  The rollout of millimeter-wave (mmWave) cellular network enables us to
realize the full potential of 5G/6G with vastly improved throughput and
ultra-low latency. MmWave communication relies on highly directional
transmission, which significantly increase the training overhead for fine beam
alignment. The concept of using out-of-band spatial information to aid mmWave
beam search is developed when multi-band systems operating in parallel. The
feasibility of leveraging low-band channel information for coarse estimation of
high-band beam directions strongly depends on the spatial congruence between
two frequency bands. In this paper, we try to provide insights into the answers
of two important questions. First, how similar is the power angular spectra
(PAS) of radio channels between two well-separated frequency bands? Then, what
is the impact of practical system configurations on spatial channel similarity?
Specifically, the beam direction-based metric is proposed to measure the power
loss and number of false directions if out-of-band spatial information is used
instead of in-band information. This metric is more practical and useful than
comparing normalized PAS directly. Point cloud ray-tracing and measurement
results across multiple frequency bands and environments show that the degree
of spatial similarity of beamformed channels is related to antenna beamwidth,
frequency gap, and radio link conditions.
