Vortex EM Wave-Based Rotation Speed Monitoring on Commodity WiFi

I.   Introduction

Monitoring rotation speed is crucial in both industrial settings and daily life. Real-time speed estimation helps assess whether equipment with spinning components is operating normally [1]. For instance, measuring aircraft turbine speed is vital. Abnormal speeds, either too fast or too slow, can lead to overheating or reduced efficiency. Slow speeds may indicate inadequate lubrication, while fast speeds may suggest power overload [2]. Abnormal rotation speeds can severely damage components and trigger accidents. Thus, monitoring rotation speed is essential for devices like motors, engines, and fans.

Various methods exist for rotation speed estimation, broadly categorized as contact and non-contact approaches [3]. Contact methods involve mechanical transmission, where the measuring device directly contacts the target. However, this method’s scalability is limited, especially for equipment in closed or hard-to-reach places. Non-contact methods include traditional approaches like photoelectric encoders [4], magnetic sensors [5], Hall sensors [6], and lasers [7]. Photoelectric encoders require encoder design and mounting on the target shaft, while magnetic and Hall sensors need installation on the target shaft and can be influenced by magnetic field interference. Laser methods are constrained by line-of-sight limitations. Additionally, sound-based sensing is impractical in noisy environments.

WiFi signals, unaffected by illumination or occlusion, are widely used in non-contact sensing applications like localization [8], human activity recognition [9], [10], and gesture recognition [11]–[13]. The Fresnel zone model [14] explains the principle of WiFi sensing. It consists of concentric ellipses with the WiFi devices as focal points. When a target crosses the Fresnel zone boundary, it alters the WiFi channel state information (CSI) amplitude and phase, enabling target activity inference. Wi-Rotate [15], a WiFi-based rotation estimation study, offers real-time rotation monitoring for fan-like spinning devices. It calculates rotation speed by analyzing WiFi CSI amplitude or phase changes. The method relies on fan blades intersecting the WiFi Fresnel zone boundary, causing CSI amplitude variations. If no amplitude change is detected, it counts phase variations based on the number of fan blades.

When the spinning target lacks blades, like the uniform circular surface in Figure 1, it does not cross the Fresnel zone boundary or cause radial movement toward or away from the direct WiFi link. Whether the rotation axis is perpendicular (case 1 in Figure 1(a)) or parallel (case 2 in Figure 1(b)) to the WiFi transmitter-receiver line, notable fluctuations in WiFi CSI amplitude aren't noticeable. Detecting rotation becomes difficult unless the speed induces vibration, allowing the inference of rotation speed through the vibration-induced micro Doppler effect [16]. However, if vibration is unstable or hard to detect, the WiFi sensing system considers the self-spinning target as stationary, making monitoring impractical.

Figure  1.  Conventional WiFi sensing for self-spinning target.

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To address the challenge of sensing self-spinning targets, we propose using vortex electromagnetic (EM) waves on standard WiFi for estimating rotation speed, as shown in Figure 2. The WiFi transmitter emits vortex EM waves to monitor the target, and the WiFi receiver captures the echo waves.

Figure  2.  Vortex EM wave-based rotation speed monitoring on WiFi.

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Vortex waves carry orbital angular momentum (OAM) and are characterized by a spiral phase front [17]. Unlike traditional spherical or plane waves, vortex waves rotate around their propagation axis as they propagate due to OAM, and their wavefront structure is helical. The rotational Doppler effect occurs when vortex waves interact with a spinning target, causing the echo wave to exhibit a frequency shift $\Delta f$ compared to its original wave frequency $f_0$. Moreover, this frequency shift $\Delta f$ is proportional to the target’s rotation.

Using vortex EM waves on WiFi for rotation estimation faces three main challenges. First, there is no existing work generating vortex EM waves on WiFi devices, so feasibility is unknown. Second, vortex wave phase variations complicate multipath reflections from the target, making it difficult to extract reflection signals representing only the spinning target from WiFi CSI. Lastly, the micro Doppler effect from inevitable vibrations of spinning targets may overshadow the rotational Doppler effect, making it challenging to determine the frequency shift corresponding to the rotational Doppler effect from CSI data and derive the rotation speed.

