multiple people identiﬁcation through walls using off-the

INTERNET OF THINGS JOURNAL 1

Multiple People Identification Through WallsUsing Off-The-Shelf WiFi

Belal Korany, Student Member, IEEE, Hong Cai, Student Member, IEEE, and Yasamin Mostofi, Fellow, IEEE

Abstract—In this paper, we are interested in through-wall gait-based identification of multiple people who are simultaneouslywalking in an area, using only the WiFi magnitude measurementsof a small number of transceivers. This is a considerablychallenging problem as the gait signatures of the walking peopleare mixed up in the WiFi measurements. In order to solvethis problem, we propose a novel multi-dimensional framework,spanning time, frequency, and space domains, that can separatethe signal reflected from each walking person and extract itscorresponding gait content, in order to identify multiple peoplethrough walls. To the best of our knowledge, this is the first timethat WiFi signals can identify multiple people in an area. Weextensively validate our proposed system with 92 test experimentsconducted in 4 different areas, where the WiFi transceivers areplaced behind walls, and where 2 or 3 people (randomly selectedfrom a pool of 6 test subjects) are walking in the area. Oursystem achieves an overall average accuracy of 82% in correctlyidentifying whether a person walking in the test experiment(referred to as a query) is the same as a candidate person, basedon 6,404 query-candidate test pairs. It is noteworthy that noneof the test subjects/areas has been seen in the training phase.

Index Terms—WiFi, Multi-Person Identification, RF Sensing,Gait Analysis, Through-Wall Sensing

I. INTRODUCTION

Due to the emergence of smart homes and internet ofthings, recent years have seen a rapid growth in the numberof devices with wireless capabilities. These devices emitRadio Frequency (RF) signals (e.g., WiFi), which interactwith people and objects in the environment. As such, therehas been considerable interest in utilizing these RF signals toextract various types of information about the people and/orthe environment, e.g., occupancy estimation [1], [2], activitydetection/recognition [3], localization [4], tracking [5], andimaging [6]. In particular, identifying a person based on theirgait signature (i.e., the way they walk), using RF signals, hasrecently started to gain a considerable attention [7], [8], [9].Using RF signals for identification is appealing since it canrecognize a person from a distance, without requiring themto perform any specific active task (e.g., fingerprint scanning).In addition, unlike cameras, it is more versatile as it doesnot require a clear, unobstructed view of the walking person,and is not affected by lighting conditions. Utilizing off-the-shelf WiFi for person identification is, in addition, usefuldue to the low cost and ubiquity of WiFi transceivers. Ingeneral, using existing RF signals for identification can openup new possibilities in the areas of security, personalizedservice provisioning, crowd analytics, and public health. Forinstance, an existing home WiFi network can identify thehouse members who just entered the house and provide per-sonalized service accordingly. In addition, the WiFi network

B. Korany, H. Cai, and Y. Mostofi are with the Department of Electricaland Computer Engineering, University of California, Santa Barbara, CA,93106 USA. E-mail: belalkorany, hcai, [email protected]. This workis funded by NSF grant #1816931 and ONR grant #N00014-20-1-2779.

in a mall can identify the people (while anonymizing thedata) and track where they go, which will be helpful foranalyzing people’s shopping preferences and the traffic flow.Furthermore, thanks to the wide coverage of WiFi nowadays,RF-based identification can also be used for contact tracing tohelp slow down the spread of diseases (e.g., COVID-19).

All the existing RF-based gait identification approaches,however, can only be used in situations where there is onlyone person walking in the area, which is an overly restrictivecondition that significantly limits the practical use of thistechnology. In addition, most of the existing work on personidentification with RF signals require training the system withextensive measurements of the same subjects to be identified,as well as training in the same operation area. This furtherlimits the applicability of these systems since they cannot beused for new people or in new areas, without additional datacollection and retraining.

In this paper, we propose a novel multi-person identificationsystem, using off-the-shelf WiFi devices, which is capableof recognizing the identities of multiple people when theyare simultaneously walking in an area behind a wall. Morespecifically, given only the WiFi Channel State Information(CSI) magnitude signal received when a number of unknownpeople are walking in an unknown area behind a wall, ourproposed system is able to extract the gait information ofeach individual person and identify them from the overallWiFi magnitude measurement. By identifying a person, wemean determining if this person is the same as the personthat was walking in another area where a WiFi receivermeasured its received power. In other words, given a WiFisample measurement where a person was walking in an area(candidate sample) and WiFi measurements where a numberof people are walking in another area behind the wall (querysamples), our system can determine if the candidate person isamong those behind the wall, without any need for collectingtraining data of any of these people. Moreover, our proposedsystem only uses the CSI magnitude measurements of a WiFilink, which is more preferable in practice since the phasemeasurements are either unavailable or not reliable on off-the-shelf devices [10]. To the best of our knowledge, this is thefirst time that WiFi-based identification is made possible forthe setting of multiple simultaneously-walking people, whichcan lead to a significantly broader applicability of WiFi-basedgait identification systems. Furthermore, the ability to identifypeople, without any prior training data of them, can have atremendous impact on this technology.

