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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS: IN PRESS. DOI: 10.1109/JSAC.2020.3020606 1 Respiration Monitoring with RFID in Driving Environments Chao Yang, Student Member, IEEE, Xuyu Wang, Member, IEEE, and Shiwen Mao, Fellow, IEEE Abstract—To improve driving safety and avoid accidents caused by driving fatigue, drowsiness detection aims to alarm the driver before he/she falls asleep. Since breathing rate is a key indicator of the drowsy state, respiration monitoring in the noisy driving environment is critical for developing an effective driving fatigue detection system. In this paper, we propose, for the first time, an RFID based respiration monitoring system for driving environments. The system estimates the respiration rate of a driver based on phase values sampled from multiple RFID tags attached to the seat belt, while exploiting the tag diversity to combat the strong noise in the driving environment. Both tensor completion and tensor Canonical Polyadic Decomposition (CPD) are applied to process the phase values, to overcome the influence of frequency hopping, random sampling, vehicle vibration, and other environmental movements. The proposed system is analyzed and implemented with commodity RFID devices. Its accurate and robust performance is demonstrated with extensive experiments conducted in a real driving car. Index Terms—Radio-frequency identification (RFID); Respi- ration monitoring; Tensor Decomposition; Driving Environment I. I NTRODUCTION Vehicles play a critical role in our society. With the drastic increase of the number of vehicles as well as driving time, driving safety has become ever more important than before. Driving fatigue is one of the primary causes of car accidents, which takes many lives every year [1]. It has been reported that there are on average 6 million car accidents in the U.S. every year [2], and more than 90 lives are lost every day. Such car accidents could be effectively avoided and human lives could be saved, if drivers are warned when they become sleepy. Drowsy driving can be indicated by multiple features of the driver, such as eyelid movements, driving movements, and human vital signs. Among various types of vital signs, respiration rate is a useful indicator of driver’s fatigue state. It has been shown that the breathing rate usually decreases notably (i.e., for about 3 breaths per minute (bpm)) before the driver falls asleep [3]. Thus, accurately monitoring the respiration of the driver is a promising way, and the first step, to prevent drowsy driving. However, respiration monitoring Manuscript received Dec. 6, 2019; revised Jan. 30, 2020; accepted Mar. 14, 2020. This work is supported in part by the US National Science Foundation (NSF) under Grant ECCS-1923717, and through the Wireless Engineering Research and Education Center (WEREC) at Auburn University. C. Yang and S. Mao are with the Department of Electrical and Computer Engineering, Auburn University, Auburn, AL 36849-5201, USA. X. Wang is with the Department of Computer Science, California State University, Sacramento, CA 95819-6021, USA. Email: [email protected], [email protected], [email protected]. Digital Object Identifier 10.1109/JSAC.2020.3020606. for drivers is challenging, due to the highly strong noises in the driving environment, such as vehicle vibration and movements of the driver and passengers. Several techniques have been proposed for respiration monitoring using different types of signals, including video, ultra sound, and RF signals. Vision based methods detect respiration by analyzing the chest movements captured by a video camera [4], but it may not work well when lighting is poor (e.g., driving at night) and may raise privacy concerns. RF signals, such as WiFi [5] and UWB radar [6], have also been exploited, with the advantage of not requiring sufficient lighting inside the vehicle. However, due to the mutipath effect, such non-invasive RF sensors may be easily affected by the movements of driver and passengers. Recently, ultra sound signals generated by smartphones have been considered in [7]. Acoustic signals are shown to be effective to capture the human breathing signal [8], but as RF signals, they are also sensitive to the strong noises in the driving environment. To this end, radio frequency identification (RFID) provides a promising alternative solution. RFID based sensing has become a hot problem area recently. Unlike other contact- free sensors, RFID tags are much cheaper and can be easily attached to the target object. As a near-field communication technology, it is more robust to surrounding noises. However, to exploit commodity RFID (rather than customized hard- ware) for respiration monitoring, many challenges should be addressed. For example, frequency hopping, as required by the Federal Communications Commission (FCC), causes large phase offsets, making received phase data useless. With the Slotted ALOHA medium access control protocol, the tags are sampled randomly, and it is common that the readings from the same tag are sparse (many are missing). There have been several recent works employing RFID for respiration monitoring [9]–[11], but all the existing schemes work in a static indoor environment. The strong interference from the driving environment prevents their application for driver respiration monitoring. In this paper, we address the above challenges with novel, effective solutions, and propose an RFID based respiration monitoring system for the driving environment. Specifically, we propose to attach multiple tags to the driver’s seat belt, which allow us to exploit the tag diversity. Although the same respiration signal is sampled by all the tags, the reader collected data is of high diversity as resulted from the multiple independent sampling. We also develop an effective tensor completion technique to mitigate the effect of frequency hopping and random sampling. The recovered phase difference

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Page 1: IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS: IN …eng.auburn.edu/~szm0001/papers/jsac2020.pdf · missing readings in collected phase data, and a tensor de-composition approach

IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS: IN PRESS. DOI: 10.1109/JSAC.2020.3020606 1

Respiration Monitoring with RFID in DrivingEnvironments

Chao Yang, Student Member, IEEE, Xuyu Wang, Member, IEEE, andShiwen Mao, Fellow, IEEE

Abstract—To improve driving safety and avoid accidentscaused by driving fatigue, drowsiness detection aims to alarmthe driver before he/she falls asleep. Since breathing rate is akey indicator of the drowsy state, respiration monitoring in thenoisy driving environment is critical for developing an effectivedriving fatigue detection system. In this paper, we propose, forthe first time, an RFID based respiration monitoring system fordriving environments. The system estimates the respiration rateof a driver based on phase values sampled from multiple RFIDtags attached to the seat belt, while exploiting the tag diversityto combat the strong noise in the driving environment. Bothtensor completion and tensor Canonical Polyadic Decomposition(CPD) are applied to process the phase values, to overcomethe influence of frequency hopping, random sampling, vehiclevibration, and other environmental movements. The proposedsystem is analyzed and implemented with commodity RFIDdevices. Its accurate and robust performance is demonstratedwith extensive experiments conducted in a real driving car.

Index Terms—Radio-frequency identification (RFID); Respi-ration monitoring; Tensor Decomposition; Driving Environment

I. INTRODUCTION

Vehicles play a critical role in our society. With the drasticincrease of the number of vehicles as well as driving time,driving safety has become ever more important than before.Driving fatigue is one of the primary causes of car accidents,which takes many lives every year [1]. It has been reportedthat there are on average 6 million car accidents in the U.S.every year [2], and more than 90 lives are lost every day.Such car accidents could be effectively avoided and humanlives could be saved, if drivers are warned when they becomesleepy. Drowsy driving can be indicated by multiple featuresof the driver, such as eyelid movements, driving movements,and human vital signs. Among various types of vital signs,respiration rate is a useful indicator of driver’s fatigue state.It has been shown that the breathing rate usually decreasesnotably (i.e., for about 3 breaths per minute (bpm)) beforethe driver falls asleep [3]. Thus, accurately monitoring therespiration of the driver is a promising way, and the first step,to prevent drowsy driving. However, respiration monitoring

Manuscript received Dec. 6, 2019; revised Jan. 30, 2020; accepted Mar. 14,2020. This work is supported in part by the US National Science Foundation(NSF) under Grant ECCS-1923717, and through the Wireless EngineeringResearch and Education Center (WEREC) at Auburn University.

