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Transmission techniques for the wireless multi-antenna broadcast channel often require that the receivers feed back their channel state information (CSI) to the transmitter. In this paper, we propose a limited feedback method to approximate zero-forcing beamforming. Each user feeds back quantized information about channel direction and a deterministic lower bound on its signal-to-interference-plus-noise ratio (SINR), which require no more than an integer and a real number. With this information, the Base Station performs user scheduling, beamforming and rate adaptation. In this method, the information from both receiver and transmitter sides are taken into account to arrive at a tight lower bound on the supported rate of each user. Since a lower bound on the SINR is fed back, the proposed method avoids outage. We discuss the feedback load of the method, and show numerical results of the relationship between sum-rate and feedback load, SNR and number of users, as well as a comparison with similar methods.