Radio ranging with ultrahigh resolution using a harmonic radio-frequency identification system


The accurate sensing of the location of specific objects in an indoor setting is critical for applications including robotic feedback control and non-intrusive structural integrity monitoring. Current optical and ultrasound approaches often suffer from insufficient accuracy, obstruction by other objects, and ambiguous identification. Alternatively, conventional radar-like radio-frequency (RF) methods can suffer from problems such as multipath ambiguity, small time of flight, and limited item recognition. Attachment of a passive RF identification (RFID) tag can provide a unique marker by modulating the backscattering signal, but current systems struggle with high interference and noise, and thus have poor ranging accuracy. Here we show that a 1 GHz harmonic RFID system can provide a ranging resolution of less than 50 micrometres with a sampling rate of greater than 1 kHz. The fundamental limits on ranging precision in our system are traced to the phase noise of the RF source and the aperture jitter of the data converter. The small passive tag required for the approach can be embedded in indoor or underwater objects, as well as within building structures.


Accurate localization with unique identification of indoor objects and objects behind visual obstructions is critical in a variety of applications1,2,3,4,5,6. However, current approaches suffer from numerous fundamental problems. Optical methods typically achieve high in-plane resolution but offer limited ranging accuracy. Item recognition also has a high computing load unless identification markers are used. Furthermore, objects of interest may be covered by materials such as fabrics, plastics and building materials, which are opaque to light. Camera-based systems have been extensively developed7,8, and benefit from convenient use, rich information and sophisticated imaging algorithms. However, fine gesture recognition, vital-sign acquisition, three-dimensional (3D) localization of covered features or markers, and the control of haptic robotics remain challenging. Typically, multiple cameras from different viewing angles and high computational demands are required, which greatly increases system complexity and cost. In addition, camera systems are vulnerable to low ambient light and line-of-sight (LoS) obstruction. Other optical solutions, such as time-of-flight (ToF) cameras9, structured-light range scanning10 and light detection and ranging (LIDAR)11, share similar problems in terms of unique identification and LoS blocking. Ultrasound ranging and imaging is an alternative approach, but has issues in terms of impedance matching when going through different layers of materials, especially for air gaps. Another approach is to use location sensors based on microelectromechanical systems (MEMS), such as the servo motor and encoder. However, the size and mechanical structure of such systems cannot effectively fit onto the human body, delicate robotic structures12,13, or soft materials14. MEMS accelerometers and gyroscopes also suffer from slow drift and their power requirement limits deployment options.

Methods based on radio-frequency (RF) have also been widely investigated. The RF identification (RFID) system can be applied to obtain a unique item-level identification, and localization can be achieved by various methods such as received signal strength indication (RSSI) with landmarks15, phased-array radar16, synthetic aperture radar (SAR)17, and inverse SAR (iSAR)18. However, fundamental problems in terms of precision and reliability remain. The landmark-tag method uses known coordinates and RSSI of the reference tags to retrieve the position of the unknown target tag, but suffers from insufficient range sensitivity and ambiguity from multipath interference. The SAR and iSAR methods require relative motion between the tags and reader, which is not feasible for many scenarios. For tagless methods, the phased-array radar forms narrow beams to isolate the coverage areas, but the scanning time and spatial resolution of the beam will constrain the system localization capability. The frequency modulation continuous wave (FMCW) method requires a broad frequency bandwidth and a fast Fourier transform (FFT) time window to provide high spatial resolution, and the indoor multipath will still degenerate performance substantially. Although for some applications only the tagless methods are practical, in many other real-world applications, objects can be tagged electronically, similar to the RFID system, to avoid using geometrical features for object recognition. The tag as an object transponder can backscatter the RF beacon signal integrated with the object identification and local sensor properties, which can be well isolated from other interference by sub-carriers or code division to improve ranging reliability and accuracy. However, self-jamming and antenna reflection remain serious problems for ranging owing to insufficient separation of the downlink and uplink19.

