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This work considers a multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing based multiuser broadcast system with precoding at the transmitter and feedback of channel state information. A general framework is presented for the transceiver design, and also for the design of the feedback link based on the quantization of the users' MIMO channel Gram matrices. The proposed design of the feedback link exploits the correlation of the channel response in the frequency domain due to the finite length of the channel time impulse responses to outperform other schemes based on feedback of the per carrier frequency responses. The transceiver design framework is based on a unitary linear transformation applied at the receivers which allows the computation of equivalent triangular channel response matrices at the transmitter. An analytic study of the error propagation due to the channel quantization in the feedback link and the computation of the equivalent triangular channel matrices is also performed. Based on the previous concepts, all the usual transceiver design criteria can be applied within this framework, and the particular case of a space-frequency precoder for robust mean square error minimization is derived as an example. Finally, the benefits of the proposed strategy are evaluated by means of numerical simulations and compared to other existing techniques.