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We consider the effect of imperfect separability in the received signals on the detection performance of multi-input multi-output (MIMO) radar with widely separated antennas. The mutual orthogonality among the received signals is often assumed but cannot be achieved in practice for all Doppler and delay pairs. We introduce a data model considering the correlation among the data from different transmitter-receiver pairs as unknown parameters. Based on the expectation maximization algorithm, we propose a method to estimate the target, correlation, and noise parameters. We then use the estimates of these parameters to develop a statistical decision test. Employing the asymptotic statistical characteristics and the numerical performance of the test, we analyze the sensitivity of the MIMO radar with respect to changes in the cross-correlation levels of the measurements. We demonstrate the effect of the increase in the correlation among the received signals from different transmitters on the detection performance.