Learning to Localize with Attention: from sparse mmWave channel estimates from a single BS to high accuracy 3D location

One strategy to obtain user location information in a wireless network operating at millimeter wave (mmWave) is based on the exploitation of the geometric relationships between the channel parameters and the user position. These relationships can be easily built from the LoS path and/or first order reflections, but high resolution channel estimates are required for high accuracy. In this paper, we consider a mmWave MIMO system based on a hybrid architecture, and develop first a low complexity channel estimation strategy based on MOMP suitable for high dimensional channels, as those associated to operating with large planar arrays. Then, a deep neural network (DNN) called PathNet is designed to classify the order of the estimated channel paths, so that only the line-of-sight (LOS) path and first order reflections are selected for localization purposes. Next, a 3D localization strategy exploiting the geometry of the environment is developed to operate in both LOS and non-line-of-sight (NLOS) conditions, while considering the unknown clock offset between the transmitter (TX) and the receiver (RX). Finally, a Transformer based network exploiting attention mechanisms called ChanFormer is proposed to refine the initial position estimate obtained from the geometric system of equations that connects user position and channel parameters. Simulation results obtained with realistic vehicular channels generated by ray tracing indicate that sub-meter accuracy (<= 0.45 m) can be achieved for 95% of the users in LOS channels, and for 50% of the users in NLOS conditions.