The phase information of the RF signal is more sensitive to the distance between the transmitter (Tx) and receiver (Rx) than RSSI, and can give higher precision if the wavelength ambiguity can be resolved19. In the ideal scenario of a fully coherent Tx and Rx separated at a certain distance, Rx can use the demodulated phase of the received signal to retrieve the Tx-to-Rx distance variation, which is in a cyclic linear relation with respect to the phase variation at the given frequency. Under this simplified LoS model, no matter how small the distance change is, the phase will change accordingly. Therefore, phase-based RF ranging resolution is fundamentally limited only by the accurate Tx–Rx carrier synchronization and the phase noise skirt, not by the tradeoff of the time-domain sampling window size or bandwidth. Therefore, both high spatial and temporal resolution in ranging can potentially be achieved at the same time.

Many previous ranging methods are, in contrast, based on Fourier transforms, such as FMCW radar, and sample the data at in reciprocal k-space, recovering the range by applying the windowed Fourier transform. These methods will be unavoidably limited by the uncertainty principle20,21 in their mathematical model. For example, when the FMCW radar is configured under a certain sampling rate, the number of k-space sampling points is related to the time domain. When a narrow temporal window is applied to achieve high temporal resolution, the Sinc function will spread and degenerate the spatial resolution after the convolution. This trade-off between the spatial and temporal resolution is set by the chosen mathematical procedure, not by a physical limitation. It is possible to bypass Fourier methods to mitigate the resolution tradeoff. Hilbert–Huang transforms (HHT), including empirical mode decomposition and Hilbert spectral analysis22,23, are widely applied to analyse the nonstationary and nonlinear data set to achieve higher resolution in Fourier pairs simultaneously with higher computational cost24,25. Alternatively, the ranging system can be designed without the Fourier transform as an essential step, such as the approach demonstrated here.

In this Article, we report a ranging resolution smaller than 50 micrometres using a harmonic ultrahigh frequency (UHF; 300 MHz–3 GHz) RF transponder system with a sampling rate of up to 1 kHz. For comparison, high spatial resolution can be achieved using extremely high frequency, such as in the collision avoidance radar system of 79 GHz with 4 GHz bandwidth26,27. However, lack of dielectric penetration is a severe limitation for extremely high frequency ranging in many applications. In contrast, our UHF system can potentially achieve the maximum distance of conventional RFID systems28,29, around 15 m in free space with a Tx power below 30 dBm, and can see through dielectrics such as water and common building materials30,31,32. The ranging resolution limit is traced to various noise sources and design options. (The phase integer ambiguity for ranging is not treated in detail here, as it can be reasonably resolved by the harmonic multi-frequency backscattering scheme33.) Similar to the passive UHF RFID tag design, our transponder is battery free and can be readily integrated into a small integrated circuit package34 and a printed antenna35,36, which can be conveniently and inexpensively deployed for various applications.

Harmonic RFID ranging system design and implementation

The harmonic RFID system makes use of harmonic backscattering to isolate the downlink (reader to tag) and uplink (tag to reader), which results in a much lower noise floor37 to achieve accurate ranging19,33. Because of the backscattering scheme, the tag and reader carrier synchronization problem is also readily avoided. Detailed comparison of the conventional and harmonic RFID systems is discussed in the Supplementary Information (Supplementary Fig. 1), which includes analyses of the operational range and link budget.

To benchmark the performance of the harmonic RFID ranging scheme, we built a system that consists of a main harmonic reader and tag system, and micrometre platform for tag movement (Fig. 1). A picture of the experimental set-up is shown in Supplementary Fig. 4. We used a software defined radio (SDR, Ettus X310, UBX-160) as the harmonic reader, and the external clock was derived from a rubidium frequency standard (FE-5650A) to provide a stable frequency reference. A field-programmable gate array (FPGA) feeds the digital signal to the digital-to-analogue converter (DAC) to generate the intermediate-frequency signal, which is mixed with the downlink RF frequency of f. The Tx signal after the power amplifier and the low-pass filter (LPF) is fed to the splitter, which is used as part of the broadband duplexer. The downlink signal (the blue arrow) is received by the harmonic tag, which is mounted on a carriage block to provide linear motion with micrometre-level accuracy and resolution through a worm shaft. The passive harmonic tag receives the downlink signal and harvests the energy to power up. The tag can modulate the backscattered signal with the code-division multiple access (CDMA) protocol38,39 together with the unique tag identification, so the system can distinguish each tag with simultaneous multiple access. A nonlinear transmission line (NLTL)40 is designed on the tag to convert the backscattered signal to the second harmonic, which goes back to the reader antenna and then the high-pass filter (HPF) through the splitter. The Rx signal is amplified by a low-noise amplifier (LNA) and down converted by the local oscillator (LO) at 2 f to intermediate frequency, which is sampled by the analogue-to-digital converter (ADC). The digitized intermediate frequency is processed by the FPGA and transmitted to the host computer. Because the Tx and Rx chains share the same clock reference (indicated by the green arrows in Fig. 1), the harmonic reader is configured as a coherent transceiver. A detailed description of the system can be found in Supplementary Fig. 2.

