ABSTRACT
Beamforming for transmission in a network is, in several aspects, more difficult than beamforming for reception. At first sight, the problems appear to be equivalent; because the radio channel is reciprocal, a good uplink beamformer should also work well in the downlink. Another fundamental difference is the channel knowledge. A receiver equipped with an antenna array can estimate the channel, or train a beamformer adaptively, using known pilot symbols in the transmitted signal. In a system with time division duplex, the uplink and downlink transmission shares the same frequency using different time slots. As long as the delay between the uplink and downlink time slots is short compared with the coherence time of the channel, the reciprocity principle of electromagnetics shows that the spatial signature of the downlink is identical to that of the uplink. If however, the duplex time separation is larger than the coherence time, instantaneous downlink channel is more or less uncorrelated with the estimated uplink channel.