C. Yang and S. Mao are with the Department of Electrical and ComputerEngineering, Auburn University, Auburn, AL 36849-5201, USA. X. Wangis with the Department of Computer Science, California State University,Sacramento, CA 95819-6021, USA. Email: [email protected],[email protected], [email protected].

Digital Object Identifier 10.1109/JSAC.2020.3020606.

for drivers is challenging, due to the highly strong noisesin the driving environment, such as vehicle vibration andmovements of the driver and passengers. Several techniqueshave been proposed for respiration monitoring using differenttypes of signals, including video, ultra sound, and RF signals.Vision based methods detect respiration by analyzing the chestmovements captured by a video camera [4], but it may notwork well when lighting is poor (e.g., driving at night) andmay raise privacy concerns. RF signals, such as WiFi [5] andUWB radar [6], have also been exploited, with the advantageof not requiring sufficient lighting inside the vehicle. However,due to the mutipath effect, such non-invasive RF sensors maybe easily affected by the movements of driver and passengers.Recently, ultra sound signals generated by smartphones havebeen considered in [7]. Acoustic signals are shown to beeffective to capture the human breathing signal [8], but asRF signals, they are also sensitive to the strong noises in thedriving environment.

To this end, radio frequency identification (RFID) providesa promising alternative solution. RFID based sensing hasbecome a hot problem area recently. Unlike other contact-free sensors, RFID tags are much cheaper and can be easilyattached to the target object. As a near-field communicationtechnology, it is more robust to surrounding noises. However,to exploit commodity RFID (rather than customized hard-ware) for respiration monitoring, many challenges should beaddressed. For example, frequency hopping, as required bythe Federal Communications Commission (FCC), causes largephase offsets, making received phase data useless. With theSlotted ALOHA medium access control protocol, the tagsare sampled randomly, and it is common that the readingsfrom the same tag are sparse (many are missing). There havebeen several recent works employing RFID for respirationmonitoring [9]–[11], but all the existing schemes work ina static indoor environment. The strong interference fromthe driving environment prevents their application for driverrespiration monitoring.

In this paper, we address the above challenges with novel,effective solutions, and propose an RFID based respirationmonitoring system for the driving environment. Specifically,we propose to attach multiple tags to the driver’s seat belt,which allow us to exploit the tag diversity. Although thesame respiration signal is sampled by all the tags, the readercollected data is of high diversity as resulted from the multipleindependent sampling. We also develop an effective tensorcompletion technique to mitigate the effect of frequencyhopping and random sampling. The recovered phase difference

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS: IN PRESS. DOI: 10.1109/JSAC.2020.3020606 2

by tensor completion helps to combat the effect of vehiclevibration and driver/passenger body movements. Finally weapply tensor Canonical Polyadic Decomposition (CPD) toseparate the small respiration signal from strong noises. Theidea of increasing the dimension of data is essential to detectthe weak respiration signal from noisy and sparse samples.

Specifically, we first provide an analysis of the sampledphase data that is used in the proposed system, and investigatethe impact of frequency hopping offset as well as the chal-lenges of respiration monitoring in driving environments. Theproposed system is designed with several novel componentsto address these challenges, including data collection, datapreprocessing, CPD, and respiration signal estimation. Withmultiple tags attached to the seat belt, the breathing signalcan be effectively embedded in the phase data captured by thereader. However, the sampled phases are sparse due to randomsampling, and are greatly distorted by channel hopping, vehi-cle vibration, and body movements. To combat such noises,we propose a High Accuracy Low Rank Tensor Completion(HaLRTC) based technique to estimate the phase differencebetween each pair of tags in each time slot, and to eliminatethe frequency hopping effect simultaneously [12]. To extracta clean breathing signal, we leverage a CPD based techniqueto decompose the tensor data constructed by the previousestimated phase difference. Finally, the breathing signal isrecovered from decomposed tensor data, and the breathing ratecan be estimated with a peak detection algorithm.

The main contributions of this paper are summarized below.• To the best of our knowledge, this is the first work

on respiration monitoring in driving environments usingcommodity RFID reader and tags.

• We propose a tensor completion technique to recovermissing readings in collected phase data, and a tensor de-composition approach to extract the respiration signal ofthe driver from phase values sampled from multiple RFIDtags. The proposed techniques are effective in combatingthe strong noises caused by frequency hopping, randomsampling, vehicle vibration, and other movements in thedriving movement.

• We develop a prototype system with commodity RFIDdevices and test the system in real driving environments.Extensive experiments are conducted to evaluate thesystem performance in various driving scenarios, suchas parked, in city streets, and on a highway, and sys-tem configurations, where a highly accurate and robustperformance is demonstrated.

In the following, we review related work in Section II andpresent the preliminaries and system overview in Section III.The detailed system design is introduced and analyzed in Sec-tion IV. We present our experimental performance evaluationin Section V and conclude this paper in Section VI.

II. RELATED WORK

This work is closely related to RF based vital sign moni-toring and RFID based sensing. We mainly review these twoclasses of systems in this section.

RF based health sensing systems have been developedthat employ Radar, WiFi, and RFID techniques. Radar based

vital sign monitoring systems include frequency modulatedcontinuous wave (FMCW) radar [13] and Doppler Radar [14].However, they usually require customized hardware and op-erate over a wide spectrum. WiFi based systems mainly usereceived signal strength (RSS) and channel state information(CSI). For example, UbiBreathe [15] and mmVital [16] utilizeWiFi RSS at 2.4 GHz and 60 GHz, respectively. To improveaccuracy, CSI based systems leverage the amplitude or phasedifference information of CSI for estimating single or multiplepersons’ breathing and heart rates [17]–[20]. Moreover, severalbimodal CSI data based systems have been proposed to tacklethe weak breathing signals at some special positions [21]–[23].

Recently, several RFID based breathing monitoring systemshave been proposed. For example, RFID tags have been usedfor breathing rate estimation in [9], breathing and heart ratesestimation in [24], and breathing monitoring and sleepingposture recognition in [25]. Furthermore, the RF-ECG systemis proposed for heart rate variability assessment using anRFID tag array [26]. To mitigate the frequency hoppingoffset in FCC-compliant RFID systems, the AutoTag systemis proposed for breathing monitoring and apnea detection witha variational autoencoder [10], [11]. However, these existingsystems are designed for the indoor, static environment; theymay not be effective in the highly dynamic, highly noisydriving environment.

Recently, WiFi based [5], acoustic based [7], and UWBbased [6] systems have been developed for breath monitoringin driving environments. In fact, these existing systems aresensitive to the environmental interference, such as the bodymovements of the driver himself/herself and of the passengers,due to their relatively large transmission ranges.

In addition to vital sign monitoring, RFID tags have alsobeen applied for many other applications, such as indoorlocalization [27], [28], user authentication [29], material iden-tification [30], object orientation estimation [31], vibrationsensing [32], anomaly detection [33], and drone localizationand navigation [34], [35]. To overcome the low accuracy whenRSS values are used [36], recent works are mainly focusedon the phase for indoor localization, which can be used toderive the distance and direction of arrival (DOA). To solve thephase ambiguity problem, synthetic aperture radar (SAR) [37]and the hologram techniques [27], [38] are proposed. TheRFind system estimates time-of-flight with a special hardwareto achieve high localization precision [39].

