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A multiple antenna downlink channel where limited channel feedback is available to the transmitter is considered. In a vector downlink channel (single antenna at each receiver), the transmit antenna array can be used to transmit separate data streams to multiple receivers only if the transmitter has very accurate channel knowledge, i.e., if there is high-rate channel feedback from each receiver. In this work it is shown that channel feedback requirements can be significantly reduced if each receiver has a small number of antennas and appropriately combines its antenna outputs. A combining method that minimizes channel quantization error at each receiver, and thereby minimizes multi-user interference, is proposed and analyzed. This technique is shown to outperform traditional techniques such as maximum-ratio combining because minimization of interference power is more critical than maximization of signal power in the multiple antenna downlink. Analysis is provided to quantify the feedback savings, and the technique is seen to work well with user selection and is also robust to receiver estimation error.