"To perform transmit beamforming, the transmitter needs to have accurate knowledge
of the channel, which in the case of TDD is easily available owing to channel reciprocity but for FDD requires a feedback channel to learn the channel characteristics."
What's meant by channel reciprocity?
And how it could be used for channel estimation?
I suspect that the receiver performs analysis on the phases and amplitudes of the received signals form several antennas in a phased array and from them deduces the azimuth of the received signal. It then sets the amplitudes and phases of the signals sent to the transmitter phased array antennas to make the beam pattern maximum at the azimuth of the received signal.
This will produce the most likely probability of the remote terminal receiving the best possible quality of signal in the reverse direction.
So the problem with FDD is that the uplink is on other channel than the down link so the Tx can't estimate the downlink channel model based on the received data on the uplink channel.
Reciprocity implies that the channels is very nearly the same in both directions, and so information gathered by reception can be used to do beamforming in tranmsit direction. in FDD since uplink and downlink frequencies are different, this cannot be done, which is not the case for TDD.
-b