This work, to the best of our knowledge, is the first toapply RFID based sensing for monitoring breathing signals ina driving environment. The proposed system consists of noveland effective solutions for noise and movement interferenceremoval and breathing signal separation. The tensor basedapproach in this work has been analyzed and proven to beeffective for the noisy driving environment.

III. CHALLENGES AND SYSTEM OVERVIEW

A. Phase of the RFID Signal

To detect the breathing signal from received phase valuesfrom multiple RFID tags, we should firstly know how thesephase samples are collected by the RFID reader. In RFID

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS: IN PRESS. DOI: 10.1109/JSAC.2020.3020606 3

systems, phase information is one type of low level data,which is collected when the RFID reader receives the Elec-tronic Product Code (EPC) from interrogated tags. When themultipath effect is negligible, the measured phase sample canbe written as [40]

ϕ = mod (2π(2D) · f/c+ ϕtag + ϕT + ϕR, 2π) , (1)

where D is the distance between the sampled RFID tag and thereader antenna, f is the frequency of the currently occupiedchannel, and c represents the speed of light. Moreover, ϕtag ,ϕT , and ϕR are the additional phase rotation for the tag,the transmitter, and the receiver, respectively. These additionalphase rotations are mainly caused by the circuits in the readerand tag hardware. Furthermore, different reflection character-istics of these devices also contribute to the phase distortion.

This model implies that we could use phase values to detectthe changes in the distance between the antenna and the tag.When the tag is attached to the human chest, the phase changesare indicative of the breathing signal. However, in addition toD, the other parameters, i.e., f , ϕtag , ϕT , and ϕR, are allsusceptible to the current channel used by the reader. Thus, themeasured phase value will have a different phase offset whenthe system hops to a new channel. Following FCC regulations,the Ultra-High Frequency (HUF) RFID system should hopamong 50 channels within 10 seconds, so the sampled phasedata will be heavily corrupted by frequency hopping. Thefrequency hopping effect poses a big challenge for extractingthe respiration signal.

B. Respiration Monitoring in Driving Environments

To capture the respiration of a driver, we attach RFID tagson the seat belt, as illustrated in Fig. 1. Since the seat belt isbonded on the driver’s body, it (and the tags) moves along withthe rise and fall of the chest. Such movements are carried inthe sampled phase values of each tag (see (1)), which will becaptured by the RFID reader placed on the ceiling above thedriver seat. A big challenge is that, the seat belt/tag movementsare no only caused by breathing, but also affected by otherenvironmental factors in the car.

Fig. 1 presents the sampled phase signal from a single RFIDtag collected in different scenarios. For better illustration,the plotted phase data has already been preprocessed byremoving the frequency hopping effect (to be discussed inSection IV-A). Theoretically, without the influence of channelhopping, the phase samples should exhibit the periodicity ofhuman respiration. In fact, the collected phase signal, whenthe car is parked, exhibits strong periodicity. However, thesampled phase values in a moving vehicle, as shown in thesecond subplot in Fig. 1, are highly random, i.e., far from aperiodic signal. This is because that respiration monitoring ina driving environment is very different from other respirationmonitoring scenarios, in which the user is usually in a relativestable state, such as sleeping or sitting [10], [11], [19], [41].This assumption does not hold true in driving environments.First, the vehicle vibrates when moving fast on the road,which makes the seat belt vibrate along with the car. Second,drivers do not remain completely still. For example, the arms

Distance between the

radar and tag

Respiration

Tag shift

caused by

respiration

Signal collected

when driving

Signal collected

when parked

Ideal signal

Fig. 1. Illustration of the respiration monitoring mechanism.

move when the driver turns the steering wheel, and the headmoves when the drive looks around to check traffic conditions,which will cause additional movements to the tags. Suchenvironmental movements also cause time-varying multipathinterference by reflecting the RFID signal. Accordingly, how tomitigate the impact of vehicle vibration and body movementsposes another challenge (in addition to frequency hopping),to be addressed in our system.

C. System Architecture Overview

To overcome the above challenges, we develop a tensorbased breath monitoring system with an architecture shownin Fig. 2. The proposed system consists of four modules,including data collection, breathing data preprocessing, tensordecomposition, and respiration signal estimation.

In the data collection module, the reader keeps on interro-gating the RFID tags attached to the seat belt and collectingphase samples from each tag. The data preprocessing moduleis to remove the channel hopping offset and to mitigate thenoise from the driving environment. Since the raw phasedata is corrupted by frequency hopping, it cannot be directlyemployed for breathing signal extraction. Fortunately, thephase variation within each individual channel is not affectedby channel hopping; this fact is leveraged in our system torecover the phase data for a certain channel (see next section).Vehicle vibration mitigation is accomplished by calculating therecovered phase difference between a pair of tags. Since thevibration has a similar impact on the two tags, subtractingthe phase data from the two tags can effectively mitigate thevehicle vibration noise. However, the challenge is that, thephase data is not sampled simultaneously from all the tags;there is only one phase reading from one of the tags in eachtime slot. To calculate the phase difference between two tagsin each time slot, the missing phase sample(s) in the same timeslot should be accurately estimated. To this end, we leveragea compressed sensing technique named HaLRTC to estimatethe missing phase data [12], so that we can calculate accuratephase difference for each pair of tags.

Next, we hankelize all calculated phase difference valuesto construct a tensor for the following tensor decompositionmodule. After the phase difference tensor is constructed, we

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS: IN PRESS. DOI: 10.1109/JSAC.2020.3020606 4

Fig. 2. Architecture of the proposed system.

leverage CPD to extract the components related to driver’srespiration. Finally, we recover the respiration signal of thedriver by fusing all breathing related components and estimatethe breathing rate with a peak detection algorithm. The systemdesign will be elaborated and analyzed in the next section.

IV. SYSTEM DESIGN AND ANALYSIS

A. Combating Frequency Hopping Offset

The FCC regulation requires frequency hopping for UHFRFID systems. The phase offset generated by frequency hop-ping should be firstly removed in signal preprocessing. Werewrite (1) for the phases sampled from the 50 channels as

ϕ = mod (4πDfK/c+ ϕK , 2π) , K = 1, 2, ..., 50, (2)

where K is the channel index, fK represents the frequency ofchannel K, and ϕK is the sum of ϕtag , ϕT and ϕR, because allthese values are irrelevant to D but are affected by frequencyhopping. From (2), we can see that the phase offset due tochannel hopping is actually caused by fK and ϕK .

Several techniques have been proposed to remove the effectof these two factors. For example, in AutoTag [10], the phaseoffset between two adjacent channels is estimated by thedifference between the mean value near the end of the previouschannel and that at the beginning of the next channel. Thistechnique achieves a very good performance when the numberof interrogated RFID tags is no more than 3. However, as thenumber of tags is increased, it would be hard to guarantee thatenough samples can be collected from all the tags, which areneeded for calculating the mean values. In addition, Tagyroleverages a full channel scan and calibration to measure ϕK

0 5 10 15 20 25 300

2.0

4.0

6.0

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ase

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d)

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0 5 10 15 20 25 30

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-0.2

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Fig. 3. Raw phase and the filtered phase variation signal.

in each channel [31]. The technique is suitable for RFIDsystems with more tags. In a driving environment, however, theestimated ϕK could be greatly affected by vehicle vibrationand driver’s body movement.

