  This paper presents a linear least squares method for fiber-longitudinal
power profile estimation (PPE), which estimates an optical signal power
distribution throughout a fiber-optic link at a coherent receiver. The method
finds the global optimum in least square estimation of longitudinal power
profiles, thus closely matching true optical power profiles and locating loss
anomalies in a link with high spatial resolution. Experimental results show
that the method achieves accurate PPE with an RMS error from OTDR of 0.18 dB.
Consequently, it successfully identifies a loss anomaly as small as 0.77 dB,
demonstrating the potential of a coherent receiver in locating even splice and
connector losses. The method is also evaluated under a WDM condition with
optimal system fiber launch power, highlighting its feasibility for use in
operations. Furthermore, a fundamental limit for stable estimation and spatial
resolution of least-squares-based PPE is quantitatively discussed in relation
to the ill-posedness of PPE by evaluating the condition number of a nonlinear
perturbation matrix.
