WiDRa -- Enabling Millimeter-Level Differential Ranging Accuracy in Wi-Fi Using Carrier Phase

TL;DR

This paper tackles the limited absolute ranging accuracy of Wi‑Fi RTT methods by introducing WiDRa, a carrier-phase–based differential ranging approach that leverages the passband information of frame exchanges. By forming a sum-CP metric and carefully compensating symbol timing, CFO, and hardware impairments, WiDRa yields differential range estimates that track changes with millimeter precision, independent of system bandwidth. The authors develop a theoretical channel model, estimation strategies for CP values and CFO, and a robust differential-range estimator, validating the approach through simulations and real Wi‑Fi hardware experiments that show orders-of-magnitude improvements over RTT-based methods in LoS channels with high Rician factors. The work also outlines practical limitations (cycle slips, multi-path, overhead) and highlights future directions, including passive ranging, fusion with RTT, and direction finding, to broaden WiDRa’s applicability in real-world deployments.

Abstract

Although Wi-Fi is an ideal technology for many ranging applications, the performance of current methods is limited by the system bandwidth, leading to low accuracy of $\sim 1$ m. For many applications, measuring differential range, viz., the change in the range between adjacent measurements, is sufficient. Correspondingly, this work proposes WiDRa - a Wi-Fi based Differential Ranging solution that provides differential range estimates by using the sum-carrier-phase information. The proposed method is not limited by system bandwidth and can track range changes even smaller than the carrier wavelength. The proposed method is first theoretically justified, while taking into consideration the various hardware impairments affecting Wi-Fi chips. In the process, methods to isolate the sum-carrier phase from the hardware impairments are proposed. Extensive simulation results show that WiDRa can achieve a differential range estimation root-mean-square-error (RMSE) of $\approx 1$ mm in channels with a Rician-factor $\geq 7$ (a $100 \times$ improvement to existing methods). The proposed methods are also validated on off-the-shelf Wi-Fi hardware to demonstrate feasibility, where they achieve an RMSE of $< 1$ mm in the differential range. Finally, limitations of current investigation and future directions of exploration are suggested, to further tap into the potential of WiDRa.

Figures (12)

• Figure 1: An illustration of the $p$-th frame exchange between two Wi-Fi STAs for RTT-based range estimation. In EDCA Fine Time Measurement (FTM) protocol, the Request frame is an FTM frame and the Response frame is an ACK frame IEEE_11az. In trigger-based and non-trigger-based FTM protocol, the Request frame is an I2R NDP frame and the Response frame is an R2I NDP frame IEEE_11az. Here the clocks represent the fact that the time reference can be different at the two STAs.
• Figure 2: An illustration of absolute range $A_p$, differential range $D_p \triangleq A_p-A_{p-1}$ and relative range $R_{q,p} \triangleq A_p-A_{q}$ frame exchanges $p \in \{1,2,3\}$ between two Wi-Fi STAs.
• Figure 3: An illustration of the CP Request and Response frame exchange between two stations to enable ranging.
• Figure 4: Frame exchanges and steps performed by the STA 1 and STA 2.
• Figure 5: A scatter plot of $\widehat{\psi}^{(4)}_{p} - \widehat{\psi}^{(2)}_{p} - \widehat{\psi}^{(4)}_{p-1} + \widehat{\psi}^{(2)}_{p-1}$ versus $t_p^{(4)} + t_p^{(2)} - t_{p-1}^{(4)} - t_{p-1}^{(2)}$ from a measurement campaign involving two Intel AX210 chips, with other parameters as in Section \ref{['subsec_real_data']}. The data belongs to a time window of $W=0.5$ s with the STA 2 speed being $0.35$ m/s.

Theorems & Definitions (9)

• Lemma 1
• proof
• Lemma 2
• proof
• Remark 1
• Remark 2
• Remark 3
• proof : Proof of Lemma \ref{['Lemma_CSI_acq']}
• proof : Proof of Lemma \ref{['Lemma_CSI_resp']}