Since our system needs to interrogate at least 4 tags for tagdiversity (see Section IV-B), we propose a novel approach toremove the channel hopping effect. If we subtract the sampledphase ϕn from the previous sampled phase ϕn−1, given in (2),we can obtain the nth phase variation on channel K as

vn = 4πfK(Dn −Dn−1)/c, (3)

where vn represents the phase variation between the currentand the previous phase sample, Dn is the antenna-tag distancein the nth sample. We find that the phase variations onthe same channel are not related to the initial phase offsetϕK . With (3), we can easily translate the variations from allchannels to a reference channel R by multiplying a factorfR/fK . In fact, the reference channel can be any one of the50 channels. In our system, we set R = 1 to make channel1 the reference channel for convenience. However, when thenth sample and the (n − 1)th sample are not from the samechannel, Eq. (3) should be updated as

vn = 4π(fKDn − fK−1Dn−1)/c+ ϕK − ϕK−1. (4)

Eq. (4) shows that when two adjacent phase samples arenot collected from the same channel, the phase variation isstill affected by the initial phase offsets of the two differentchannels. To mitigate the frequency hopping offset, we shoulddrop these distorted phase variations. Fortunately, since onlya single phase variation is affected once the system hops to anew channel, most of the remaining data are still usable. Suchresults are illustrated in Fig. 3. We calculate the phase variationfrom the raw, sampled phase data, and delete the distortedphase variations when hopping to a new channel. It can beobserved that although the phase is corrupted by frequencyhopping (the upper plot), the phase variation is confined within[-0.15 rad, 0.1 rad]. This result shows that most of the phasevariations are not affected by channel hopping.

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS: IN PRESS. DOI: 10.1109/JSAC.2020.3020606 5

Fig. 4. Slotted ALOHA based random sampling in RFID systems.

B. Recovering Phase for Each Time Slot

To combat vehicle vibration, we propose to leverage thephase difference between two tags. However, following theGen2 protocol [40], when one tag is sending its EPC to thereader, all other tags should remain silent to avoid collision.The random sampling details are illustrated in Fig. 4, whichshows the phase data sampled by the reader from multiple tags.A colored square indicates that a valid phase value is sampledfrom the tag, a blank square means the tag is not sampled inthat time slot, and all the same colored squares are sampledfrom the same channel. Because the entire transmitting processis based on slotted ALOHA, the tags are sampled randomly.That is, phase can be collected from only one tag in each timeslot, and the sampling interval for each tag is random.

Because calculating phase difference between two tagsrequires to sample phase data from both tags in the same timeslot, we need to estimate the missing phase data of all tagsin every time slot, i.e., the blank squares in Fig. 4. Severalcompressed sensing approaches have been shown to achievea good performance on recovering the missing RFID phasedata [42], [43], where the number of deployed tags are lessthan 3. For example, in [42], a missing phase is estimatedfrom neighboring sampled phase values with a Blackmanwindow, where a pair of tags are used. However, these existingtechniques are not suitable for our system, where more tagsare deployed. When there are more tags, the sparsity of databecomes higher, thus resulting in a lower recovering accuracy.

Tensor completion is another powerful tool of compressedsensing, which has been adopted to recover missing data inRFID systems in our recent work [44]. We propose a tensorcompletion based method to recover the phase sequences forall tags in every time slot. Rather than directly recovering thephase sequence as in [44], we recover the sequence of phasevariation for each tag, and then calculate phase by integratingthe recovered phase variation. This is motivated by the factthat phase variation is not affected by frequency hopping, asproven in Section IV-A.

We first define the ideal matrix we aim to recover, given by

VT.=

v1t1 v1t2 v1t3 . . . v1tnv2t1 v2t2 v2t3 . . . v2tn

......

......

...vmt1 vmt2 vmt3 . . . vmtn

, (5)

where m is the tag index, tn is the nth time slot, and vmtn

is the real phase variation of tag m at time tn. Due toslotted ALOHA, only one value in each column of VT can

be sampled. The goal is to estimate a matrix VT , such thatVT ≈ VT , based on collected sparse samples. We first builda sampled matrix VT , which is of the same size as VT , butall the missing data elements are set to 0. We then filter outthermal noise from the phase variation signal using a low-pass filter with a 15 Hz cutoff frequency, and map the signalto the sampled elements in VT . Moreover, all the distortedphase variations in VT that satisfy (4), are also set to 0 (i.e.,dropped) to avoid the influence of frequency hopping.

In the proposed system, 4 to 8 tags are attached to theseat belt and the frequency of time slots is about 220 Hz,which means the sparsity of VT is higher than 75%, andthe number of columns is much larger than the number ofrows. Because of the high sparsity and the limited numberof rows, the traditional singular value decomposition (SVD)based matrix completion method would not be effective forsuch VT , Therefore, we transform the data into a tensor formand apply tensor completion to estimate the missing data.Specifically, we reshape each row into a generalized Hankelmatrix as the frontal slice of the tensor, which has the sameformat of Hankel matrix but is not square. The sparse matrixVT is thus transformed into a tensor, given by

V(:,:,m).=

vmt1 vmt2 . . . vmt(n−r+1)

vmt2 vmt3 . . . vmt(n−r+2)

......

......

vmtr vmt(r+1). . . vmtn

, (6)

where r denotes the number of rows of the generalized Hankelmatrix. Note that a large row number in Hankelization willlead to high complexity, while a small number of rows (i.e.,less than 10) could considerably affect the recovering accuracy.Thus, we set r = 20 in our system (see Section V-B6).

Since thermal noise is filtered before tensor construction,the ideal tensor V , which is constructed by the ideal phasevariation matrix VT , can be considered as low rank data. Thus,V can be estimated from the sampled sparse tensor V by low-rank tensor completion, which is accomplished by solving thefollowing optimization problem [45]:

minV‖V‖∗, s.t. Ω ∗ V = Ω ∗ V, (7)

where V is an estimate of the ideal tensor V , and Ω is atensor of 0 and 1 elements, where Ωijk = 1 when Vijk issampled, and Ωijk = 0 otherwise. ‖.‖∗ denotes the trace normof tensor [45]. We adopt the HaLRTC algorithm for tensorcompletion, which can solve the optimization problem (7) withthe Augmented Lagrange Multiplier Method (ADMM) [12].Compared with other tensor completion algorithms, HaLRTCusually achieves a higher accuracy at an acceptable complex-ity. A comparison of HaLRTC and a classic matrix completionmethod on phase variation recovery is shown in Fig. 5.

