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The space-time adaptive processing in the presence of Doppler and direction-of-arrival (DOA) mismatches have been addressed. Doppler and DOA mismatches degrade the performance of the minimum variance distortion less response (MVDR) processor because of the signal cancellation. In this paper, we first choose weights that minimize the total power output of the space-time adaptive processor with imposing two quadratic constraints such that the magnitude of space-time response of two points exceed unity. Then, the magnitude of space-time response within a range of the Doppler frequencies and angles of arrival is forced to exceed unity. The simulation results show that this method is robust against such these mismatches.