We describe an RFID tag reading system comprising a plurality of transmit/receive antennas to provide spatial transmit/receive signal diversity, and a tag signal decoder. The system combines received RF signals from the antennas, and the antennas are spaced apart from one another sufficiently for one said antenna not to be within the near field of another. The system performs a tag inventory cycle comprising a plurality of tag read rounds, each having a set of time slots during which a said tag is able to transmit tag data including a tag ID. The system is configured to perform, during a tag inventory cycle, one or both of: a change in a frequency of the tag interrogation signals transmitted simultaneously from the plurality of antennas, and a change in a relative phase of a the RF tag interrogation signal transmitted from one of the antennas with respect to another.