To make the comparison, we interrogate a single tag for10 s, and repeat for 5 times as if there were 5 virtual tags.Since there is only one tag being interrogated each time, nodata will be missing in VT . We thus obtain the ideal phasevariation data VT as ground truth, and then remove someelements in VT according to the slotted ALOHA protocolto obtain VT . The remaining elements used for recovery are

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-0.1

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0 50 100 150 200 250 300 350 400 450 500Sequence Number

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0.1Data Recovered by Matrix Completion

Fig. 5. Recovered signals using HaLRTC and Matrix Completion.

marked with in Fig. 5. Since there are 5 virtual tags inthe emulated data, the sparsity is higher than 80%. Fig. 5shows the first 500 samples recovered by tensor completionand matrix completion, respectively. It can be seen that therecovered signal by HaLRTC is very similar to the originalsignal, while the recovered signal by matrix completion isnot good. Many values recovered by matrix completion arestill very close to 0. This is because there are only 5 rowsin VT , but the number of columns is now 500. SVD basedmatrix completion cannot obtain sufficient singular values foraccurate estimation. In contrast, although tensor completionalso requires singular values for estimation, the unfoldingprocess can provide a sufficient matrix size for decomposingsingulars values.

Once VT is successfully recovered by HaLRTC, we can eas-ily recover the phase sequence of each tag for all time slots byintegrating the corresponding phase variations. Furthermore,the recovered phase data will not be affected by frequencyhopping, because all the distortion related phase variations aredeleted when building VT .

C. Dealing with Vehicle Vibration and Body Movements

Interference caused by vehicle vibration and body or en-vironment movements is another big challenge for breathmonitoring in driving environments, which should be mitigatedbefore tensor decomposition. The driving movement couldhave different impacts for different tags, because the tagsare deployed at different parts of the seat belt. Fortunately,most of the driving related body movements are not fast,and the resulting interference can be considered as a directcurrent (DC) component (with frequencies around 0) in therecovered phase signal. We thus apply a Hampel filter with awindows size of 3 s and a threshold of 0.001 to extract theDC component and then subtract it from the original signal.

The filtered signals from 4 tags are illustrated in Fig. 6. Wefind that the DC components are successfully removed, but therespiration signal is still hard to see. This is because the phasesignals are also influenced by vibration of the moving vehicle.The noise generated by vibration is hard to be estimated,because both strength and frequency of the noise are relatedto road conditions and speed of the car.

-1012

Tag1

-2-101

Ph

ase

for

Eac

h T

ag (

rad

)

Tag2

-2-101

Tag3

0 5 10 15 20 25 30Time (s)

-2-101

Tag4

Fig. 6. Recovered phase after DC removal.

0 10 20 30

-2

0

2

Tag2-Tag1

0 10 20 30-2

0

2Tag3-Tag1

0 10 20 30-2

0

2P

has

e D

iffe

ren

ce f

or

Eac

h T

ag P

air

(ra

d)

Tag4-Tag1

0 10 20 30-2

0

2Tag3-Tag2

0 10 20 30Time (s)

-2

0

2Tag4-Tag2

0 10 20 30Time (s)

-2

0

2Tag4-Tag3

Fig. 7. Phase difference for each pair of RFID tags.

However, since all the tags are attached to the seat belt,the noise generated by vibration has a similar effect on them.With filtered recovered phase variation signal, we can obtainthe phase difference for each tag pair in each time slot. Theresulting phase difference is plotted in Fig. 7, where mostphase difference curves exhibit strong periodicity, meaning theinfluence of vibration has been effectively mitigated.

D. CPD based Respiration Signal Separation

1) Tensor Data Construction with Hankelization : Ex-tracting a clean respiration signal from the calibrated phasedifference data for different tag pairs, as shown in Fig. 7, isstill challenging, because the periodicity strength of differenttag pairs could vary with the movements of the driver andin the driving environment. It means no such tag pairs thatcould always reveal the highest periodicity, and the worst pairscould have no periodicity in the estimated phase difference.Some traditional signal processing techniques, such as discretewavelet transform (DWT), can extract the respiration signalfrom the signal with sufficient periodicity, but the performancecould be poor when DWT is applied to noisy signals.

However, since the respiration signal captured by phasedifference is the same for all tag pairs, each phase difference

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Fig. 8. Flow-chart of the CPD based respiration extraction method.

sequence can be considered as the same respiration signalcorrupted by different noises. Rather than employing signalprocessing techniques for each individual tag pairs, we cananalyze the entire group of estimated phase difference data.Tensor decomposition is widely used to separate a correlatedsignal from multiple datasets [19], [46]. For example, inTensorBeat [19], CPD is used to separate multiple breathingsignals from WiFi phase difference data. We can decomposethe breathing signal from noises in driving environments usinga CPD tensor decomposition method. The detailed process ofrespiration signal extraction is shown in Fig. 8.

As Fig. 8 shows, the respiration signal is extracted from theseparated signals from CPD, so that the breathing rate couldbe estimated based on the interval of the detected signal peaks.Before decomposing the data with CPD, we transform thephase difference matrix into a tensor structure, by reshapingeach phase difference sequence into a generalized Hankelmatrix. Hankelization is essential before CPD decompositionis applied, because its special structure helps to separate aperiodic signal (i.e., the breathing signal) from the data. Wesummarize the relationship between periodic signals and theproposed Hankel matrix in Theorem 1. The proof is providedin Appendix A.

Theorem 1. If the generalized Hankel matrix H with r rowsis constructed from a sinusoidal wave with length n, it can bedecomposed as: H =

∑2i=1 αi · βT

i , where both αi ∈ Rr,1

and βi ∈ R(n−r+1),1 represent sinusoidal signals with thesame frequency as the original signal.

Theorem 1 provides the theoretical underpinning for esti-mating respiration rate from the generalized Hankel matrixderived from the phase difference sequence. It also determinesthe number of sinusoidal components to be decomposed fromthe generalized Hankel matrix. In our system, we build thegeneralized Hankel matrix with 30 s of data and leverage 10s of data to build each column of the matrix. This is because10 s of data can guarantee that at least one full period of thebreathing signal can be decomposed in αi.

2) CPD Based Breathing Signal Separation : With the ten-sor constructed by Hankelization, denoted by Γ, the respirationsignal can be separated from noise by applying CPD, whichdecomposes the tensor into a sum of the outer products of

three vectors as [47]

Γ ∈ RI,J,K ≈M∑

m=1

~am ~bm ~cm, (8)

where M is the tensor rank used for CPD, which also indicatesthe number of components in the decomposition result; ~am,~bm, ~cm are the vectors at the mth position for the threedimensions, respectively. We have ~am ∈ RI,1 ,~bm ∈ RJ,1,~cm ∈ RK,1, and (~am ~bm ~cm)(i, j, k) = ~am(i)~bm(j)~cm(k),for all i, j, k. According to the definition of outer product, wecan construct the matrix from the vectors for each dimension.For example, matrix A is defined as [~a1,~a2, ...,~aM ], andmatrices B and C are defined similarly with ~bm and ~cm,respectively. The process of CPD is implemented by solvingthe following optimization problem.

minA,B,C

‖Γ−M∑

m=1

~am ~bm ~cm‖2F . (9)

Although the above problem is not convex, CPD leverages theAlternating Least Squares (ALS) algorithm to optimize onematrix while fixing the other two. With the ALS algorithm, theoptimization problem can be reduced to a linear least squaresproblem, and the three matrices can be finally estimated.

In CPD, the number of components M should be prescribed,which is determined by the target signal and the uniqueness ofthe decomposition. Thus, we propose Theorem 2 to determinethe range of M , which is proved in Appendix A.