The main challenge in identifying multiple simultaneously-walking people is that their gait information will be all mixedup in the received WiFi signal magnitude measurement. Wethen propose a novel technique that jointly processes thereceived signal across time, frequency, and the Angle-of-Arrival (AoA) domains, in order to separate, extract, and track


the parts that correspond to each person’s gait from the overallreceived WiFi signal magnitude. We then extract key featuresfrom each separated part of the signal for the purpose ofidentification. We extensively evaluate our proposed approachusing a large test set, where all the test subjects and test areasare completely disjoint from the training data, thus allowing usto demonstrate the applicability of our system to new peopleand new areas. In the test set, there are 6 subjects and 4areas where the transceivers are placed behind a wall. In eachtest experiment, 2 or 3 randomly selected test subjects walksimultaneously in a test area, amounting to a total of 92 suchtest experiments. Given a candidate spectrogram generatedfrom the received WiFi signal measured when a person waswalking in another area, our system then determines if a personbehind the wall, among the multiple walking people, is thesame as the candidate person. For the two-people case, given apair of query and candidate spectrograms, our proposed systemachieves an identification accuracy of 82%, in determiningwhether the two data samples belong to the same person, basedon 4,892 test pairs. Additionally, for the test experiments with3 simultaneously-walking people behind a wall, our systemachieves an identification accuracy of 83%, based on 1,512test pairs. Overall, our results demonstrate the performance ofthe proposed approach for multiple people identification.

II. RELATED WORK AND PRELIMINARIES

In this section, we provide a brief overview of the relatedwork on gait-based person identification using RF signals anda brief primer on spectrogram-based gait analysis.

A. RF-Based Gait Identification

Early work on gait analysis utilize dedicated radar hardwareand/or wideband signals to analyze a single person’s walkingpattern. For instance, [11], [12] use radar to estimate themotion parameters of different body parts. In [13], the authorsdiscuss the challenge of multi-person gait analysis, stating thatit was not possible to interpret the individual gait signaturesof simultaneously-walking people without sophisticated radarequipment with a very high range resolution.

Recently, there has been considerable interest in using off-the-shelf WiFi devices for gait-based person identification.WiFiU [7] uses WiFi CSI to generate spectrogram-basedgait features, which are then used to classify the identitiesof a pre-defined set of people. WiWho [14] uses the time-domain signals, measured when a person is walking, foridentification. Similarly, [15], [16], [17], [18] identify a personfrom a pre-defined set of people. In our previous work [9], wehave proposed XModal-ID, a cross-modal person identificationsystem from video to WiFi. More specifically, XModal-IDidentifies whether a single walking person measured by WiFiis the same as a walking person in a video footage [9].

All the existing gait-based identification systems, however,are only applicable to situations where there is only oneperson walking in the WiFi area, and will fail when multiplepeople are simultaneously walking. In addition, with the onlyexception of our previous work [9], all the existing RF-basedwork on person identification need to collect training data of

Time (sec)

0

50

100

150

Fre

qu

ency

(H

z)

Torso reflection Leg reflection

Tx Rx

φT φR

Motion direction

410 2 3

Fig. 1. (Left) Single-person gait-based identification scenario, wherethe person walks near a WiFi link. (Right) Spectrogram of thereceived WiFi magnitude measurements capturing the reflections offof different body parts.

the same person that they want to identify. Furthermore, theyneed the training and test areas to be the same.

In this paper, we propose a novel through-wall gait-basedmulti-person identification system using off-the-shelf WiFidevices. Our system is able to extract the gait informationof each individual person from the aggregate WiFi magnitudemeasurement when multiple people walk simultaneously inan area. Furthermore, it does not require training with priormeasurements of the subjects to be identified, does not needprior knowledge of the test/operation areas, and can identifypeople through walls. Finally, it only uses the CSI magnitudemeasurements of the received signal.

B. Spectrogram-Based Gait Analysis

Spectrograms are commonly utilized in existing work ongait analysis and gait-based person identification to extract theattributes of a person’s gait [7], [9], [19], [17]. In this part, weprovide some preliminaries on spectrograms and discuss thegait information that they capture.

Consider the scenario shown in Fig. 1 (left), where oneperson is walking near a pair of WiFi transmitter (Tx) andreceiver (Rx). The squared magnitude of the received signalcan be written as follows, as a function of time [9]:

s(t) = PDC +∑m

αm cos

(2π

λψvm(t)t+ Ω

), (1)

where PDC is the DC component that does not carry motioninformation about the gait, αm is the magnitude of thereflection of the m-th body part, vm is the speed of the m-thbody part as a function of time, ψ = cosφR+cosφT with φR

and φT defined in Fig. 1 (left), Ω is a random initial phase,and λ is the wavelength of the wireless signal. It should benoted that ψ can, in general, be time varying. Eq. 1 showsthat the received signal consists of multiple sinusoids whosefrequencies are related to the speeds of different body parts.Hence, by utilizing a time-frequency analysis technique (e.g.,Short-Time Fourier Transform), one can obtain the frequencycontent of the signal (i.e., the speed profile of the body parts)as a function of time, which is called the spectrogram of thesignal. Fig. 1 (right) shows a sample spectrogram of the signalmeasured when a person is walking near the WiFi link. Inthe spectrogram, for instance, the stronger signal (indicatedby the brighter colors) corresponds to the strong reflectionfrom the torso of the person, while higher-frequency weakersignals represent the reflections from the legs, which havehigher speeds as compared to the average torso speed.


