  Hybrid analog and digital BeamForming (HBF) is one of the enabling
transceiver technologies for millimeter Wave (mmWave) Multiple Input Multiple
Output (MIMO) systems. This technology offers highly directional communication,
which is able to confront the intrinsic characteristics of mmWave signal
propagation. However, the small coherence time in mmWave systems, especially
under mobility conditions, renders efficient Beam Management (BM) in standalone
mmWave communication a very difficult task. In this paper, we consider HBF
transceivers with planar antenna panels and design a multi-level beam codebook
for the analog beamformer comprising flat top beams with variable widths. These
beams exhibit an almost constant array gain for the whole desired angle width,
thereby facilitating efficient hierarchical BM. Focusing on the uplink
communication, we present a novel beam training algorithm with dynamic beam
ordering, which is suitable for the stringent latency requirements of the
latest mmWave standard discussions. Our simulation results showcase the latency
performance improvement and received signal-to-noise ratio with different
variations of the proposed scheme over the optimum beam training scheme based
on exhaustive narrow beam search.
