Previously, the Generalized Likelihood Ratio Test - Linear Quadratic (GLRT-LQ) has been extended to the Multiple-Input Multiple-Output (MIMO) case where all transmit-receive subarrays are considered jointly as a system such that only one detection threshold is used. The new MIMO detector is Constant False Alarm Rate (CFAR) with respect to the clutter power fluctuations. In this paper, the adaptive version of this detector is considered, as well as a fluctuating target model similar to that of the Swerling Target. The degradation of the detection performance due to the estimation of the covariance matrix and the fluctuation of the target is studied through simulations for both the well-known Optimum Gaussian Detector (OGD) and the new MIMO detector under Gaussian and non-Gaussian clutter.