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A wireless relay which forms a one-to-one mapping from the inputs (uplinks) to the outputs (downlinks) is called a Multiple-Input-Multiple-Output (MIMO) switch. The MIMO switch carries out pre-code-and-forward, where all users send their signals in the uplink and then the MIMO switch pre-codes the received vector signal for broadcasting in the downlink. Ideally, each user employs a receive filter to recover its desired signal from one other user with no or little interference from other users. The authors propose a joint design of the pre-coder and the receive filters to achieve the Minimum-Mean-Square-Error (MMSE), assuming full channel state information is available at the relay.
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