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We investigate transmission strategies for flat-fading multiple antenna channels with t transmit and r receive antennas, and with channel state information (CSI) partially known to the transmitter. We start with an assumption that the first n eigenvectors of H/sup /spl dagger//H, where 0/spl les/n/spl les/min(t,r) and H is the channel matrix in /spl Copf//sup r/spl times/t/, are available at the transmitter as partial spatial information of the channel. A beamforming method is proposed in which a beamforming matrix is determined from the n eigenvectors in some predefined way; as a result, the receiver also knows the beamforming matrix. With this beamforming scheme, we develop a new multiple antenna system concept that provides a mechanism to reduce the amount of channel feedback information. This paper focuses on deriving the channel capacity of the multiple antenna channels employing the proposed beamforming and feedback methods. An important task for achieving capacity is the solution of interesting optimization problems for the optimal power allocation over the transmit symbols. The results show that the proposed methods lead to systems wherein the amount of feedback information can be significantly reduced with a minor sacrifice of achievable transmission rate.