  Channel charting (CC) consists in learning a mapping between the space of raw
channel observations, made available from pilot-based channel estimation in
multicarrier multiantenna system, and a low-dimensional space where close
points correspond to channels of user equipments (UEs) close spatially. Among
the different methods of learning this mapping, some rely on a distance measure
between channel vectors. Such a distance should reliably reflect the local
spatial neighborhoods of the UEs. The recently proposed phase-insensitive (PI)
distance exhibits good properties in this regards, but suffers from ambiguities
due to both its periodic and oscillatory aspects, making users far away from
each other appear closer in some cases. In this paper, a thorough theoretical
analysis of the said distance and its limitations is provided, giving insights
on how they can be mitigated. Guidelines for designing systems capable of
learning quality charts are consequently derived. Experimental validation is
then conducted on synthetic and realistic data in different scenarios.
