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A wireless relay with multiple antennas is called a Multiple-Input-Multiple-Output (MIMO) switch if it forms a one-to-one mapping from the inputs (uplinks) to the outputs (downlinks). This paper studies the case with N source stations and N destination stations (which may be the same set), so that the mapping is any permutation of the N inputs. Moreover, the switching is achieved by "Pre-code-and-forward", i.e., the relay pre-codes the received vector signal by a zero-forcing matrix and transmits it, so that each destination station receives only its desired signal with enhanced noise but no interference.
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