Channel Charting: an Euclidean Distance Matrix Completion Perspective

Channel charting (CC) is an emerging machine learning framework that aims at learning lower-dimensional representations of the radio geometry from collected channel state information (CSI) in an area of interest, such that spatial relations of the representations in the different domains are preserved. Extracting features capable of correctly representing spatial properties between positions is crucial for learning reliable channel charts. Most approaches to CC in the literature rely on range distance estimates, which have the drawback that they only provide accurate distance information for colinear positions. Distances between positions with large azimuth separation are constantly underestimated using these approaches, and thus incorrectly mapped to close neighborhoods. In this paper, we introduce a correlation matrix distance (CMD) based dissimilarity measure for CC that allows us to group CSI measurements according to their co-linearity. This provides us with the capability to discard points for which large distance errors are made, and to build a neighborhood graph between approximately collinear positions. The neighborhood graph allows us to state the problem of CC as an instance of an Euclidean distance matrix completion (EDMC) problem where side-information can be naturally introduced via convex box-constraints.