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.

💡 Research Summary

The paper addresses the problem of precise user trajectory estimation and subsequent optimal path planning in outdoor millimeter‑wave (mmWave) multiple‑input multiple‑output (MIMO) networks. It introduces a two‑stage framework that first extracts a Beamformed Fingerprint (BFF) – a binary matrix obtained by sweeping a predefined beam codebook at the base station and recording the power‑delay profile (PDP) for each beam – and then feeds sequences of BFFs into a Transformer Network (TN) to predict the user’s continuous 2‑D positions over time. The BFF representation reduces dimensionality and noise sensitivity while preserving rich spatial‑temporal information inherent to mmWave propagation.

In the first stage, the authors design a sequence‑to‑sequence Transformer architecture equipped with positional encodings that capture both beam order and temporal order. Multi‑head self‑attention learns the relative importance of each beam’s PDP pattern, enabling detection of subtle direction changes that traditional recurrent models (RNN, LSTM) often miss. The loss combines mean‑squared error for coordinate regression with a regularization term that enforces smoothness across consecutive predictions. Training is performed on a large synthetic dataset generated by 28 GHz ray‑tracing simulations covering thousands of grid points and multiple time steps. Experimental results show that the Transformer reduces average localization error by roughly 15 % compared with state‑of‑the‑art CNN‑RNN hybrids and generalizes well to unseen trajectories.

The second stage integrates the predicted trajectory into an Informed Rapidly‑exploring Random Tree (iRRT*) algorithm. Conventional iRRT* limits sampling to an ellipsoidal region defined by the start‑goal Euclidean distance; the proposed method further restricts sampling to the corridor suggested by the Transformer’s output, thereby accelerating convergence. Moreover, the attention weight variance is interpreted as a measure of prediction uncertainty and incorporated as a cost penalty for regions with high uncertainty, effectively steering the planner away from potentially hazardous zones (e.g., areas with weak signal). The resulting planner consistently finds near‑optimal paths within an average of 1.2 seconds, with path lengths within 2 % of the theoretical optimum, outperforming standard RRT* and PRM baselines.

The authors discuss practical considerations such as the trade‑off between codebook size and measurement latency, the need for real‑world validation beyond static ray‑tracing environments, and potential extensions including adaptive online codebook design and reinforcement‑learning‑based replanning for dynamic obstacles. Overall, the work demonstrates that combining rich BFF data with modern attention‑based deep learning and informed sampling‑based planning yields a powerful solution for high‑precision navigation in future mmWave‑enabled outdoor networks.