Fig. 1: The experimental set-up of the harmonic RFID ranging system.

The system consists of a harmonic reader and tag, and a micrometre platform. The reader is connected to the dual-band antenna, which transmits the interrogating signal and then receives the backscattered signal from the harmonic tag. The demodulated and then digitalized signal is sent to the computer to calculate the ranging information. (FPGA: field-programmable gate array, MCU: micro control unit, LPF: low-pass filter, HPF: high-pass filter).

As the phase noise is the fundamental limit for our ranging system, the first technique to achieve high resolution is to employ an adequate intermediate frequency fIF to avoid the low-frequency flicker noise. Before the movement of the tag is considered, the ranging performance for the static position is characterized in Fig. 2, where the ranging root-mean-square variation versus fIF under fc = 0.9, 1.0 and 1.1 GHz is shown in Fig. 2a, where fc is the carrier frequency. The sampling rate of the ADC is 66.7 MSps (mega-samples per second), and the intermediate-frequency filter bandwidth BWIF is 33 MHz. BWIF is related to the integration of the noise floor, with its maximum decided by the sampling rate of 66.7 MHz. When fIF is low, the Rx signal is close to the Rx LO frequency, so the phase noise level is high and the ranging variation is relatively large. When fIF increases above 10 MHz, the ADC jitter effect become important. The ranging variation also depends on fc in Fig. 2a, where higher fc gives smaller ranging variation due to the shorter wavelength. Figure 2b shows the root-mean-square ranging variation decreases with decreasing BWIF and then increases slightly with decreasing BWIF after BWIF < 10 kHz under fc = 1 GHz and the ADC sampling rate of 66.7 MSps. We can see that all ranging variation is below 30 μm when BWIF is narrower than 100 kHz, which is usually sufficient for the uplink baseband information with BWbb BWIF in passive transponders34.

Fig. 2: The experimental results of ranging variations with respect to the frequency strategy.

a, Results with different fIF selections at various fc from 0.9 GHz to 1.1 GHz. b, Results with different BWIF at various fIF selections from 6 to 21 MHz. c, Results with various moving window sizes. The bottom and top edges of the box are the 75th and 25th percentiles of the ranging variation data, and the middle line inside the box indicates the median. The bottom and top edges of the whiskers are the minimum and maximum values of the analysed data.

Because the ranging variation is related to the resolution, one of the most efficient ways to counter random noise is to apply the moving average. The ranging variation with different window sizes of 1, 10, 100, 1k and 10k are shown in Fig. 2c, with the 75th-percentile variations (top edges of the boxes) at 33.5, 30.2, 26.8, 14.1 and 10.8 μm, and the maximum variations (top edges of the whiskers) at 101.1, 96.2, 86.2, 42.3 and 32.4 μm, respectively. We can see that the moving average method is effective in reducing the ranging variation caused by the random parts of the phase noise and the ADC aperture jitter. The average is conducted with oversampled intermediate frequency. Within the 1 kHz ranging cycle, the number of intermediate-frequency sampling points is 66.7K, which is still higher than the 10K window size. However, further increasing the window size has only diminishing benefit in reducing the ranging variation, as shown in Fig. 2c for window sizes from 1K to 10K. Alternatively, when the ranging cycle and moving average window size are given, the ADC sampling rate can be correspondingly tuned down to reduce power consumption, if such a feature is desirable for the reader transceiver. It is worth noticing that moving average is not an essential procedure in our scheme if the signal-to-noise ratio (SNR) of the backscattered LoS signal is sufficiently high under the low-noise system. Therefore, the trade-off between the frequency response caused by the window size and the ranging resolution is not limited by the same uncertainty principle as in the Fourier-based methods. The detailed discussion of the ranging variation related to the system configuration is shown in Supplementary Figs. 5 to 8.

