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The problem of allocating network resources to the users of a cellular network with multiple antennas in a fair way is investigated. We propose a packet scheduler called MIMO packet-by-packet generalized processor sharing (MPGPS). The scheduler can provide fair access to the channels for users and is work conserving. It also compensates lagging users and decreases the average delay of users. Comparisons with a couple of scheduling algorithms considering traffic characteristics and the mobility of users demonstrate the superior performance of our scheduler.