The performance of multiuser MIMO systems can be significantly increased by channel-aware scheduling and signal processing at the transmitters based on channel state information. In the multiple antenna uplink multicarrier scenario, the base station decides centrally on the optimal signal processing and spectral power allocation as well as scheduling. An interesting challenge is the reduction of the overhead in order to inform the mobiles about their transmit strategies. In this work, we propose to reduce the feedback by chunk processing and quantization. We maximize the weighted sum rate of a MIMO OFDM MAC under individual power constraints and chunk size constraints. An efficient iterative algorithm is developed and convergence is proved. The feedback overhead as a function of the chunk size is considered in the rate computation and the optimal chunk size is determined by numerical simulations for various channel models. Finally, the issues of finite modulation and coding schemes as well as quantization of the precoding matrices are addressed.