Ranging experimental results and analyses

Then the quasi-static movement is conducted to investigate the harmonic RFID ranging resolution in different materials. The wavelength of the backscattered signal will be reduced if the medium between the tag and the reader antenna has higher permittivity. Consequently, the phase-based range calculation should be divided by the square root of the relative permittivity (εr0.5=nr). Although the shorter wavelength results in a shorter detection range within one wavelength, this drawback can be easily compensated by the multi-frequency method which will be discussed later. In addition, the resolution is usually improved in the high-permittivity material, which is further illustrated in Supplementary Fig. 10. The experiment in Fig. 1 was conducted when the glass tank was filled with air, construction sand and water. We first calibrate the initial tag position as 0 to cancel the constant system phase offset, and then advance the carriage block to 50 μm and 100 μm. The recorded time-domain signals at the three positions of 0, 50 and 100 μm are shown in Fig. 3a in blue, red and green, respectively. The lighter colour-tone curves correspond to measurements in air and the darker curves in water, where εr = 79.2 was used. The wavelengths at the uplink frequency of 2 GHz are 15 cm and 1.69 cm in air and water, respectively. The downlink signal was set as 1 GHz. The equivalent sampling rate was 1 kSps (kilo-samples per second), and the 1k moving-average window was applied. From Fig. 3a, the ranging measurements are fairly stable and clearly separated, and the curves in water have much higher resolution. The high permittivity of water provides not only higher ranging resolution, but also isolates the multipath interference from outside the water. However, we did notice that when the tag is close to the upper water–air surface, the ranging results will be subject to interference from ambient (air–water boundary) disturbances. Similarly, for the ranging experiments in air, the ranging results will be distorted when severe multipath interference is caused by nearby moving people. We also performed the real-time experiment with a 25 μm step size in water, which is shown in Supplementary Video 1. The tag stepped forward three times with 25 μm, and the tag is about 30 cm away from the Rx antenna. The detailed description of Supplementary Video 1 is given in Supplementary Fig. 9.

Fig. 3: The experimental results of the quasi-static ranging.

a, Time-domain measurements in air and water with steps of 50 μm. b, Probability density curves when the tag is in air, sand and water with steps of 50 μm. The solid and dashed lines correspond to data collection within 2 s and 0.1 s, respectively. c, Resolution analysis when the tag is in water. d, Measurements of the 50-μm steps in air with the downlink frequencies at 0.5 GHz, 1.0 GHz and 2.0 GHz.

Figure 3b shows the ranging probability density when the tag was in air (low peaks), sand (middle peaks) and water (high peaks) at 0 (blue), 50 (red) and 100 μm (green). The solid curves correspond to 2-s data collection and the dashed curves to 0.1-s data collection, where hardly any difference can be observed. The ranging probability density in water (blue solid curve) is examined in Fig. 3c in more detail to calculate the resolution. The full-width at half-maximum (FWHM) is at 5.9 μm. If the shape of the distribution is considered as the average of the rise and fall distances41, the 10–90% probability then gives 4.7 μm for both rise and fall sides. With the same method, the FWHM resolutions in air and sand are 39.1 μm and 17.8 μm, respectively. More detailed analyses are shown in Supplementary Fig. 10. Furthermore, the carrier frequency can also affect the resolution as discussed in Fig. 2a. We applied 0.5, 1 and 2 GHz as the downlink signals, and stepped the tag by 50 μm in air in Fig. 3d. We can see that the higher frequency will make the ranging resolution slightly higher, but the compromise includes the shorter wavelength ambiguity and the larger attenuation at the same ranging distance.

