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Using two receive antennas at a mobile phone improves downlink performance. But because of the correlation of the two antennas, using one of them to transmit in the uplink is a good performance-complexity tradeoff. This creates an interesting scenario of asymmetric channel state information at the transmitter in a time division duplex system, where the downlink channel coefficients related to one of the two receive antennas can be learned by the base station from the uplink training due to reciprocity. We provide near optimal transmitter design by obtaining upper and lower bounds of the downlink ergodic capacity.