Magnitude-Based

Angle-of-Arrival

Extraction and Tracking

Spectrogram Generation

and Segmentation

Feature Distance

Calculation

Decision

Module

Identification

Decision

WiFi CSI Magnitude Measurements

When Multiple People Are Present

Spectrogram Feature

Extraction

Candidate Person

WiFi Signal

Spectrogram Feature

Extraction

Spectrogram

Generation

Fig. 2. Flowchart showing the modules of our proposed system formultiple people identification.

III. SYSTEM OVERVIEW

In this paper, we propose a system that can perform through-wall person identification on multiple people walking simulta-neously in an area, all of whom have not been seen during thetraining phase of the system. The overall system architectureis outlined in the flowchart of Fig. 2, and summarized below:• Given the CSI magnitude of a WiFi signal measured at

a small number of receivers when multiple people arewalking simultaneously behind the wall in an area, wefirst detect and track the Angles-of-Arrival (AoAs) of thesignal reflections from these people, using a combination of2D spectrum analysis, Joint Probabilistic Data AssociationFilter (JPDAF), and track management techniques.

• Given the AoAs corresponding to the different walkingpeople in the area as a function of time, we extract thegait signal of each walking person by projecting the totalreceived signal to the AoA of this person. Next, given theseparated WiFi signal of one person (referred to as thequery), we calculate the spectrogram of this signal to capturethe time-frequency characteristics of this person’s gait.

• We then detect the segments from each spectrogram thatare informative for identification. For each such segment, weextract several features to capture the person’s gait signature.

• In order to determine whether a detected spectrogram seg-ment (i.e., a query segment) belongs to the same personas the candidate person, we calculate the feature distancesbetween a query segment and a candidate spectrogram, andfeed them to a neural network which determines whetherthese two spectrograms correspond to the same person. Asthere can be multiple informative segments from the queryspectrogram of a person’s entire track during a measurementperiod, we use an algorithm based on maximum likelihoodestimation to fuse the segment-based decisions. The com-bined decision then indicates whether the query person of awalking track is the same as a candidate person.

IV. PROPOSED METHODOLOGY

In this section, we describe our proposed methodology formultiple people identification. We first describe the multi-person identification scenario and the corresponding signalmodel. We then show how to estimate and track the Angles-of-Arrival (AoAs) of the reflections from the walking people,

based on only the received signal magnitude measurements,and subsequently separate the signals relevant to each walkingperson by projecting the overall signal to the respective AoAs.Given the separated signal that contains the walk of oneperson, a frequency-time spectrogram is generated and theinformative segments of it are extracted for identification.

A. Signal Model for Joint Processing Based on Only Magni-tude Measurements

Consider the scenario shown in Fig. 3, where a WiFitransmitter (Tx) transmits WiFi signals that are reflected offof N people walking in an area with S static objects, and thenreceived by a receiver array (Rx). The received signal is thena combination of the direct signal from the Tx to the Rx, thereflected signals off of the S static objects, and the reflectedsignals off of the N walking people. More specifically, thetime-domain received signal as a function of the distance `along the array, where ` is measured with respect to the firstantenna, can be written as follows [5]:

c(t, `) =

Direct signalfrom Tx to Rx︷︸︸︷

αDe−j 2π

λ ` cos θD +

S∑s=1

Reflected signal off ofthe s-th static scatterer︷︸︸︷αse−j 2π

λ ` cos θs

+

N∑n=1

(∑m

αn,me−j 2π

λ vn,mψTn t

)e−j

2πλ ` cos θn

︸︷︷︸Reflected signals off of the n-th person

+η(t, `),

(2)

where αD, αs and αn,m are, respectively, the complex valuesof the direct path from Tx to Rx, the s-th static path (pathreflected off of a static object), and the reflected path off ofthe m-th body part of the n-th person at ` = 0, while θD, θs,θn are their AoAs (measured with respect to the x-axis). Sis the total number of static paths , vn,m is the speed of them-th body part of the n-th person, ψTn = cosφTn + cosφRn isa parameter related to the motion direction of the n-th person(see Fig. 3 for definitions of φTn and φRn ), η(t, `) is additivenoise, and λ is the wavelength of the WiFi signal.

Traditional AoA estimation relies on phase measurementsacross the receiver array. In our case, however, we onlyhave the received magnitude measurements. We next showhow the AoA information can be preserved in the magnitudemeasurements as well. The squared magnitude of the receivedWiFi signal can be calculated from Eq. 2, as shown in Eq. 3.In Eq. 3, P = |αD|2+

∑n

∑m |αn,m|2+

∑s |αs|2 denotes the

total power of the signal, ψAn = cos θD − cos θn is the differ-ence between the cosine of the AoA of the direct path and thecosine of the AoA from the n-th person, ψAs = cos θD−cos θsis the difference between the cosine of the AoA of the directpath from Tx to the Rx and the cosine of the AoA from thes-th static object, and η′(t, `) is additive noise. Since the Txand the Rx are close to each other, the direct path from Txto Rx will be much stronger than the other reflected paths(i.e., |αD| |αn,m| and |αD| |αs|). Hence, the first threeterms in Eq. 3 dominate the rest of the terms, which canthen be neglected. Furthermore, by subtracting the temporalmean of the received signal at each of the receiver antennas(which can be easily implemented in practice), all the time-independent terms of Eq. 3 are zeroed out. More specifically,


|c(t, `)|2 = c(t, `)c∗(t, `) = P +

N∑n=1

∑m

2|αDαn,m| cos

(2π

λ

(ψAn `+ vn,mψ

Tn t)