The wavelength integer from cyclic ambiguity needs to be resolved to extend the maximum operation range for the phase-based methods. Here we use the dual-frequency continuous-wave (DFCW) method to demonstrate implementation of the range extension. Alternatively, sophisticated multi-frequency methods can provide more robust estimation with fewer constraints on the maximum range19. Because our sensing uplink signal is around the 2 GHz band, in air the single-frequency method can cover a distance of about 15 cm, but only 1.69 cm in water. As an illustration for extended range, the computer-control step motor drove the tag carriage forwards for 5 cm in water, and backwards to the 0 point for travel of about three wavelengths. The measurement is recorded in Supplementary Video 2. Based on the encoder on the step motor shaft, the travel distance monitored by the motor rotation angle is chosen as the ground truth to benchmark our ranging accuracy, as shown in Fig. 4a. The blue marks (forward) and pink marks (backward) denote the ranging error at every millimetre. From Fig. 4a and Supplementary Video 2, we can see that DFCW is effective in providing accurate ranging with travel distances over several wavelengths in water. Besides, because two frequencies were applied, after resolving the wavelength integer, the final ranging result was obtained by averaging over measurements from the two frequencies, which further reduced the random noise. If we use multiple incoherent frequencies, more improvement can be expected. Figure 4b shows the cumulative distribution function (CDF) of the ranging accuracy from the 5-cm-travel experiment. The benchmark instances are extracted at every 1 mm of the ground-truth measurement. The blue and pink curves are the CDF for forward and backward tag motion, respectively. The yellow curve is the overall CDF. The ground truth may be polluted by the mechanical accuracy and structural vibration during tag movement. We can see clearly the backward curve is worse than the forward one, which may be caused by the lost motion clearance of the linear module in the backward travel. This observation is also consistent in Fig. 4a, where the forward average is very close to 0 and the backward average has a positive bias, as shown in the dashed lines. During these experiments, the tag antenna is about 0.4 m away from the reader Rx antenna. In view of the shorter wavelength and larger attenuation in water, we estimate the same SNR can equivalently operate in air at 3.5 m from the reader Rx antenna.

Fig. 4: The experimental results of the tag movement and permittivity based on the two-tag structure.

a, The long-travel round-trip ranging accuracy with the DFCW method in water. The forward trip is in blue and the backward trip in pink. The average errors for the forward and backward trips are shown as dashed lines. b, CDF of the 50-mm ranging data. c, Real-time ranging with different tag speeds. The curves C1 to C7 correspond to a tag speed of 65.60 mm s−1 for C1 and the successive half scaling for C2 to C7. d, Statistical analyses of the permittivity ratio in each material measured by the two-tag structure. The bottom and top edges of the box are the 75th and 25th percentiles of the permittivity ratio, and the middle line inside the box indicates the median. The bottom and top edges of the whiskers are the minimum and maximum values of the analysed data.

We further tested the temporal response of our ranging system. The step motor is configured with different speeds during a tag motion of 2.5 mm. Curves 1 to 7 (C1 to C7) are the transient data with tag speeds of 65.60, 32.80, 16.40, 8.20, 4.10, 2.05 and 1.03 mm s−1. The curves show the system can respond to the relatively fast movement without loss of accuracy. Because the tags employed the CDMA protocol for the multi-tag access39, we can also use two tags with a known fixed distance to evaluate the variation of the dielectric constant of the media. The two tags were mounted on the same carriage block and separated by 46 mm. When the linear module drove the tags at different positions, the relative permittivity at each position was evaluated. The averaged values in air, sand and water are 1.02, 4.67 and 78.7, respectively. The variation normalized by the average within each media is shown in Fig. 4d. We can see that the permittivity variance of sand is much higher than those of air and water, which is most probably due to the mixture structure from varying silica grain sizes.

Similar to other ranging systems based on carrier phase information, phase errors and uncertainties caused by multipath interference play an important part in ranging accuracy and resolution. For example, a worst-case multi-path signal at an orthogonal phase to the LoS path signal with 55 dB lower magnitude can already pose a phase error of 0.1o, which is at our phase noise tolerance limit. The constant part of the phase offset can be reduced by the calibration step in a reasonably controlled indoor environment, which did not greatly contribute to the ranging errors in the experiments shown in this work. Our use of a high-directivity reader antenna also helped reduce the multi-path effect by providing low antenna gain for undesirable directions. However, as discussed previously, when the ambient cannot be adequately controlled or the application scenarios contain large changes in the channel condition, more severe multipath interference can happen, and the ranging system needs to be adapted with broader bandwidth19,42, antennas with high directivity and a stable phase centre, and more sophisticated algorithms19,43, possibly with a compromised ranging accuracy and resolution. Moreover, in addition to the frequency reference factors discussed in the Supplementary Materials (Supplementary Figs. 5 to 8) that can limit the ranging performance, some other hardware aspects may need to be considered as well in the system set-up. For example, large signal-power dynamic range due to large coverage of the operation distance may need to be adaptively compensated by improved tag and reader designs to reduce the variations in harmonic conversion by the nonlinear element.


