Beamformed Fingerprint-Based Transformer Network for Trajectory Estimation and Path Determination in Outdoor mmWave MIMO Systems

Radio transmissions in millimeter wave (mmWave) bands have gained significant interest for applications demanding precise device localization and trajectory estimation. This paper explores novel neural network (NN) architectures suitable for trajectory estimation and path determination in a mmWave multiple-input multiple-output (MIMO) outdoor system based on localization data from beamformed fingerprint (BFF). The NN architecture captures sequences of BFF signals from different users, and through the application of learning mechanisms, subsequently estimate their trajectories. In turn, this information is employed to find the shortest path to the target, thereby enabling more efficient navigation. Specifically, we propose a two-stage procedure for trajectory estimation and optimal path finding. In the first stage, a transformer network (TN) based on attention mechanisms is developed to predict trajectories of wireless devices using BFF sequences captured in a mmWave MIMO outdoor system. In the second stage, a novel algorithm based on Informed Rapidly-exploring Random Trees (iRRT*) is employed to determine the optimal path to target locations using trajectory estimates derived in the first stage. The effectiveness of the proposed schemes is validated through numerical experiments, using a comprehensive dataset of radio measurements, generated using ray tracing simulations to model outdoor propagation at 28 GHz. We show that our proposed TN-based trajectory estimator outperforms other methods from the recent literature and can successfully generalize to new trajectories outside the training set. Furthermore, our proposed iRRT* algorithm is able to consistently provide the shortest path to the target.