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Transmission precoding in MIMO wireless systems is an effective technique that can significantly improve system capacity and diversity gain. In general, the effectiveness of MIMO precoding depends critically on the knowledge of channel state information available at the transmitter. In this work we describe a novel method for the downlink channel estimation based on a novel feedback mechanism. To minimize processing need at mobile units, the receiver in this new framework returns a fraction of its received data back for the base-station to extract downlink channel information in the form of a quadratic channel product. The base-station can then utilize the quadratic channel product to design channel-aware downlink precoders. This bandwidth efficient feedback scheme applies to both flat fading and frequency selective MIMO channels.