To address the first challenge, we use a q-shaped patch antenna that can connect to commodity WiFi devices, enabling the generation of vortex EM waves in the WiFi communication channel. The spiral phase front of the radiated waves is verified using an antenna scanning method. For the second challenge, we design signal preprocessing methods to eliminate random phase offsets in WiFi CSI data, amplify the Doppler effect from spinning targets, and filter out strong reflection signals from the WiFi direct link and static targets. We then apply a bandpass filter to eliminate environmental noise, allowing us to extract the signal primarily reflected by the spinning target. To address the third challenge and eliminate the micro Doppler effect associated with rotation, we adopt a $2\times3$ MIMO (Multiple-Input Multiple-Output) configuration on the WiFi transceiver. Two antennas are connected to the transmitter: a common WiFi rod antenna for transmitting regular EM waves, and a q-shaped patch antenna for transmitting vortex EM waves. The WiFi receiver uses three regular WiFi rod antennas to receive the reflected signals. Regular EM waves capture the frequency shift generated by the micro Doppler effect, while vortex EM waves capture both the micro Doppler frequency shift (MDS) and the rotational Doppler frequency shift (RDS) of the target. By using the CSI ratio to divide the received signals from different transmitting antennas in the time domain, we can eliminate the MDS while retaining the RDS primarily reflected by the spinning target. Additionally, we derive the relationship between WiFi CSI and RDS based on the WiFi sensing scattering model, helping us determine the RDS and calculate the corresponding rotation speed of the target.

The main contributions of this paper include:

● We attempt the vortex EM wave generation on commodity WiFi by using a q-shaped patch antenna. We simulate and test the antenna performance to verify its spiral phase front in practice.

● We provide a theoretical derivation of the rotational Doppler frequency shift from WiFi CSI. We also design signal preprocessing methods to extract signals reflected from spinning targets and calculate their corresponding rotation speeds based on RDS.

● We conduct various experiments on spinning targets of different materials, sizes, shapes, and with varying rotation speeds. This validates the effectiveness of the proposed vortex EM wave based rotation estimation method in this paper.

II.   Preliminaries

This section discusses the characteristics of vortex EM waves and how their interaction with spinning targets produces the rotational Doppler effect. We also explain how to infer the target’s rotation speed from the RDS.

1   Characteristics of vortex EM wave

When EM waves propagate in space they pose both energy and momentum. Linear momentum drives the EM waves to spread outward from the source, while angular momentum can be further classified into spin angular momentum (SAM) and orbital angular momentum (OAM) [18]. SAM determines the polarization state of the EM waves, such as linear polarization or circular polarization. OAM describes how EM waves rotate around their propagation axis in space. EM waves carrying OAM are termed vortex EM waves, for convenience, this paper abbreviates them as OAM waves [19].

OAM wave has a quantified magnitude, which is known as topology charge and denoted by $l$. The electrical field of vortex waves can be expressed as [19]:

where $r$ is the radiation radius and $\varphi$ is the azimuthal angle to the wave propagation axis, $l$ denotes the OAM mode. The phase term $\mathrm{e}^{\mathrm{j}l\varphi}$ in (1) creates twisted wave fronts. The first column of Figure 3 shows the structural differences among vortex waves with OAM modes 1 and 2 and plane waves with mode 0. Vortex waves have helical wave fronts, and higher absolute values of $l$ mean more tightly twisted waves. Vortex waves with non-zero $l$ result in a doughnut-shaped intensity with a zero-energy center, as shown in the second column of Figure 3. Plane waves spread energy outward from the center, while vortex waves have a hollow intensity distribution. Larger mode numbers create larger hollow areas, indicating a larger divergence angle of the wave beam. Thus, using OAM waves with higher mode numbers to illuminate a spinning target requires monitoring a larger area, as their hollow intensity distribution might miss the target.

Figure  3.  Characteristics of vortex EM waves in different OAM modes.

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The phase distribution in the third column of Figure 3 describes the number of phase changes from $-180^\circ$ to $180^\circ$ within one full rotation (360°) of the observation plane. The helix number (one helix exhibits a phase change from $-180^\circ$ to $180^\circ$) in the phase front distribution corresponds to its OAM mode number $l$. The larger the mode number, the more phase changes occur, and consequently, the more number of helices are displayed in the figure.

On the other hand, the value of OAM mode $l$ can be positive or negative, with the sign indicating the direction of the helical phase distribution of its wavefront. This sign has no impact on the OAM intensity plots. When the helical phase rotates clockwise, the OAM mode number $l$ is negative, and the mode number becomes positive when the rotation is counterclockwise. In addition, the OAM mode number of plane waves or spherical waves generated by regular WiFi rod antennas is zero, and their phase remains constant at a fixed propagation distance.

2   Rotational doppler effect

The unique characteristics of OAM waves compared to plane waves enable the rotational Doppler effect when interacting with spinning objects. In this section, we discuss why OAM waves can induce the rotational Doppler effect and explain the mathematical derivation between RDS and target rotation speed. To better understand the phenomenon of the rotational Doppler effect, we first examine the concept of the linear Doppler effect [20].

