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 built from the line-of-sight (LOS) path and first-order reflections, or purely first-order reflections, requiring high resolution channel estimates to ensure centimeter level accuracy. In this paper, we consider a mmWave multiple-input multiple-output (MIMO) system employing a hybrid architecture, and develop a low complexity two-stage multidimensional orthogonal matching pursuit (MOMP) algorithm suitable for accurate estimation of high dimensional channels. Then, a deep neural network (DNN) called PathNet is designed to classify the order of the estimated channel paths, so that only the LOS path and first-order reflections are selected for localization. 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 geometric localization. Simulation results obtained with realistic vehicular channels indicate that localization errors below 28 cm can be achieved for 80% of the users when the LOS path is present, while sub-meter accuracy can be achieved for 55% of the users in NLOS conditions.