Theorem 2. The tensor rank used for CPD in the proposedsystem should satisfy 2 6M 6 4 and the CPD is unique.

The noise in the tensor is usually considerably large indriving environments (i.e., much larger than the respirationsignal). Some other noise components could also be decom-posed. To separate noise and precisely extract the respirationsignal, we set M = 4 for CPD. The decomposed matrix Bis illustrated in Fig. 9. We can see that two sinusoidal signalswith the same period are decomposed by CPD (i.e., the 3rdand 4th components), while the other components (i.e., thefirst and 2nd components) are for the residual noise after datapreprocessing.

E. Breathing Rate Estimation

With the respiration signal separated by CPD, we canestimate the breathing rate using a peaks detection algorithm.However, we still need to differentiate the periodic signalfrom all decomposed signals before we estimate the breathingrate. Thus, we leverage a frequency spectrum based methodto figure out which decomposed signal is for the breathingsignal. We first calculate the proportion of the power spectrumbetween 0.2 Hz and 0.5 Hz in the frequency domain, whichis the range of normal human breathing. Then, we search forthe two signals with the first two largest proportions and fusethem to obtain the final breathing signal. The fused signal isillustrated in Fig. 10. It can be seen that the respiration signalis precisely extracted and the noises from vehicle vibrationand other movements in the driving movement are effectively

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Fig. 9. Decomposed signals by CPD.

0 5 10 15 20Time (s)

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Ph

ase

(ra

d)

Fig. 10. Signal fused by all breathing related components.

removed. The intervals τ between each pair of adjacent peaksare calculated and the breathing rate F is determined by theaverage interval τave as F = 60/τave.

V. SYSTEM PERFORMANCE EVALUATION

A. Experiment Configuration

To evaluate the performance of our respiration monitoringsystem in the driving environment, we implement a prototypesystem with an Impinj R420 reader equipped with a polarizedantenna S9028PCR.1 The setup up of the system is illustratedin Fig. 11. As the figure shows, multiple ALE-9470 RFIDtags are attached to the seat belt of the driver. The size ofthe polarized antenna utilized in the system could be smaller,because many small-sized antennas have been developed, suchas Keonn Advantenna-p11 and Thingmagic EL6E.

Although the cost of the RFID reader used in the prototypesystem is not very low, some other cheaper readers could beadopted for reduced cost. For example, since only one antennais required in our system, one port reader like Impinj R120

1Although we used such commodity RFID devides in our proof-of-conceptprototyping and experiments, the size of the system can be greatly reducedby using smartphones with an attached reader, e.g., made by Zebra.

Fig. 11. Illustration of the system setup in a car in our experiments.

can be used. Furthermore, medium range readers, such asFeig MRU102-PoE, will be another low-cost option, becausethe interrogate range for car environment monitoring is notdemanding. Furthermore, our system is currently composedof multiple commodity devices. The cost of the future systemcould be further reduced, if customized readers are used andmass produced.

The channel used by the reader hops every 0.2 s among50 channels from 902 MHz to 928 MHz when interrogatingRFID tags. The processor used for signal processing is anMSI laptop with a Navidia GTX 1080 GPU and Intel Core i7-6820HK CPU. The model of the test vehicle is BMW 328i.Five volunteers (1 female and 4 males) are tested with ourprototype system. The breathing rates of the volunteers arealso estimated by a NEULOG sensor, which is considered tobe the ground truth in our experimental result analysis.

B. Results and Discussions

1) Overall Accuracy for Different Rates: Our system istested by five volunteers with different breathing rates. Thecumulative distribution function (CDF) of estimation errors ispresented in Fig. 12. The figure shows that the median errorsfor the three ranges of breathing rates are 0.11 bpm, 0.12 bpm,and 0.14 bpm, respectively, which are all very close to eachother. However, the maximum error for the 10 ∼ 15 bpm rangeis 0.33 bpm, which is much smaller than that for the 16 ∼ 23bpm range and that for the 24 ∼ 30 bpm range. This impliesthat the accuracy of the system is higher when the driverbreaths slowly. This is because breathing rate is calculatedby F = 60/τave, where τave is estimated by peak detection.As the driver’s breathing gets faster, τave will become smaller,and the estimation error in τave will be amplified in F .

We next compare with the traditional RFID based methodpresented in [10], [11] in Fig. 13, when the driver is driving ona highway (i.e., interstate I-85). Other RFID based respirationmonitoring techniques, such as Tagbreathe [9], can achievehigh accuracy in a stationary testing environment. However,the Tagbreathe system is not well suited for operation withUltra High Frequency (UHF) RFID devices in the US, whichrequires frequency hopping. Thus, we only provide the exper-imental result of the RFID breathing monitoring system in a

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Estimation Error (bpm)

0

0.2

0.4

0.6

0.8

1C

DF

10~15 bpm

16~23 bpm

24~30 bpm

Fig. 12. System performance for different breathing rates.

0 1 2 3 4 5 6Estimation Error (bpm)

0

0.2

0.4

0.6

0.8

1

CD

F

Proposed Method

Traditional Method

Fig. 13. System performance compared with a traditional RFID basedrespiration sensing technique for stationary environments [10], [11].

stationary environment proposed in [10], [11] to illustrate therobustness of our system in noisy driving environments.

The CDFs of estimation errors achieved by the traditionaland proposed methods are presented in Fig. 13. We find thatthe median error of the traditional method is 1.71 bpm and36.11% data has an estimation error larger than 2 bpm. Incontrast, the median error of our proposed method is 0.12and the maximum error is 0.36 bpm. From the results, wecan conclude that the performance of the traditional methodis quite limited in driving environments, because of theconsiderable interference caused by the vehicle, driver, andpassengers. However, due to effective noise mitigation, ourproposed method can achieve high accuracy in respirationmonitoring in such noisy environments.

To compare the accuracy of breathing rate estimation fordifferent types of systems, we summarize the mean estimationerror as provided in related papers [4], [6] in Table I (note thatwe compare mean error rather than median error here, sincethose are provided in the two related papers). As shown inthe table, the video camera based method and UWB radarbased method have higher estimation errors, which are 0.79

TABLE ICOMPARISON OF DIFFERENT BREATHING RATE MONITORING SYSTEMS

FOR THE DRIVING ENVIRONMENT

Employed Device Mean Estimation Error

Video Camera (Kinect) 0.79 bpmUWB Radar 0.31 bpmRFID Tags and Reader 0.11 bpm

0 0.1 0.2 0.3 0.4 0.5

Estimation Error (bpm)

0

0.2

0.4

0.6

0.8

1

CD

F

Parked

Highway Driving

In-town Driving

Fig. 14. System performance for different driving scenarios.

bpm and 0.31 bpm, respectively. The mean estimation error ofthe proposed system is 0.11 bpm, which is much lower thanthe other two. This is because RFID tags can provide highaccuracy as wearable sensors, and the effect of interferencefrom other passengers is limited too. Moreover, with measuredphase from multiple RFID tags, the CPD based approach caneffectively mitigate the influence of vehicle vibration and othernoises in driving movements.