As shown in Figure 4, there is a disc-shaped object moving horizontally at a velocity $v$. Plane waves are emitted at an angle $\theta$ with respect to the direction of motion of the object, with $\lambda$ representing the wavelength. Due to the component of the target velocity projected onto the wave propagation axis, which is $v{\mathrm{cos}}(\theta)$, there is relative motion between the target and the plane wave source. This results in the linear classic Doppler effect, where the frequency shift $\Delta f$ of the echo signal can be expressed using (2), where $f_0$ represents the original signal frequency, and $c$ is the speed of light.

Figure  4.  Linear Doppler effect.

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When the linear velocity $v$ is zero, the frequency shift disappears. Equation (2) can also explain why plane waves are ineffective in detecting the self-spinning objects without radial motion.

Regarding the monitoring of rotation speed for self-spinning targets, numerous studies [21]–[23] have utilized the rotational Doppler effect generated by the interaction between OAM waves and spinning targets for speed estimation. An illustrative diagram of the rotational Doppler effect is shown in Figure 5. The EM energy transfer direction (Poynting vector) of the OAM wave forms an angle $\alpha$ with its beam axis (propagation direction). Due to the presence of this tilt angle $\alpha$, EM wave will produce a component in the transverse direction of the target surface. When the target starts to spin, the OAM wave leads to a frequency shift $\Delta f$ in its echo wave, which is referred to as the rotational Doppler effect. The tilt angle $\alpha$ shown in Figure 5 has been experimentally determined in the field of optics [24]. It can be calculated as:

Figure  5.  Rotational Doppler effect.

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In (3), $r$ represents the radius of the OAM wave beam. $\alpha$ is usually small. According to the small angle approximation, $\sin (\alpha ) \approx \alpha$. By substituting this into (2) for linear Doppler frequency shift, the rotational Doppler frequency shift [25] can be further derived as:

According to (4), given the RDS $\Delta f$ and the mode number $l$ of the OAM wave, the rotation speed $\Omega$ of the target can be calculated, with the unit being ${\mathrm{rad/s}}$.

III.   System Design

Current WiFi sensing generally relies on CSI obtained from network interface cards (NICs). To use CSI for target rotation speed estimation, we need to derive the mathematical relationship between WiFi CSI and the RDS generated by the spinning target. This relationship will then allow us to build the system model for rotation estimation.

1   RDS extraction from WiFi CSI.

RDS extraction from collected WiFi CSI is the core problem to be solved. First, we introduce the essential background knowledge related to WiFi CSI. With the modulation technique of orthogonal frequency division multiplexing (OFDM), WiFi CSI can describe the signal propagation changes of multiple subcarriers in space, which are complex-values include spatial multipath information. For a single WiFi subcarrier with a center frequency of $f_0$, the transmitted signal can be represented as follows [26]:

where, $\alpha$ represents the signal amplitude. Assuming there are no other dynamic objects in the environment, the received signal after reflection from the spinning target can be represented as:

In (6), the first term represents the static component in the received signal, where $\alpha'$ is the attenuated signal amplitude, and $\tau_s$ is the propagation delay of the static path. The second term represents the dynamic component of the signal received after reflection from the spinning target, where $\alpha''$ and $\tau_d$ are the corresponding amplitude and delay. $f_r$ here is the new frequency of the reflected signal, which has a frequency shift relative to the original signal $f_0$. This shift mainly stems from the micro-Doppler frequency shift (MDS) generated by the vibration of the target surface, and the rotational Doppler frequency shift (RDS) caused by the rotation itself. Therefore, $f_r$ is a summation of follows:

Since WiFi CSI is the ratio of the received signal $Y$ to the transmitted signal $X$, i.e., the division of (6) by (5), CSI can be denoted by $H$ as follows:

Equation (8) illustrates the relationship between WiFi CSI and the MDS, as well as RDS caused by a spinning target. To further simplify the formula, the first term in the equation is caused by reflections from static targets in the environment, which can be considered as a constant and eliminated by subtracting the mean signal from CSI. In the second term, due to the wide divergence angle of the vortex EM waves and the short distance selected when illuminating the spinning target, the delay $\tau_d$ can be neglected for small-scale signal propagation distances in this paper. The MDS can be eliminated by dividing the CSI signals collected from vortex EM waves by those from ordinary EM waves. Therefore, the CSI related to the RDS can be simplified to the form ${\alpha _2}{{\mathrm{exp}}({{\mathrm{j}}2\pi \Delta {f_{{\mathrm{RDS}}}}t}})$. Performing fast Fourier transform (FFT) on the CSI data to convert it into the frequency domain allows extraction of the corresponding frequency shift $\Delta f_{{\mathrm{RDS}}}$ from the CSI, which can then be substituted into (4) to obtain the corresponding target rotation speed.