+ ∠αD − ∠αn,m

)+

S∑s=1

2|αDαs| cos

(2π

λψAs `+∠αD−∠αs

)+∑

(n,m)

∑s

2|αn,mαs| cos

(2π

λ

(vn,mψ

Tn t+ (cos θn − cos θs)`

)+∠αn,m−∠αs

)+∑s

∑s′ 6=s

αsα∗s′e

j 2πλ (cos θs−cos θs′ )` +

∑(n,m)

∑(n′,m′)

(n′,m′)6=(n,m)

αn,mα∗n′,m′ej

2πλ ((vn,mψ

Tn−vn′,m′ψTn′ )t+(cos θn−cos θn′ )`) + η′(t, `) (3)

Small number

of receivers

Tx

1Tφ

N

Tφ 1Rφ

RφN

Nθ

x

y

1θ

Fig. 3. Multiple people are walking simultaneously in an area, wherea WiFi transmitter and a small number of receivers (placed behind awall, without a direct view of the people) are used to collect WiFimeasurements. The black arrows in the figure indicate the respectivewalking directions of the people.

after subtracting the temporal mean, the squared magnitude ofthe received signal can be approximated as:cmov(t, `) = |c(t, `)|2 − Et|c(t, `)|2

≈N∑n=1

∑m

2|αDαn,m| cos

(2π(ψAn `+vn,mψ

Tn t)

λ+µ

)+η′(t, `),

(4)

where µ=∠αD−∠αn,m, and Et. denotes the temporal meanof the argument. The first term in Eq. 4 is a superposition ofN terms, each of which corresponds to one of the movingpersons, and contains a combination of sinusoids whose fre-quencies depend on the AoA of that person to the receiver(ψAn ) and the speeds of that person’s body parts (vn,mψTn ).This shows that cmov(t, `) carries vital information about theAoAs of the reflected signals off of the walking people.

By taking the 2D Fourier Transform of cmov(t, `) withrespect to time t and distance `, we then have

C(fT , fD) =

∣∣∣∣∣∫∫

cmov(t, `)e−j2πλ (fT t+fD`)dt d`

∣∣∣∣∣=

N∑n=1

∑m

|αDαn,m|δ(fT − vn,mψTn , fD − ψAn

)+

N∑n=1

∑m

|αDαn,m|δ(fT + vn,mψ

Tn , fD + ψAn

)+N,

(5)

where fT is the temporal frequency, fD is the spatial fre-quency, δ(∗, ∗) is the 2D Dirac Delta function, and N is thenoise floor.

It can be seen from Eq. 5 that each reflector in the operationarea results in 2 deltas in the 2D spectrum C(fT , fD). Byplacing the Tx such that the AoA of the direct path fromTx to Rx is zero (i.e., cos θD = 1), the values of ψAn = 1 −cos θn are restricted to the interval [0, 2], which is disjoint from

Fig. 4. A sample 2D spectrum in the (fT , fD) domain for the casewhere two people are walking simultaneously in an area, based ona 0.4-second WiFi measurement. It can be seen that there are twopeaks appearing in the 2D spectrum, corresponding to the strong torsoreflections of the two walking people.

the range of values of −ψAn [5]. Therefore, by constrainingthe search space for ψAn to [0, 2] (e.g., using only positivevalues for fD), we obtain only one delta function for eachreflector in the area at (fT , fD) = (vn,mψ

Tn , ψ

An ) in the 2D

spectrum. For the delta functions of the body parts of the sameperson, the one with the largest coefficient corresponds to thestrongest reflecting part of the body, which is the torso. Werefer to this strongest delta of a person as a peak and denoteits location in the 2D spectrum by (ψTn , ψ

An ). Fig. 4 shows an

example of a 2D spectrum C(fT , fD) generated from WiFimeasurements collected using an 8-element antenna array in areal experiment, where two people are walking simultaneouslyin an area. The ground-truth AoAs of the two people are 90

and 125 (i.e., ψA1 = 1 and ψA2 = 1.57), respectively. It canbe seen that there are two peaks at (fT , fD) = (−25, 1) and(fT , fD) = (54, 1.6) in the 2D spectrum, which correspondto the strong torso reflections of the two walking people.

Our new 2D model can additionally detect whether a personis walking towards or away from the link. As can be seen fromFig. 3, the reflected signal from a person walking away fromthe link has a negative ψT , while that from a person walkingtowards the link has a positive ψT . The peak location in the2D spectrum then indicates the walking direction, as can beseen in Fig. 4, where the first person (whose ψT = −25) iswalking away from the link while the second person (whoseψT = 54) is walking towards it. Hence, even if two peoplehave the same AoA at the receiver array but are walking indifferent directions, their reflections are separable in the 2Dspectrum C(fT , fD). On the other hand, in the traditional 1Dsignal model of Eq. 1, the peak corresponding to a walkingperson appears twice, at ±vmψT at each time instance, whichmakes the motion direction of the walking person ambiguous,unless the information of all the subcarriers are exploited.

