Complex-Valued Hierarchical Fusion Network for Single-Frame Cross-Range Velocity Estimation With Millimeter-Wave MIMO Radar

Abstract

Conventional frequency-modulated continuous-wave (FMCW) processing directly measures radial velocity but does not provide the cross-range component from a single Doppler peak. This limitation constrains real-time motion sensing in short-range applications, especially in automotive traffic scenarios involving pedestrians and vehicles. This article investigates whether weak motion-induced curvature and joint chirp–antenna phase structure can support single-frame estimation of the 2-D in-plane velocity vector with a compact 24-GHz 2Tx–4Rx multiple-input multiple-output (MIMO) radar. A hierarchical dual-branch network is proposed: a position branch processes a complex range–angle (RA) map for localization, while a velocity branch processes complex range–velocity (RV) and velocity–angle (VA) maps together with a magnitude range–Doppler (RD) map for kinematic estimation, followed by a transformer decoder for set-based multitarget prediction. On simulated multitarget scenarios at short range, the method achieves an $F1$ -score of 0.959 (full held-out test set, gate-2.0 global Hungarian matching) with root-mean-square errors (RMSEs) of 0.64 and 1.05 m/s for radial and cross-range velocity, respectively, and an $F1$ -score of 0.904 with a cross-range RMSE of 1.894 m/s on a frame-disjoint, within-session real-world pedestrian evaluation. On the same real evaluation, the sign-error rate is 19.8% and the $\vert $ vcr $\vert $ RMSE is 1.52 m/s; an independent simulated diagnostic evaluation (not the primary $F 1=0.959$ result) yields 7.5% and 0.86 m/s. These results indicate that cross-range velocity is estimable from a single frame with a compact array. Detection accuracy decreases as the number of targets increases in the evaluated multitarget scenarios. Across the evaluated 0–20 m range, cross-range RMSE remains 1.04–1.14 m/s, while the simulated sign-error rate increases from 2.8% at 0–5 m to 13.3% at 15–20 m.