2   System overview

In this section, we elaborate how to generate vortex EM waves on commodity WiFi, and how to calculate the target rotation speed based on extracted RDS. The system overview is shown in Figure 6, it includes three main modules: OAM wave generation, signal preprocessing, rotation estimation.

Figure  6.  System overview.

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For OAM wave generation, we adapt a q-shaped patch antenna [27] compatible with the WiFi RF frontend, replacing the regular WiFi rod antenna. Furthermore, we configure a $2 \times 3$ MIMO setup for spinning target monitoring. Regular WiFi antenna is used for generating OAM mode 0, and the q-shaped patch antenna is responsible for OAM mode 1 wave generation. The WiFi receiver maintains three regular WiFi rod antennas to receive signals from multipath reflections.

In the signal preprocessing module, we first limit the CSI amplitude to avoid abnormal overshoot caused by device imperfections. Then we apply conjugate multiplication to eliminate random phase shifts in the CSI. We adjust the CSI amplitudes to amplify dynamic signal components influenced by micro Doppler and rotational Doppler effects, and eliminate the direct WiFi link and other static components. Finally, we employ a Butterworth band-pass filter to remove high-frequency components in the CSI caused by environmental interference, retaining the signal primarily reflected by the spinning target. A Hampel filter is also used to eliminate any possible outliers in the data.

The last module of Figure 6 is designed for rotation estimation. WiFi CSI is a two-dimensional matrix containing information from multiple subcarriers, but the sensed rotation information encoded in these subcarriers can be redundant, causing unnecessary data processing overhead. Therefore, we utilize principal component analysis (PCA) for data dimension reduction, transforming the two-dimensional CSI matrix into one-dimensional data for subsequent spectral analysis. When detecting spinning targets using OAM waves, MDS and RDS are parasitic in the echo signal. To eliminate MDS while retaining RDS, we separate the obtained signals from emitted OAM waves and plane waves in the time domain, and take the CSI ratio of the two to eliminate MDS, as they both incorporate the signal component influenced by target vibration. FFT is then performed on the denoised signal, and we apply a peak detection algorithm in the frequency domain to locate the first peak frequency, which corresponds to the RDS. Finally, we substitute this frequency shift into (4) to calculate the target rotation speed.

1   OAM wave generation

The q-shaped patch antenna we adopt for simulation and fabrication refers to the [27]. This q-shaped design allows its emitted signal posses negative OAM values (the phase front is distributed in a clockwise helical pattern). As for the choice of negative OAM values, we would like to highlight that the rotation sensing performance remains unaffected by the sign of OAM mode $l$, as it merely denotes the direction of rotation. Positive OAM modes could be equally utilized if a p-shaped patch antenna is used. Another antenna of the WiFi transmitter adopts a regular rod antenna and emits spherical waves (which can be approximately regarded as plane waves). The antennas of the WiFi receiver remain unchanged as regular rod antennas. The transceiver devices are placed on the same plane to sense spinning targets.

The detailed structure of the q-shaped patch antenna is shown in Figure 7, with its front view on the left and its bottom view on the right. The patch antenna consists of three layers: the top layer is the q-shaped copper layer, the middle layer is the dielectric layer with permittivity 2.65 (colored in light blue of Figure 7), and the bottom layer is a ground copper layer. The thickness of the dielectric layer is set to 2 mm, while the thickness of both the top radiation layer and the bottom ground layer is set to 0.018 mm.

Figure  7.  Design of q-shaped patch antenna.

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The q-shaped patch antenna is specifically chosen for its simple structure and OAM generation flexibility. In the q-shaped design [27], the desired OAM mode for vortex wave generation is related to the radius $r$ in Figure 7. By substituting the wavelength $\lambda$ corresponding to the specified WiFi channel frequency, and the OAM mode number $l$ into (9), the required radius $r$ for the q-shaped antenna can be determined. For example, the OAM 1 patch antenna we use in this work has a radius $r$ of 16.4 mm.

The other parameters labeled in Figure 7 do not affect the OAM mode, but only influence the operating frequency of the antenna. Therefore, parameter tuning can be achieved during the antenna simulation through feedback on the antenna’s operating frequency. Table 1 provides the specific parameters of the designed q-shaped patch antenna with an OAM mode equals to −1, enabling it to operate at 5.825 GHz. The q-shaped radiation layer of the antenna is attached to a square base with a side length of 45 mm. The circular region of the radiation layer is located at the center of the square. The feeding line length $h$ is half of the side length, the feeding line width $c$ is 2.2 mm, and the length of $d$ is 5.46 mm.

