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Multiuser interference (MUI) and co-space interference (CSI) are two challenging issues in design of multicarrier code-division multiple-access (MC-CDMA) systems when multiple antennas are used at both the transmitter and receiver sides (MIMO transmission). On the other hand, in cognitive radio (CR) system, the secondary users that use MC-MCDA technique must deactivate the subcarriers used by the primary users. This leads to loss of orthogonality of the conventional spreading codes such as Hadamard Walsh codes. In this paper, we have modified two recently proposed linear receivers to be deployed in MIMO MC-CDMA based CR downlink transmission where some of the subcarriers are turned off. To solve the resultant non-orthogonality problem, the complex carrier interferometry (CI) codes are utilized that exist for any length. The first method, called total interference cancellation (CI-TIC), is able to completely eliminate the CSI and the MUI. The other method is called CI symbol-chip level minimum mean square error (CI-SC-MMSE) that shows superior bit error performance with respect to CI-TIC. For different scenarios, simulation results show that the proposed CI based receivers are able to effectively mitigate the MUI and the CSI in comparison with the case where Hadamard Walsh codes are utilized.