to enhance the detection performance. Motivated by extending the detection problem of multiple-input multiple-output radar to such cases, this study mainly addresses the adaptive detectors design with an unknown covariance matrix based on Rao and Wald criterions. The two-step design strategy is adopted. Three estimation strategies of covariance with secondary data, such as sampled covariance matrix (SCM), normalised sampled covariance matrix (NSCM) and fixed point estimation (FPE) matrix, are introduced to make derived receivers fully adaptive. A thorough performance assessment is given by several numerical examples, the results of which show that Rao and Wald tests can provide good detection performance in even spikier clutter, and the polarimetric diversity can also be exploited to improve the detection performance. Meanwhile, the FPE strategy is more suitable to implement the adaptive detection algorithms, and the adaptive loss is completely acceptable in practical applications.