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The theoretical feasibility is explored of spectrum-sharing between radar and wireless communications systems via an interference mitigation processing approach. The new approach allows radar and wireless systems to operate at the same carrier frequency if the radar possesses a multiple-input multiple-output (MIMO) structure. A novel signal processing approach is developed for coherent MIMO radar that effectively minimizes the arbitrary interferences generated by wireless systems from any direction, while operating at the same frequency using cognitive radio technology. Various theoretical aspects of the new approach are investigated, and its effectiveness is further validated through simulation.