2) Accuracy in Different Driving Scenarios: The systemis evaluated in 3 different scenarios, including (i) driving ona highway, (ii) driving in a city street, and (iii) parked. TheCDF of errors for the three scenarios are plotted in Fig. 14. Themedian error is 0.11 bpm for the parked scenario and 0.12 bpmfor the two driving scenarios. It proves that the influence of thedriving environment is effectively mitigated by the proposedscheme. The figure also shows that the maximum error forin-town driving is 0.48 bpm, which is the highest among thethree scenarios. This is because the driver needs to turn thewheel frequently and stops from time to time when driving intown, and the influence of the driving movements cannot becompletely eliminated.

3) Impact of Passenger Movement: We also test the per-formance of our system when there are different numbers ofpassengers. In these experiments, all the passengers are askedto move naturally. As Fig. 15 shows, when no passenger ispresent, the median error is 0.09 bpm, which is the smallestamong all the cases. The error increases to 0.11 bpm whenthere is one passenger in the car. The movement of thepassenger does affect the sampled phase data, although theimpact is small. The median error is not obviously affected byincreased number of passengers, and the maximum errors are

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0 0.1 0.2 0.3 0.4 0.5Estimation Error (bpm)

0

0.2

0.4

0.6

0.8

1C

DF

No Passenger

1 Passenger

2 Passengers

3 Passengers

Fig. 15. System performance with different numbers of passengers.

almost the same for the different cases. This result shows thatthe performance of our system is not sensitive to the movementof passengers, because the tags are only attached to the seatbelt of the driver as well as the near-field nature of RFIDcommunications.

4) Impact of Antenna Position: We try different antennadeployment in our experiments to identify the most suitableway to place the antenna. The first scenario is to attach theantenna on the ceiling above the driver seat, as shown inFig. 11. The second deployment is to attach the antenna tothe front control panel of the vehicle. The third scenario is tobond the antenna on the side of the back of the co-pilot seat.The CDF results are plotted in Fig. 16. It can be seen that thedeployment of the antenna has a considerable impact on thesystem performance. The median error is 0.73 bpm when theantenna is placed on the side of the diver, because the phasechanges caused by the movement of human chest is harderto detect. The accuracy is also not high when the antenna isattached to the front panel, with a median error of 0.28 bpm.This is because the range of the polarized antenna is limited,and some of the tags cannot be scanned by the antenna. Thus,we conclude that the best deployment position of the antennais the ceiling, which can guarantee full-tag interrogation andhigh sensitivity of detecting the respiration signal.

5) Impact of Number of Tags and Coupling Effect: We nextevaluate the accuracy of our system with different numbers oftags. Since we need to calculate phase difference between tagpairs and build the tensor data, the minimum number of tagsis 3 in our system. Fig. 17 shows the accuracy under differentnumbers of tags. The mean error is relatively high when only3 tags are deployed, which is 0.45 bpm. This is because the3 tags can only generate 3 phase difference sequences forCPD. The respiration signal is hard to be decomposed fromthe small tensor constructed by 3 tags. We also observe thatwhen 5 or more tag are deployed, the error is reduced to 0.11bpm. However, the error becomes 0.21 when 9 tags are used,because the error in recovering the missing samples becomeslarge with 9 tags. Moreover, more time will be consumed indata recovering and tensor decomposition when more tags areused. We use 5 tags on the seat belt in our system.

0 0.5 1 1.5 2 2.5

Estimation Error (bpm)

0

0.2

0.4

0.6

0.8

1

CD

F

Ceiling

Front Panel

Co-pilot Seat

Fig. 16. System performance under different deployment locations of thepolarized antenna.

3 4 5 6 7 8 9Number of Tags

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Est

imat

ion

Err

or

(bp

m)

Fig. 17. Estimation error for different numbers of deployed tags.

Fig. 17 also shows that the accuracy of the system isnot seriously affected by the coupling effect, because theestimation error remains small (around 0.11 bpm) even when 8tags are used. With 8 tags attached to the seat belt, the densityof RFID tags is quite high, which generates large mutualcoupling among these tags. Fortunately, the coupling effectonly affects the phase value received by the reader [31], whilethe breathing rate estimation is dependent on the periodicityof the signal. Thus the system is robust to the mutual couplingeffect. The figure also shows that, the error increases a little(to 0.2 bpm) when 9 tags are deployed. This is because theconsiderable larger mutual coupling effect may introduce lowbackscattering power from the tags in this case. Since thereader uses a power threshold for receiving tag response, tagswith low backscattering power will hardly be interrogated bythe reader. To make sure that all tags can provide enoughinformation to the reader, we conclude that 8 tags are themaximum number of tags for the prototype system.

6) Complexity Reduction: Since the system requires solv-ing two optimization problems for data recovery and tensordecomposition, the complexity of the algorithm could be a

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0

2

4

6

8

10C

on

sum

ed

Tim

e (

s)

2 5 10 20 30 40 50Number of Rows

0

0.2

0.4

0.6

RM

SE

(ra

d)

1.26

0.05

Fig. 18. Impact of Hankelization size on HaLRTC complexity and recoveringaccuracy.

problem that needs to be investigated. We aim to reduce thecomplexity of HaLRTC and CPD by reducing the size of thetensors and by downsampling. For phase recovery, we canreduce the size of the tensors by adjusting the number of rowsin Hankelization. We utilize the 20 s data used in Fig. 5 totest the influence of the number of rows on complexity andaccuracy. The results are shown in Fig. 18. We can see that asthe number of rows is increased, the consumed time increasesexponentially, while the Root Mean Square Error (RMSE)decreases exponentially. To trade off between accuracy andcomplexity, we choose 20 as the row number for buildinggeneralized Hankel matrix.

Downsampling is not implemented in the phase recoveringprocess, because the sparsity of the data is very high anddownsampling could considerably affect the recovery perfor-mance. However, downsampling is an effective way to reducethe complexity of CPD. Following Theorem 1, the rows of thegeneralized Hankel matrix in CPD should be large enough, orthe periodicity of the signal can hardly be revealed in αi.Thus, we fix the number of rows and test the performanceof CPD with different downsampling indices. As Fig. 19shows, when the index is larger than 12 the consumed timeby CPD is shorter than 0.82 s, and the estimation error issmaller than 0.2 bpm when the index is smaller than 14. Whenthe downsampling index gets higher, the accuracy decreasessharply, because the remaining data is not enough for CPDto precisely separate the breathing signal. To achieve highaccuracy with an acceptable complexity, we downsample thedata by 12 before constructing the tensor input for CPD.

In conclusion the total time consumed for data processingin our system is about 2 s. Since drowsy driving is a relativelylong, slowly developing process (i.e., people do not fall asleepsuddenly), such a latency should be sufficient to warn thedriver in advance (e.g., the safe distance to the vehicle aheadof one’s car is 2 or 3 s). In addition, the processing speed canbe improved by specific embedded hardware. The complexityof the prototype system is acceptable.

0

20

40

60

Co

nsu

med

Tim

e (s

)

0 2 4 6 8 10 12 14 16 18 20

Downsampling Index

0

0.3

0.6

0.9

Est

imat

ion

Err

or

(bp

m)

0.821.13

Fig. 19. Impact of downsampling on CPD complexity and system perfor-mance.

