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A multi antenna channel with partial channel state information at the transmitter (CSIT) is studied. The partial CSIT takes the form of the channel matrix corrupted by additive white Gaussian noise (AWGN) with a variance that is assumed to decay as a power of the signal-to-noise ratio (SNR). It is shown that under a long-term power constraint and in the regime of asymptotically high SNR, a large diversity gain over the channel can be achieved by using rarely a high power at the transmitter that compensates for bad channel realizations. Examples relating the diversity gain of the systems with the channel Doppler bandwidth are discussed.