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In a generic switching problem, a switching pattern consists of a one-to-one mapping from a set of inputs to a set of outputs (i.e., a permutation). The authors propose and investigate a wireless switching framework in which a multi-antenna relay is responsible for switching traffic among a set of N stations. They refer to such a relay as a MIMO switch. With beamforming and linear detection, the MIMO switch controls which stations are connected to which stations. Each beamforming matrix realizes a permutation pattern among the stations. They refer to the corresponding permutation matrix as a switch matrix. By scheduling a set of different switch matrices, full connectivity among the stations can be established.
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