Based on the properties of the Fourier Transform, we sum-marize the following properties about the shape of C(fT , fD)in the fD dimension:


• The width of a peak in the fD dimension is inverselyproportional to the length of the Rx antenna array. Thus, toincrease the resolution (or separability) of the measurementsin the AoA domain, one can increase the length of the array.

• Based on the Nyquist sampling theorem, the maximumallowable antenna separation in the antenna array is deter-mined by the maximum possible ψA. More specifically, themaximum antenna separation is given by: ∆` = λ/(2ψAmax).Therefore, if the AoAs of the reflected signals from thewalking people span the range of [0, 180], the maximumallowable antenna separation is λ/4.

Let Ct(fT , fD) be the 2D spectrum generated from a timewindow of the WiFi measurements from t to t + Twin. Wethen measure the temporal sequence of peaks appearing inconsecutive snapshots of Ct(fT , fD)|t=0:∆t:Tmax

(where Tmaxis the total measurement duration and ∆t is the time step) tokeep track of the AoAs of different people, as we show next.

B. AoA Tracking

Given the 2D spectrum Ct(fT , fD) generated from a timewindow of the received WiFi signal from t to t + Twin, weextract a set of Jt peaks located at ψj = (ψTj , ψ

Aj ), for j ∈

1, ..., Jt. We denote the set of peak locations at this timeinstance by Ψt = ψj : j = 1, . . . , Jt. In order to separateand extract the part of the received signal that is relevant toeach of the walking people in the area, the system needs toperform two main tasks as described below.1. AoA Track Management: A track T is defined as atemporal sequence of peaks in the 2D spectrum resultingfrom the same moving person. As we do not assume thatthe system has any prior knowledge about the number ofpeople in the area or when each person starts walking, itis necessary to automatically initialize a track when a newperson starts walking in the area, or terminate a track whenthe corresponding person stops walking or leaves the area. Werefer to a track for a person currently walking in the area asan active track, a newly initialized but not yet confirmed track(due to the possibility of false alarm) as a potential track, anda terminated track for which the person does not walk in thearea anymore as a finished track.2. AoA Data Association: At each time instance, given a setof active and potential tracks and the set of new peaks in the2D spectrum, the system needs to automatically associate eachpeak with the track of the corresponding walking person.

In order to perform these tasks, we propose an AoA trackingalgorithm, as described in Alg. 1. The algorithm takes asinput the measurement sequence, in the form of the set ofpeaks in the 2D spectrum over time. We then utilize the JointProbabilistic Data Association Filter (JPDAF) to associate thepeaks with the current active or potential tracks (lines 3 and 4in Alg. 1), with filter parameters pertaining to the associationprocess estimated from the training measurements. We referthe reader to [20] for more details on JPDAF. During theassociation, a measured AoA closer (in terms of Euclideandistance) to the current AoA of a track is more likely to belongto that track, as compared to an AoA that is farther away.

Algorithm 1 Angle-of-Arrival Tracking Algorithm

Input: Set of peaks in the 2D spectrum over time: Ψt|t=0:∆t:TmaxOutput: Set of active tracks and finished tracks: A, F

1: Initialize the sets of active tracks A, potential tracks P , andfinished tracks F to empty sets: A = ∅, P = ∅, F = ∅.

2: for t = 0 : ∆t : Tmax do3: Find the association between the current set of peaks Ψt in the

2D spectrum Ct(fT , fD) and the current active and potentialtracks using the JPDAF.

4: For each track T ∈ A ∪ P that is associated with a peak inΨt, update its ψT and ψA using the associated peak.

5: For each peak ψj ∈ Ψt that is not associated with any activeor potential tracks in A ∪ P , initialize a new potential trackTnew with ψj and add it to the current set of potential tracks:P = P ∪ Tnew.

6: for each T ∈ P do7: if the potential track T meets confirmation criteria then8: T is confirmed as an active track and is then moved to

the set of active tracks: P = P\T , A = A ∪ T .9: else

10: T is a false alarm and is then deleted from the set ofpotential tracks: P = P\T .

11: end if12: end for13: for each T ∈ A do14: if the active track T meets the termination criteria then15: remove T from A and add it to the set of finished tracks:

A = A\T , F = F ∪ T .16: end if17: end for18: end for

Once the JPDAF associates the peaks/measurements to thecurrent set of tracks, our proposed algorithm enforces thefollowing set of rules for track management:

• Initialization criterion (line 5 in Alg. 1): A potential track isinitialized if a peak in the 2D spectrum is not associated withany active or potential tracks at the current time instance.

• Confirmation criterion (line 7 in Alg. 1): A potential trackis confirmed active if it is associated with some peaks in the2D spectrum for more than a percentage pTC of the timeduring the first TC seconds after initialization. Otherwise, itis considered as a false alarm and discarded.

• Termination criterion (line 14 in Alg. 1): An active track isfinished if it is not associated with any peaks for more thana percentage pTF of the time during the past TF seconds.