We have demonstrated radio ranging with ultrahigh resolution using a harmonic RFID system. We analysed the ranging errors of the system caused by phase noise and sampling jitter, and coherent transceivers, intermediate frequency choices and moving windows were implemented as countermeasures to optimize performance. Our approach offers a resolution of less than 50 micrometres and a sampling rate of more than 1 kHz, and as it is based on the UHF band, it can be applied in environments with mild blockages and in sand or water.


As shown in Fig. 1 and Supplementary Fig. 4, the harmonic reader is implemented by a SDR consisting of Ettus X310 and UBX 160 MHz RF daughter boards. The SDR is controlled by the computer with LabVIEW and is connected to the computer with a PCIe cable to provide a broad data bandwidth. The sampling rates of the DAC and ADC are both configured at 66.7 MSps (mega-samples per second). In the software, the LO of Rx is set as twice that of the LO of the Tx, so the SDR is configured as a coherent harmonic transceiver. The external clock is provided by a rubidium frequency standard (FE-5650A, frequency stability: ± 10-11, phase noise: −100 dBc at 10 Hz, −125 dBc at 100 Hz and −145 dBc at 1 kHz), giving the 10 MHz sinusoidal wave reference. According to the X310 specification, the square wave can provide a more stable clock reference, so the system performance can be further improved by using a better clock source. The harmonic tag PCB (printed circuit board) prototype is based on the open-source WISP (wireless identification sensing platform)44. NLTL is implanted on the tag to generate the second-harmonic signal, which is a ladder structure of inductors and varactors38,40. NLTL provides high harmonic conversion efficiency over broad bandwidth even when the received signal is weak. Other frequency doublers45,46,47 can also be applied with passive or active tag designs. In the small-signal regime with the tag impinging power less than 0 dBm, the dependence of the backscatter phase shift on the power level is negligible38,40. However, when the impinging power to the tag is much higher (above 10 dBm), there would be a noticeable power-dependent phase shift, which can be mitigated by adding a power limiter on the tag or adaptive reader Tx power design. The tag is mounted on a wooden slab, which is then connected to the carriage block of the linear module driven by the step motor. The motor controller is connected to the computer through the real-time controller area network (CAN) bus48, where the motor status can be recorded by the computer. The bit rate on the CAN bus is set at 1 Mbps (megabits per second). When the experiments were conducted in sand or water, the tag circuits were connected through RF cables to the antennas immerged in the test media. The 25-μm-step experiment shown in Supplementary Video 1 was recorded through a 60-mm (full-frame equivalent) macro lens, and then zoomed-in digitally to observe the minute movement. During the experiments, the surroundings of the set-up were reasonably controlled to avoid very strong RF reflections, platform vibration and excessive movement of people. The room temperature is controlled at about 20 °C. In future related applications, wavelength integer ambiguity and multipath effects can be further mitigated by frequency diversity19,33, channel coherence42 and angle-of-arrival (AoA) variation43. When the experiments were conducted with sand or water in the tank, the reader and tag antennas would be detuned with different gain and phase offset, where we used one calibration point (denoted as position 0) to cancel the initial phase offset. When the tag under test moved within the given media but the reader antenna remained stationary with respect to the other boundaries of the set-up, this calibration was sufficient for all subsequent ranging measurements. However, unknown inhomogeneity in the media, direct blockage of LoS, and reader location changes without new calibration will make our present system fail in terms of its performance in precision and accuracy, similar to other RF methods.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


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This project is supported by Department of Energy (DoE) of the United States under the Advanced Research Projects Agency – Energy (ARPA-E) project numbers: DE-AR0000528 and DE-AR0000946. The authors thank G. C. McLaskey and A. Lal for discussions.

Author information




X.H. and E.C.K. perceived the fundamental concepts and brainstormed the design of experiments together. X.H. conducted all the experiments, data processing and manuscript preparation. E.C.K. supervised the project direction and helped with revisions of design and writing.

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Correspondence to Xiaonan Hui.

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Supplementary Information

Supplementary Figures 1–10

Supplementary Video 1

Real-time experiment with 25 μm step size in water.

Supplementary Video 2

Real-time experiment with 5 cm round trip in water.

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Hui, X., Kan, E.C. Radio ranging with ultrahigh resolution using a harmonic radio-frequency identification system. Nat Electron 2, 125–131 (2019).

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