Table  1.  Parameters of the q patch antenna (Units: mm)

	W	L	h	c	d	r
$l=-1$	45	45	22.5	2.2	5.46	16.4

 | Show Table

DownLoad: CSV

2   Signal preprocessing

In the $2 \times 3$ MIMO configuration, we adopt a consistent signal preprocessing approach for CSI collected from different transmission antennas. Due to the thermal noise of WiFi devices and many other environmental interference, the amplitude of the raw CSI exhibits random fluctuations. The fluctuations often incorporate abnormal peak values. Therefore, we first sets an amplitude threshold (1.1 $\times$ the maximum amplitude) and performs amplitude clipping on the received CSI.

Furthermore, due to the separation of WiFi transceivers, the obtained CSI has inaccurate phase values due to sampling clock offset, sampling frequency offset, and carrier center frequency offset. The expression of CSI in (8) omits these offsets and only represents the MDS and RDS caused by spinning targets.

To address the phase offset problem, existing work such as [28] typically leverages the fact that different antennas on the same WiFi network card share the same RF oscillator. It is assumed that the inherent phase offset between different antennas on the same device remains constant. Therefore, the CSI data from two different antennas at the same receiver can be multiplied by their conjugates for phase offset elimination.

However, the receiver uses a WiFi NIC such as the Intel 5300, which typically has three interfaces for external antenna connection. To address this, we need a different approach before performing the conjugate multiplication on WiFi CSI. First, we select the antenna that receives the most stable signal as the reference antenna. Then, the CSI data from the other two antennas are multiplied by the conjugate of the reference antenna’s CSI to eliminate the phase offset. Specifically, we calculate the mean variance across all WiFi subcarriers for each antenna to pick out the reference antenna. A smaller mean variance indicates better data stability.

To enhance the impact of the rotational Doppler effect, we adopt the amplitude adjustment method from IndoTrack [29]. Let $H_{s}$ and $H_{d}$ represent the static and dynamic components of the CSI in (10). When the data from two antennas are used for conjugate multiplication, we can obtain:

The first term $H_{1s}H_{2s}^*$ in (10) represents the conjugate multiplication of the static components of the CSI from antenna 1 and antenna 2, resulting in a constant. The last term $H_{1d}H_{2d}^*$ represents the dynamic components of the CSI received by antennas 1 and 2, respectively. Due to the line-of-sight path between WiFi transceivers, the product of the energy of the static component is much greater than the product of the dynamic component. Therefore, the value of $H_{1d}H_{2d}^*$ can be neglected. The signal components related to the Doppler effect caused by rotation are reflected in the second and third terms of (10), ${H_{1s}}H_{2d}^*$ and ${H_{1d}}H_{2s}^*$. Since the Doppler frequency shifts obtained by adjacent antennas are similar, we only need to select one of the two Doppler-related terms to be enhanced, enabling the easy identification of RDS. We select $H_{1s}H_{2d}^*$ for subsequent processing. To enhance the impact of the dynamic component $H_{2d}^*$ and weaken the static component $H_{1s}$, we subtract the minimal amplitude value $\alpha$ of antenna#1 across all subcarriers and add a value $\beta$ to the amplitudes of antenna#2. $\beta$ is calculated as $\beta = 1000\alpha / N$, $N$ is the total number of subcarriers.

After the Doppler effect enhancement, we still have the strongest static component ${H_{1s}}H_{2s}^*$ to be removed by subtracting the signal mean. Then we apply a Butterworth bandpass filter with a cutoff frequency of 2–200 Hz to further denoise WiFi CSI. Finally, to avoid the occurrence of outliers in the CSI after the preprocessing, we use the Hampel filter with a window length of 10, treating values that deviate from the median of the window by more than 3 standard deviations as outliers and removing them. The data preprocessing module aims to extract the signal energy mainly reflected by spinning targets. After the above processing, the result of the conjugate multiplication of the two antennas can be simplified to:

By disregarding the static delay in (11), the processed CSI will mainly characterize the combined effects of target MDS and RDS.

3   Rotation speed estimation

As WiFi CSI is two-dimensional data containing information on packet transmission time and subcarrier, to avoid repetitive rotation speed calculation for each subcarrier, we implement PCA to reduce the dimensionality of CSI, condensing all subcarriers received by the antenna into a single carrier.

To extract RDS from (11) for rotation estimation, we need to eliminate the interference from MDS. Since both regular WiFi rod antenna and OAM antenna can detect the MDS induced by rotation, we utilize CSI ratio from the two different transmitting antennas to remove the influence of MDS, the CSI ratio is defined as below:

We apply FFT to the CSI from (12) to transform the data into the frequency domain. Using a threshold-based peak detection method, we identify the first amplitude peak and its corresponding frequency, recording this frequency as the RDS caused by target rotation. This RDS is then used in (4) to calculate the rotation speed. When the absolute value of the selected OAM wave mode number is 1, the rotation speed can be converted to revolutions per minute (rpm) as follows:

IV.   Experiment

In this section, we elaborate the simulation and test of the q-shaped patch antenna performance for OAM wave generation. Then we compare the sensing performance of OAM waves and plane waves on spinning targets. We estimate rotation speed of targets with different materials and sizes using the RDS. Finally, we evaluate the rotation estimation error and time consumption of the proposed method.