Then, the total number of people in the area, N , will beestimated as the total number of active and finished tracks atthe end of the experiment. We can then obtain the AoA timeseries of the n-th person: θn(t) = cos−1(1 − ψAn (t)), whereψAn (t) is the time series of ψA in the n-th track Tn. Fig. 5shows a sample output of the AoA tracking algorithm for a 40-second experiment of two people walking. The track of personA is initialized at t = 2.2 s. The AoA time series of person Ais shown by the blue solid curve in Fig. 5. Similarly, the trackof person B is initialized at t = 5.1 s, with the correspondingAoA time series shown by the red dashed curve in the figure.For each track, the AoA sequence θn(t), n = 1, . . . , N , isutilized to generate the spectrogram that only contains thegait information of the corresponding person, isolated fromthe signals of the other walking people, as we show next.


Time (sec)

100

120

140

160Person APerson B

AoA

(deg

rees

)

10 20 30 400

Fig. 5. Sample output of the AoA tracking algorithm. Measurementsof person A are first detected at t = 2.2 s (blue solid curve).Measurements of person B are first detected at t = 5.1 s (red dashedcurve). Both tracks remain active till the end of the experiment.

C. Spectrogram Generation and Segmentation

Given the time series of the AoA of the reflected path offof a walking person, we project the received signal at theRx array, cmov(t, `), to the AoA of this person. The projectedsignal contains only the reflections from this person, and thusmakes it possible to analyze this person’s gait and performidentification. We then perform time-frequency analysis on theprojected signal. More specifically, given ψAn (t), the spectro-gram for the n-th walking person is generated by

Sn(t, f)=

∣∣∣∣∣∫τ

(∫`

cmov(τ, `)e−j2πλ ψ

An (τ)`d

)︸︷︷︸

projecting the signalto the n-th person’s AoA

χ(τ ; t)e−j2πfτdτ

∣∣∣∣∣2

,

(6)where ψAn (t) = 1 − cos θn(t) and χ(τ ; t) is a time windowfunction starting at time t. In other words, the measured signalcmov(τ, `) across all the Rx antennas as a function of time isfirst projected to the n-th person’s AoA, using the operationinside the inner brackets in Eq. 6. This results in a one-dimensional signal (as a function of time) which containsonly the reflected signal off of the n-th person. This one-dimensional signal is then time-windowed using a windowχ(τ ; t) and the frequency content of the time-windowed signal(which contains that person’s gait information) is obtainedusing FFT. Different window functions χ(t) result in differentfavorable characteristics in the spectrogram. For instance, asshown in the literature, a rectangular window (in which caseSn(t, f) is the Short-Time Fourier Transform of the projectedsignal) produces a spectrogram that has clearer informationon the speeds of the limbs, whereas the Hermite windowfunctions produce spectrograms with better time-frequencyresolution [9]. As such, we utilize a multi-window spectrogramby additively combining the spectrograms generated usingdifferent window functions, as follows:Sn(t, f) =

K∑k=0

∣∣∣∣∣∫τ

(∫`

cmov(τ, `)e−j2πλ ψ

An (τ)`d

)χk(τ ; t)e−j2πfτdτ

∣∣∣∣∣2

,

where χ0(τ ; t) is the rectangular window function starting attime t, and χk(τ ; t) is the k-th Hermite function [12].

As an illustrative example for our spectrogram generationmethod, Fig. 6 (left) shows the spectrogram of the overallmeasured WiFi signal squared magnitude in a real experimentwhen two people are walking simultaneously in an area. Itcan be seen that the gait signals of the two people severely

Time (sec)

Sp

eed

(m

/s)

0 15

1

2

-1

-2

0

Reflections

of person A

Time (sec)

Sp

eed

(m

/s)

AoA (degrees)

1

2

-1

-2

0

05

1015

9078675337

0

102

Reflections

of person B

Fig. 6. (Left) Sample spectrogram of the received WiFi signal whentwo people are walking simultaneously in an area, showing thattheir gait signatures are mixed up in the overall signal. (Right) Theoutput of our 2D signal processing pipeline, showing two separatespectrograms each carrying the gait information of only one person.

interfere with each other, making it extremely challengingto identify them. On the other hand, by utilizing our AoAtracking and spectrogram generation approach, we obtain twoseparate spectrograms (Fig. 6 (right)), where each spectrogramcarries the gait information of only one individual.

When a person is walking towards/away from the WiFi link,the value of ψT is approximately constant when the Tx andRx are close to each other. Hence, the frequency componentsof the spectrogram Sn(t, f) directly correspond to the speedsof different body parts of the n-th person (see Eq. 5) and wedo not have to consider the walking route to compensate forψT .1 Furthermore, in our previous work on cross-modal personidentification [9], we have shown that the most informativesegments of a spectrogram are those that correspond to theperson walking away from the WiFi link as the reflection fromthe back of the body results in a cleaner signal. We then utilizethe spectrogram segmentation algorithm in [9] to extract theseinformative segments (where ψT is constant and the personis walking away from the link) from the spectrogram of theentire walking duration of a person, with the same algorithmparameters as in [9]. The subjects can walk on any generalpath. The segmentation algorithm will then extract only theinformative segments of each person’s walk. Note that therecan be more than one such informative segments from aperson’s track, depending on the duration and the path.

