  There is a fundamental trade-off between the channel representation
resolution of codebooks and the overheads of feedback communications in the
fifth generation new radio (5G NR) frequency division duplex (FDD) massive
multiple-input and multiple-output (MIMO) systems. In particular, two types of
codebooks (namely Type I and Type II codebooks) are introduced with different
resolution and overhead requirements. Although the Type I codebook based scheme
requires lower feedback overhead, its channel state information (CSI)
reconstruction and beamforming performance are not as good as those from the
Type II codebook based scheme. However, since the Type I codebook based scheme
has been widely used in 4G systems for many years, replacing it by the Type II
codebook based scheme overnight is too costly to be an option. Therefore, in
this paper, using Type I codebook, we leverage advances in cutting plane method
to optimize the CSI reconstruction at the base station (BS), in order to close
the gap between these two codebook based beamforming schemes. Numerical results
based on channel samples from QUAsi Deterministic RadIo channel GenerAtor
(QuaDRiGa) are presented to show the excellent performance of the proposed
algorithm in terms of beamforming vector acquisition.
