Clearing Wireless Signal Chaos in Urban Canyons: Scalable Multipath Detection from Standard GNSS Correlators via Multi-Frequency Diversity

Accurate wireless positioning and sensing in dense urban environments is fundamentally limited by multipath propagation, yet most existing countermeasures either rely on specialized hardware, major receiver redesign, or data-driven classifiers with weak physical interpretability. Here we introduce a multi-frequency cross-product area (MF-CPA) framework for multipath detection that operates entirely on standard early-prompt-late (EPL) in-phase (I) and quadrature (Q) correlator outputs and requires no modification of the receiver front-end or tracking-loop architecture. Using GNSS as a representative multi-frequency wireless positioning system, we first perform a large-scale sensitivity analysis of E/P/L correlators across multipath delay, attenuation, Doppler and phase rotation, and show that the six-branch I-Q structure, combined through a cross-product area metric, maximizes multipath information density while remaining analytically tractable. Under multipath-free conditions, we derive the closed-form distribution of the CPA statistic and its detection threshold for a prescribed false-alarm probability, and then extend this construction to MF-CPA by normalizing and projecting multi-frequency correlator vectors into fixed angular sectors in the complex plane. Hardware-in-the-loop simulations using Spirent Sim3D with a 3D model of the Lujiazui urban canyon show that MF-CPA achieves around 50-80% multipath detection rate at a few-percent false-detection rate for multi-frequency GPS, BDS and Galileo signals, and mitigates frequency-dependent blind zones inherent to single-frequency detectors. Real drive tests over a 2.7 km trajectory in the same environment confirm that the spatial patterns of MF-CPA detections on real data follow those predicted by simulation, indicating that multi-frequency cross-product geometry provides a practical and physically interpretable pathway towards robust multipath monitoring in next-generation wireless positioning and sensing systems. The code and data used in this work are open-sourced at https://github.com/SJTU-GNC/Date-and-code-for-MF-CPA.git.