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This paper discusses the reader's transmit signal design problem for RFID MIMO systems. First a mathematical model for this kind of system is developed from the viewpoint of signal processing. Then two spatial matching transmission schemes, namely matched to a fixed antenna at the tag or matched to a selected antenna at the tag, for the reader's signals are proposed. Simulation results illustrate that the proposed approaches can greatly improve the BER performance of RFID MIMO systems, compared to the uniform transmission policy.