1   OAM phase front verification

To confirm that the q-shaped patch antenna can indeed generate OAM waves, we construct its 3D model and simulate its performance at WiFi channel 165 (5.825 GHz) using CST Studio Suite. The modeling parameters align with those provided in Table 1. The simulated OAM wave intensity and phase front of the patch antenna in the far field are presented in Figures 8(a) and 9(a). The results indicate a zero-energy center hole in the intensity distribution and a single vortex rotating clockwise in the phase front plot, consistent with the OAM mode of -1.

Figure  8.  OAM patch antenna radiation intensity pattern.

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Figure  9.  OAM patch antenna radiation phase front pattern.

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To test the actual radiation characteristics of the patch antenna, we move one receiving antenna to scan its wave front at a distance of 30 cm from the OAM antenna. The OAM wave intensity and phase front are shown in Figures 8(b) and 9(b). From the experimental results, the actual radiation characteristics of the fabricated patch antenna closely match the simulated results, it successfully proves the generation of an OAM mode -1 vortex EM wave. While the slightly non-smooth testing results are due to the limited number of scanned layers, leading to coarse-grained resolution. However, this does not affect the use of the generated OAM wave for sensing.

2   Antenna comparison

In order to elaborate the advantages of OAM wave over regular wave for rotation sensing, we conduct experiments using the setup depicted in Figure 10, and adopt a 1$\times$3 SIMO configuration to monitor the rotation of a small fan. To obtain the best reflection signal intensity, tin foil was wrapped around the fan blades during the experiment.

Figure  10.  Antenna comparative experiment.

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In Figure 10, the setup difference is that the antenna used for transmission is switched from a regular WiFi rod antenna to an OAM patch antenna for different types of wave generation. Simultaneously, an infrared tachometer is used for ground truth estimation, facilitating comparison with the results of rotation speed measured using WiFi. In this test, the infrared measured rotation is 2775 rpm.

We process the CSI according to the design method described in Section III. Then, the CSI is transformed into the frequency domain for observation. The spectrum results generated by regular waves and OAM waves are shown in Figure 11(a) and (b), respectively. It can be observed that the spectrum analysis from regular wave echo includes random noises due to the micro Doppler effect, as shown in Figure 11(a).

Figure  11.  Results of antenna comparative experiment.

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While the spectrum from OAM wave echo contains a clear peak due to RDS in Figure 11(b). The peak correlated frequency (45 Hz) can be substituted into (13) to calculate the target rotation speed, yielding approximately 2700 rpm, which is close to the true value of 2775 rpm with an error of 0.027. This experiment primarily demonstrates that the performance of OAM waves for rotation estimation is superior to that of regular EM waves.

3   Micro doppler elimination

In certain cases, using a single OAM antenna may not produce a distinct single peak in the spectrum due to the Micro-Doppler effect. To further mitigate the MDS and isolate the RDS induced by pure rotation, we employ a 2$\times$3 MIMO antenna configuration for data collection. The OAM patch antenna and a standard WiFi antenna are both connected to a single transmitter.

Both OAM and regular wave echoes contain the MDS. To isolate the RDS induced only by the OAM wave, we use the CSI ratio to eliminate the common MDS from the two waves. First, we perform CSI interpolation in the time domain to align the data length from the two different waves. Then, we calculate the CSI ratio to eliminate the MDS. Figure 12 shows the spectrum analysis results before and after eliminating the micro Doppler effect. MDS caused by target vibration creates multiple peaks in the frequency domain (Figure 12(a)). After elimination, the highest spectrum peak, corresponding to the RDS (32 Hz in Figure 12(b)), can be inspected. The rotation speed is calculated as 1920 rpm, with an error of 0.04 compared to a true value of 2000 rpm.

Figure  12.  Micro-Doppler effect elimination.

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4   Rotation speed estimation

Wireless sensing is recognized for its ability to detect targets in non-line-of-sight conditions. To initiate the system evaluation, we test the method’s effectiveness in scenarios where obstacles are present.

1   Non-line-of-sight

As shown in Figure 13, the spectrum analysis indicates that identifying spectrum peaks corresponding to the rotational Doppler shift (RDS) becomes more challenging when there is occlusion. This difficulty arises because the presence of the obstacle reduces the signal energy that can directly illuminate the target. Moreover, when the target’s contact area is small, less of the OAM phase front interacts with the target surface, resulting in a less pronounced frequency shift due to the RDS.