In case the reflected signals from two (or more) peopleare not separable for a long time, e.g., due to them alwayswalking very close to each other, a corresponding extractedspectrogram segment could contain the mixed gait informationof both people. Such segments, which are not useful foridentification, can be automatically detected and removed,since their energy spread over frequency is very large dueto the combined gait patterns. More specifically, we considerthe energy spread of a segment obtained during operation tobe abnormally large if it is 20% more than the maximumenergy spread observed in the training spectrograms generatedfrom single-person walking scenarios. The energy spread of aspectrogram is measured by the 80th percentile of the differ-ence between the 60th and 40th percentiles of the frequencydistribution across time. Additionally, when two people arewalking very closely, it is also possible that a spectrogramsegment of one person gets dominated by the gait information

1See Sec. 4 and 8 in [9] for more detailed discussions on ψT .


of the other person (e.g., due to a possibly stronger reflectionfrom the person who is close-by). Such a segment can beautomatically detected and discarded, based on its very highsimilarity to the segments of another person/track. The finalremaining spectrogram segments are then considered as thevalid segments to be used for identification.

V. FEATURE EXTRACTION AND PERSON IDENTIFICATION

Given a spectrogram segment of a person’s walk derivedfrom the separated WiFi signal, our proposed system identifiesthis person by comparing this query segment with a candidatespectrogram. More specifically, we extract several featuresfrom both the query segment and the candidate spectrogram,and then compute a set of distances between them. Giventhese feature distances, we train a neural network to determinewhether a pair of query segment and candidate spectrogrambelong to the same person. In this way, the neural network isable to identify people who have not been seen during training.Furthermore, if multiple valid segments are obtained from aperson’s track, we can fuse the neural network’s decisions onthese segments via a maximum likelihood approach.

A. Spectrogram Features and Distances

We extract 10 key features from a spectrogram to capturea person’s gait. More specifically, we look at the frequencyand time dimensions of the spectrogram, which carry differenttypes of gait information that are useful for identification.The frequency dimension carries information about the speedsof different body parts, as shown in Eq. 4. We use thefollowing features to capture various aspects of the frequencyinformation:• Frequency Distribution: This feature is obtained by aver-aging the spectrogram over time. This feature captures theaverage distribution of the frequency components, i.e., thespeed distribution of the body parts, during the person’s walk.• Frequency Distribution in Four Gait Phases: These arethe time averages of the spectrogram for each of the 4 phasesof the gait cycle [7]. This feature provides more detailedinformation on the speed profile of the body parts of thewalking person in each gait phase.• Average Leg and Torso Speeds: We calculate the averagesof the torso speed curve and the leg speed curve, respectively,over time. These speed curves can be extracted from thespectrogram using the method in [7].

In addition, we use several time-domain features to capturethe temporal information on a person’s gait (e.g., the gaitcycle) as follows:• Average Autocorrelation: Given a spectrogram, we com-pute the autocorrelation across time (with a maximum lag of2 sec) for each frequency bin. We then compute a weightedsum of the autocorrelation curves of the frequency bins,based on the energy distribution over the frequencies. Thisautocorrelation-based feature captures the periodic pattern ofthe speed profile of the person’s body during walking.• Autocorrelation of Percentile Curves: Given a spectro-gram, we extract the 50th and 70th percentiles of the frequencydistribution over time. We then compute the autocorrelation of

these two percentile curves, respectively. These features alsocapture the periodicity of the gait and are more robust to noise.

In order to quantitatively compare the similarity between thequery spectrogram segment and the candidate spectrogram,for each of the 10 spectrogram features, we compute thedistance between the corresponding features of the queryspectrogram segment and the candidate spectrogram, whichresults in a vector of 10 feature distances. More specifically,for the frequency distributions, we use the Kullback-LeiblerDivergence (KLD) as the distance metric, which is commonlyused to compare distributions. For the autocorrelation-basedfeatures, we use the cosine similarity, which compares boththe values and patterns of the autocorrelations. For the averagespeed features, we use the Euclidean distance.

B. Identification

Given a pair of a query spectrogram segment and a can-didate spectrogram, we compute the 10 feature distances asdescribed previously. We then utilize a simple fully-connectedneural network, which has 1 hidden layer with 30 units, tocombine these distances into a binary identification decision.More specifically, the neural network takes as input a 10-dimension vector consisting of the feature distances andoutputs a binary classification decision indicating whetheror not the person of the query segment from the multiplepeople scenario is the same as the person of the candidatespectrogram. The neural network is trained on spectrogrampairs of subjects and locations disjoint from those of the testset (more details on the training set in Sec. VI-C). Duringtraining, these 10 distances between a pair of spectrogramsof the training subjects are fed into the neural network, alongwith a binary label indicating whether these two spectrogramsbelong to the same person. A positive label of 1 indicatesthat the pair of spectrograms belong to the same person and anegative label of 0 indicates otherwise. Utilizing the softmaxoperation, the neural network outputs a scalar soft decisions ∈ [0, 1] that resembles the probability of declaring a same-person spectrogram pair given the input, i.e., s = p(1|input).The neural network is trained using the cross-entropy loss anddoes not suffer from overfitting due to its simple structure.After training, we estimate the distribution of the values ofthe output s on all the positive-label training data, p(s|1),as well as its distribution on all the negative-label trainingdata, p(s|0). We then estimate a Likelihood Ratio function:LLR(s) = p(s|1)/p(s|0).

