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We propose and analyze a limited feedback scheme for downlink MIMO-OFDMA. Our analysis explicitly accounts for the feedback overhead by assuming a time division duplex system in which all feedback and data transmission must occur with a coherence time. As the fraction of coherence time devoted to feedback increases, the base station can allocate resources more efficiently, but has less time available for data transmission. In the proposed scheme, the base-station sequentially receives feedback from the users and decides when to stop receiving additional feedback and begin data transmission. Each user feeds back their best codeword (beam) selected from a beam-forming codebook on each group of OFDM sub-channels, provided that the channel gain exceeds a given threshold. For a given feedback threshold, the optimal stopping rule used by the base station is derived. With this rule we show that the total throughput of this scheme scales linearly with the number of users, provided that the number of OFDM sub-channels also scales with fixed ratio. The effect of varying the coherence time and feedback rate is also characterized.