Figure  13.  Non-line-of-sight evaluation.

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In Figure 13(b), the detected frequency shift is 47 Hz, corresponding to a rotation speed of 2820 rpm. This result demonstrates a relatively large error of 0.072 when compared to the true speed of 2630 rpm, underscoring the impact of obstacles on the accuracy of the proposed method. Nevertheless, the estimated result remains acceptable, especially when compared to methods that are unable to handle rotation measurements under non-line-of-sight (NLOS) conditions.

2   Multiple targets evaluation

In addition, we verify the system’s capability to distinguish between multiple targets and accurately estimate their rotation speeds. Our approach focuses on detecting the frequency shift in the echo signal caused by the rotation of the targets. When the monitored spinning targets have different rotation speeds, the processed echo signals produce distinct peaks in the frequency domain, each corresponding to the rotation speed of a different target.

For instance, in the setup shown in Figure 14(a), we monitored two spinning fans located 30 cm away from the WiFi antenna plane, each with a different rotation speed. The results depicted in Figure 14(b) show two distinct peaks at frequencies of 23 Hz and 46 Hz, corresponding to rotation speeds of 1380 rpm and 2760 rpm, respectively. These values are very close to the actual rotation speeds of 1300 rpm and 2700 rpm, demonstrating the system’s effectiveness in simultaneously monitoring multiple targets with different speeds.

Figure  14.  Multiple targets evaluation.

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5   Different rotation targets monitoring

The above experiments demonstrate the sensing capability of OAM waves for fan-like spinning targets with blades. To verify the rotation estimation performance of our proposed method, we further conduct experiments targeting objects of different materials, sizes, and with multiple rotation speed settings for validation.

As shown in Figure 15, a potter’s wheel and a grinding wheel are targeted for the subsequent evaluations. Both devices have spinning components that are uniform circular surfaces. The potter’s wheel, made of metal with a 10 cm diameter, has an adjustable speed range of 0-2000 rpm. The grinding wheel, covered in sandpaper and with a 15 cm diameter, has an adjustable speed range of 0-8000 rpm. These variable speeds cover the operating speeds of most industrial motors.

Figure  15.  Monitoring targets. (a) Pottery’s wheel; (b) Grinding wheel.

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When testing the two targets, we place all the equipment on a table, with the fixed target positioned approximately 50 cm away from the WiFi transceiver. During the test, we maintain the WiFi transmitter with a packet injection rate of 1000 Hz, and we collect 5 seconds of data at each different rotation speed setting. However, we only need to use 200 ms of data for spectrum analysis and RDS extraction.

1   Test on pottery’s wheel

We have conducted a thorough evaluation of the system’s rotation speed estimation accuracy across various distances and determined the size range of perceptible objects. For this evaluation, we test the pottery wheel with metal spinning components of varying sizes, as illustrated in Figure 16(a). The ground truth rotation speed is set at 2000 rpm, and tests are performed at different distances.

Figure  16.  Rotation estimation at different distances for different sizes.

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The results plotted in Figure 16(b) demonstrate the estimated rotation speed variations from 10 cm to 70 cm for three different target sizes. The findings indicate that larger targets (diameter = 10 cm) are easier to monitor and yield more accurate rotation speed estimations, as evidenced by the blue curve, which remains more stable and closer to the 2000 rpm ground truth line. In contrast, smaller targets result in larger estimation errors, particularly for the target with a diameter of 4.8 cm, represented by the green curve, which shows significant fluctuations far from the ground truth.

While we demonstrated estimation results for targets at distances ranging from 10 cm to 70 cm, we also observed that for distances over 1 m, the rotational frequency shift becomes very difficult to detect for all monitored targets. This highlights the importance of target size and proximity in ensuring accurate rotation speed estimation, particularly when dealing with the divergence of OAM waves.

2   Test on grinding wheel

During the experiment with the grinding wheel, we vary its rotation speed from 1000 rpm to 7000 rpm in 1000 rpm increments. Each speed setting was monitored continuously for 10 seconds. Results in Figure 17 show that speeds below 4000 rpm remained stable, with minimal amplitude variations, forming near-straight lines. However, speeds above 4000 rpm exhibit slightly larger fluctuations. These fluctuations increased due to intense vibration of the grinding wheel at higher rotation speed.

Figure  17.  Rotation speed from 1000 to 7000 rpm estimation of the knife sharpener in Figure 15(b).

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We evaluate the rotation estimation errors for the grinding wheel’s speed. For each of the seven speed settings, we repeat the estimation 150 times. The error evaluation results are shown as box plots in Figure 18. The estimation error at 1000 rpm is slightly higher than at other speeds. Between 1000-3000 rpm, the error decreases. As the speed increases further, the median error remains mostly unchanged. At 7000 rpm, the error distribution widens, ranging from 0 to 0.04. Overall, the maximum estimation error remains within 0.05.

