  In this paper, we propose an efficient downlink channel reconstruction scheme
for a frequency-division-duplex multi-antenna system by utilizing uplink
channel state information combined with limited feedback. Based on the spatial
reciprocity in a wireless channel, the downlink channel is reconstructed by
using frequency-independent parameters. We first estimate the gains, delays,
and angles during uplink sounding. The gains are then refined through downlink
training and sent back to the base station (BS). With limited overhead, the
refinement can substantially improve the accuracy of the downlink channel
reconstruction. The BS can then reconstruct the downlink channel with the
uplink-estimated delays and angles and the downlink-refined gains. We also
introduce and extend the Newtonized orthogonal matching pursuit (NOMP)
algorithm to detect the delays and gains in a multi-antenna multi-subcarrier
condition. The results of our analysis show that the extended NOMP algorithm
achieves high estimation accuracy. Simulations and over-the-air tests are
performed to assess the performance of the efficient downlink channel
reconstruction scheme. The results show that the reconstructed channel is close
to the practical channel and that the accuracy is enhanced when the number of
BS antennas increases, thereby highlighting that the promising application of
the proposed scheme in large-scale antenna array systems.
