15 treated in the existing literature prior to this paper. General Result 3 : For pairwise switch without network coding, the counter-phase scheme outperforms the basic scheme with real A . Furthermore, the counter-phase scheme has low complexity because its computation does not optimize over the phases of A . VII. CONCLUSIONS We have proposed a framework for wireless MIMO switching to facilitate communications among multiple wireless stations. In our framework, a multi-antenna relay controls which stations are connected to which other stations with beamforming. Specifically eachbeamforming matrix at the multi-antenna relay realizes a switching permutation among the stations, represented by a switch matrix. By scheduling a set of switch matrices, full connectivity among the stations can be established. A salient feature of our MIMO switching framework is that it can cater to general traffic patterns consisting of a mixture of unicast traffic, multicast traffic, and broadcast traffic flow s among the stations. There are many nuances and implementation variations arising out of our MIMO switching framework. In this paper, we have only evaluated the performance of some of the variations. We first studied the “fair switching” setting in which each station wants to send equalamounts of traffic to all other stations. In this setting, we aim to deliver the same amount of data from each station i to each station j = i by scheduling a set of switch matrices. In general, many sets of switch matrices could be used for such scheduling. The problem of finding the set that yields optimal throughput is avery challenging problem combinatorially. Fortunately, for number of stations N = 4 or 5 , our simulation results indicate that different sets of switch matrices achieve roughly the same throughput, essentially rendering the selection of the optimal set a non-issue. We conjecture this will be the case for larger N as well. If this conjecture holds, then the complexity of the optimization problem can be decreased significantly as far as engineering design is concerned. We next moved to the study of single switch matrix and investigated the performances of different realizations for the same switch matrix (i.e., realizations using different beamforming matrices). Our general conclusion is that the use of physical-layer network coding can improve the throughput performance appreciably. In addition, we discover an interesting result for pairwise switch matrices. The computation cost of the beamforming matrix could be high in general. However, when the switch matrix is pairwise and network coding is not used, the computation of the beamforming matrix can be much simplified with a “counter-phase” approach.