VI. CONCLUSIONS

In this paper, we proposed an RFID based respiration ratemonitoring system for the driving environment. The proposedsystem included several novel components, including datacollection, breathing data preprocessing, CP tensor decompo-sition, and respiration signal estimation, to combat the strongnoise caused by frequency hopping, random sampling, vehiclevibration, and other movements in the environment. Theproposed system was implemented with commodity RFID tagsand reader, and was evaluated under real driving scenarios.Our experiments showed that the tensor completion and CPDapproaches were effective for respiration monitoring in drivingenvironments.

APPENDIX APROOF AND DISCUSSION OF THE THEOREMS IN CPD

PROCESSING

A. Proof of Theorem 1

Proof. To analyze the features of the generalized Hankelmatrix, we first assume the original signal is a noise-free,discrete sinusoidal signal sampled at a constant period t, whichis given by y(n) = a sin(wtn+ϕ0), where a, w, and ϕ0 are theamplitude, frequency, and initial phase offset of the sinusoidalsignal, respectively.

For convenience, we define

~Sqp.= [sin(wtp+ ϕ0), sin(wt(p+ 1) + ϕ0), ..., sin(wtq + ϕ0)],

and rewrite the generalized Hankel matrix as

H = a ·[~S(n−r+1)1 , ~S

(n−r+2)2 , · · · , ~Sn

r

]T. (10)

We also define

~Cqp.= [cos(wtp+ϕ0), cos(wt(p+1)+ϕ0), ..., cos(wtq+ϕ0)].

Since sin(wt(n + 1) + ϕ0) = sin(wtn + ϕ0) cos(wt) +cos(wtn + ϕ0) sin(wt), we can convert the time-shift of

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Hankelization to a summation format. The generalized Hankelmatrix H can be rewritten as

H = a·

~S(n−r+1)1 cos(0) + ~C

(n−r+1)1 sin(0)

~S(n−r+1)1 cos(wt) + ~C

(n−r+1)1 sin(wt)

~S(n−r+1)1 cos(w2t) + ~C

(n−r+1)1 sin(w2t)

· · ·~S(n−r+1)1 cos(w(r−1)t)+ ~C

(n−r+1)1 sin(w(r−1)t)

.Note that both vectors [cos(0), cos(wt), ..., cos(w(r − 1)t)]and [sin(0), sin(wt), ..., sin(w(r−1)t)] are discrete sinusoidalsignals with the same period w. Thus, we can rewrite H asH = ψT

1 ·ψ2, where ψ1 = [α1, α2]T given by

ψ1 = 1 ·[cos(0), cos(wt), ..., cos(w(r − 1)t)sin(0), sin(wt), ..., sin(w(r − 1)t)

], (11)

and ψ2 = [β1, β2]T given by

ψ2 = a ·[S(n−r+1)1 , C

(n−r+1)1

]T, (12)

where each row of ψ1 and ψ2 is a sinusoidal signal withperiod w. Therefore, both αi and βi are sinusoidal signalswith the same period w.

B. Discussion of Theorem 2

Since only the driver’s breathing signal is captured by thephase difference sequence, the modified Hankel matrices canbe regarded to be generated by a single sinusoidal signal (i.e.,the breathing signal) plus noises from the driving environment.Following Theorem 1, the two related components should bedecomposed, and thus we have M > 2.

Next we consider the upper bound of M to satisfy theuniqueness requirement of CPD. It is given that the outputof CPD is unique only when RA +RB +RC ≥ 2M + 2 [47],where RA, RB , and RC are the number of independentrows in matrix A, B, and C. In the constructed tensor, RC

is determined by the number of independent signals, whileRA and RB are determined by the sampled signal used forhankelization. In our system, each tag can be consideredas an independent sensor. So RC equals to the number ofdeployed tags, which means RC > 4 (since 4 to 8 tags areused). In addition, we have RA = RB > 3 because thebreathing signal itself takes 2 rows and the noise in sampleddata occupies at least one independent row. Therefore, tosatisfy the uniqueness condition of CPD, we should have2M+2 6 minRA+minRB+minRC = 3+3+4 = 10,i.e., M 6 4. Thus, we conclude that the tensor rank used forCPD in the proposed system should satisfy 2 6 M 6 4 andthe CPD is unique.

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Chao Yang [S’18] received the B.S. degree in elec-trical engineering from Yanshan University, He’bei,China in 2015, and an MS degree in Electrical andComputer Engineering (ECE) from Auburn Univer-sity, Auburn, AL in 2017. He has been pursuinga PhD in ECE at Auburn University since Spring2018. His current research interests include healthsensing, indoor localization, internet of Things andwireless networks. He is a co-recipient of the BestPaper Award of IEEE GLOBECOM 2019.

Xuyu Wang [S’13-M’18] received the M.S. inSignal and Information Processing in 2012 and B.S.in Electronic Information Engineering in 2009, bothfrom Xidian University, Xi’an, China. He receiveda Ph.D. in Electrical and Computer Engineeringfrom Auburn University, Auburn, AL, USA in Aug.2018. He is an Assistant Professor in the Departmentof Computer Science, California State University,Sacramento, CA. His research interests include in-door localization, deep learning, and big data. He is aco-recipient of the Second Prize of Natural Scientific

Award of Ministry of Education, China in 2013, the Best Paper Award ofIEEE GLOBECOM 2019, The 2018 Best Journal Paper Award of IEEECommunications Society Multimedia Communications Technical Committee,the Best Demo Award of IEEE SECON 2017, and the Best Student PaperAward of IEEE PIMRC 2017.

Shiwen Mao [S’99-M’04-SM’09-F’19] received hisPh.D. in electrical and computer engineering fromPolytechnic University, Brooklyn, NY in 2004. Cur-rently, he is the Samuel Ginn Endowed Professorin the Department of Electrical and Computer En-gineering, and Director of the Wireless EngineeringResearch and Education Center at Auburn Univer-sity, Auburn, AL, USA.

His research interests include wireless networks,multimedia communications, and smart grid. He isan Area Editor of IEEE Transactions on Wireless

Communications, IEEE Open Journal of the Communications Society, IEEEInternet of Things Journal, IEEE/CIC China Communications, and ACMGetMobile, and an Associate Editor of IEEE Transactions on Network Scienceand Engineering, IEEE Transactions on Mobile Computing, IEEE Multimedia,and IEEE Networking Letters, among others.

Dr. Mao received the IEEE ComSoc TC-CSR Distinguished TechnicalAchievement Award in 2019, the IEEE ComSoc MMTC Distinguished ServiceAward in 2019, Auburn University Creative Research & Scholarship Awardin 2018, the 2017 IEEE ComSoc ITC Outstanding Service Award, the 2015IEEE ComSoc TC-CSR Distinguished Service Award, the 2013 IEEE ComSocMMTC Outstanding Leadership Award, and NSF CAREER Award in 2010.He is a co-recipient of the 2018 IEEE ComSoc MMTC Best Journal PaperAward, the 2017 IEEE ComSoc MMTC Best Conference Paper Award, theBest Demo Award from IEEE SECON 2017, the Best Paper Awards fromIEEE GLOBECOM 2019, 2016, and 2015, IEEE WCNC 2015, and IEEEICC 2013, and the 2004 IEEE Communications Society Leonard G. AbrahamPrize in the Field of Communications Systems. He is a Fellow of the IEEE.