Figure  18.  Boxplot of rotation estimation errors.

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6   Runtime analysis

Finally, we conduct a runtime analysis of our proposed OAM wave rotation speed monitoring method using commodity WiFi, which includes signal preprocessing, RDS extraction, and rotation speed estimation. The results, shown in Table 2, indicate that the total average runtime from loading WiFi CSI data to outputting the rotation speed estimation is approximately 68 ms. This demonstrates that our method can be applied for real-time rotation speed monitoring in practice.

Table  2.  Runtime Analysis (Unit:s)

Load 200 ms data	FFT	Rotation estimation	Total average latency
0.058	0.009	0.001	0.068

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V.   Related Work

This section reviews existing methods for rotation estimation.

Non-contact Based Rotation Estimation Non-contact speed estimation methods include techniques like optical tachometers [4], Hall effect sensors [6], image processing [30], sound sensors [31], and wireless radio frequency (RF) sensing [32]. Optical tachometers detect reflections on spinning objects using laser beams and photodetectors but require a stable light source and are limited by line-of-sight. Hall effect sensors measure speed by detecting magnetic field changes, which requires placing sensors on the equipment. Image processing analyzes motion in images to estimate speed but is less effective for targets without clear rotation points and is also affected by lighting and line-of-sight issues. Sound sensors and RF methods detect vibrations caused by rotation, but sound sensors can be unreliable in noisy environments. RF signals offer a solution to some of these limitations. In particular, we focus on speed sensing using wireless RF signals based on the Doppler effect.

RF Sensing Based Rotation Estimation RF-based methods for dynamic target sensing often rely on the Doppler effect to estimate speed and direction, including the linear Doppler effect from radial motion, the micro Doppler effect from small movements, and the rotational Doppler effect from spinning targets. Some methods, such as TagSMM [33] and RF-ear [34], utilize RFID technology to measure machine vibrations for inferring rotation speed. However, these approaches can encounter challenges related to the reliability of vibration measurements and potential interference.

Another approach, Wi-Rotate [15], uses raw WiFi signals and the Fresnel zone model to estimate speed, particularly for spinning fan blades. However, it may not be effective for uniformly spinning targets. Our proposed WiFi rotation speed estimation method, based on vortex EM waves, applies to a variety of spinning targets, including both fan blades and uniform surfaces. It establishes a mathematical relationship between WiFi CSI and rotation-induced Doppler shift, providing a practical solution for monitoring equipment rotation speed in industrial settings and expanding the use of vortex waves in WiFi devices.

OAM Wave Based Rotation Estimation OAM waves have primarily been studied in the field of optics, with several works using OAM to estimate rotation [21], [35], [36]. These optical methods require precise alignment of the OAM beam with the spinning targets to achieve accurate estimation, which limits the application in practice.

In the RF domain, studies like [23], [37], [38] have analyzed and experimentally verified the rotational Doppler effect induced by radio waves carrying OAM. However, these approaches rely on specialized equipment, such as horn antennas or uniform circular arrays, to generate OAM waves, as well as bulky equipment like vector network analyzers. This makes them impractical for use with standard WiFi devices. Additionally, [39] shows that the resolution of rotation speed estimation is influenced by the OAM index and pulse duration in radar chirp signals. RFTacho [32] uses a patch antenna on the USRP platform to generate OAM waves and measure fan speeds, but its reliance on non-commercial equipment limits its applicability in real-world scenarios.

In contrast, our work introduces the use of OAM waves in commercial WiFi devices for the first time. We derive the rotational Doppler effect using a WiFi sensing model based on CSI. Unlike previous methods, our approach requires only the replacement of the standard WiFi antenna with a q-shaped patch antenna, avoiding the need for specialized equipment. We conduct experiments in typical indoor environments, demonstrating the practical application of our method for rotation speed estimation using readily available WiFi infrastructure.

VI.   Conclusion

This paper monitors the rotation speed of spinning targets using vortex EM waves with commercial WiFi devices. First, we successfully generate vortex EM waves on WiFi devices and verify their characteristics through antenna scanning. We then derive the mathematical relationship between WiFi CSI and rotational Doppler frequency shift. This method separates the micro Doppler effect from the rotational Doppler effect, enabling more accurate estimation of the target’s rotation speed. We conduct experiments with targets of different materials, sizes, shapes, and speeds, finding that the maximum error of this method is within 5% in most cases. This demonstrates the feasibility of rotation speed monitoring using WiFi vortex EM waves. Moreover, our method is efficient in data processing, suitable for real-time monitoring systems.