  Beam codebooks are a recent feature to enable high dimension multiple-input
multiple-output in 5G. Codebooks comprised of customizable beamforming weights
can be used to transmit reference signals and aid the channel state information
(CSI) acquisition process. Codebooks are also used for quantizing feedback
following CSI acquisition. In this paper, we characterize the role of each
codebook used during the beam management process and design a neural network to
find codebooks that improve overall system performance. Evaluating a codebook
requires considering the system-level dependency between the codebooks,
feedback, overhead, and spectral efficiency. The proposed neural network is
built on translating codebook and feedback knowledge into a consistent
beamspace basis similar to a virtual channel model to generate initial access
codebooks. This beamspace codebook algorithm is designed to directly integrate
with current 5G beam management standards without changing the feedback format
or requiring additional side information. Our simulations show that the neural
network codebooks improve over traditional codebooks, even in dispersive
sub-6GHz environments. We further use our framework to evaluate CSI feedback
formats with regard to multi-user spectral efficiency. Our results suggest that
optimizing codebook performance can provide valuable performance improvements,
but optimizing the feedback configuration is also important in sub-6GHz bands.
