Metric Learning Based Positioning

We predict the physical distance between two users based on the Channel State Information (CSI) of wireless channels. The CSI of each user is measured at several multiantenna base stations. We consider a supervised metric learning framework using a neural network that ensures that the properties of a metric are fulfilled: zero distance between a point and itself, non-negativity, symmetry, and the triangle inequality. The training data set consists of CSI from pairs of points and their physical distance. As an example use case, we consider fingerprint localization, where creating large datasets is impractical. The metric can be learned from a small dataset because the number of training data pairs increases quadratically in the number of CSI-fingerprints. We use the learned metric for Weighted K-Nearest Neighbor (WKNN) localization, to find neighbors in the dataset and to compute the weighting vector. Simulation results show that the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$80^{\text{th}}$</tex> percentile error can be improved by some 70 % using the learned metric as compared to the Euclidean distance for WKNN regression.