During the testing phase, we first compute the distancesbetween the previously described 10 features of the querysegment (a valid spectrogram segment of a person among thegroup of walking people) and the candidate spectrogram. This10-dimension distance vector is then fed into the trained neuralnetwork, for identifying whether or not the query spectrogramsegment and the candidate spectrogram belong to the sameperson. The neural network outputs a soft decision s, for whichwe calculate LLR(s) using the LLR function estimated fromthe training set. If LLR(s) > 1, a positive binary decision isdeclared that the person of the query spectrogram segmentis the same as the person of the candidate spectrogram.


Otherwise, the system declares that the query segment andthe candidate spectrogram belong to two different people.

C. Multi-Segment Decision FusionAs previously discussed in Sec. IV-C, there can be multiple

valid spectrogram segments for the same track/person inan experiment. Let Gn be the number of valid segmentsfor the n-th person from a group of walking people. Letsi, i ∈ 1, ..., Gn, be the soft decision outputs when thei-th valid segment is tested against the candidate spectro-gram. To optimally combine these soft decisions, in terms ofmaximum likelihood, we adopt the following decision rule:

p(s1, . . . , sGn |1)1≷0p(s1, . . . , sGn |0). Furthermore, assuming

independent decisions by the neural network on the different

Gn inputs, the decision rule becomes:∏Gni=1 LLR(si)

1≷0

1,

where the query person is declared to be the same as the oneof the candidate spectrogram if the product of the LLR valuescorresponding to the multiple segments is greater than 1.

VI. EXPERIMENTAL SETUP AND DATA COLLECTION

In this section, we discuss our experiments used to validateour proposed system.

A. Experiment SetupFor the WiFi data collection, we use laptops equipped with

the Intel 5300 WiFi Card to act as WiFi transmitter andreceiver. For the transmitter, we use a tripod-mounted antennaconnected to one port of the Intel card in one laptop, whichtransmits 1,000 WiFi packets per second on WiFi channel 36(with a center frequency of 5.18 GHz). For the receiver array,we use 4 laptops. More specifically, we use 8 antennas in alinear placement (with antenna separation of λ/4, except forone area, for which we use λ/2 separation), mounted to atripod 1 m away from the Tx and connected to the ports ofthe Intel WiFi cards of 4 laptops, where each laptop provides2 antenna ports. Since we rely only on the CSI magnitudemeasurements of the received WiFi signals, no calibration orsynchronization between the multiple NICs is needed. Thisalso facilitates increasing the antenna array length if needed.The CSI measurements of the receiver laptops are loggedusing Csitool [21] and processed offline using our proposedalgorithm in Sec. IV. For spectrogram generation, we use atime window of length Twin = 0.4 s and a time shift of 4 ms.

The Intel 5300 WiFi cards report the CSI measurements on30 different subcarriers. We utilize the extra measurements inthe subcarrier domain to denoise the signals. More specifically,we utilize Principal Component Analysis (PCA) to find thetop 5 PCA components of the subcarrier measurements, andsum up their spectrograms in order to generate the denoisedspectrogram. As opposed to traditional PCA denoising [7],where the measurement on each subcarrier is a 1D temporalsignal, the measurement on each subcarrier in our case isa 2D spatiotemporal signal c(t, `). Hence, we utilize themultidimensional PCA to find the top 5 PCA components [22].

For the AoA track management criteria (discussed inSec. IV-B), we set the parameters as follows: pTC = 50%,TC = 2 sec, pTF = 90%, and TF = 10 sec.

B. Training Experiments

Training Subjects: We have recruited a total of 13 trainingsubjects (10 male subjects and 3 female subjects) to collectdata for training the neural network described in Sec. V-B. Thetraining subjects have an average walking speed of 1.22 m/s(standard deviation: 0.19 m/s) and an average gait cycle of 1 s(standard deviation: 0.1 s).Training Areas and Data Collection: The training data arecollected in the two areas shown in Fig. 7 (a)–(b), in a line-of-sight (non-through-wall) setting. For each training subject,we collect 9 WiFi measurements of their walk in each of thetwo training areas. For each measurement, the training subjectwalks away from the link for about 10 m. We then transformeach WiFi measurement into a corresponding spectrogram,which results in a total of 234 spectrograms for training.Training Dataset: As our neural network of Sec. V-B isdesigned to predict whether a query spectrogram segmentand a candidate spectrogram belong to the same person, weconstruct the training set in the form of spectrogram pairs.More specifically, based on the 234 training spectrograms,we generate a total of 27, 261 spectrogram pairs. For eachpair, we calculate the distances between the correspondingfeatures of the two spectrograms and use this distance vectoras one training sample. A training sample is given a positivelabel if the pair of spectrograms belong to the same trainingsubject and a negative label otherwise. Since we have differentnumbers of positive and negative training samples, we utilizeoversampling to obtain a balanced training set [23].

C. Test Experiments

Given the WiFi measurements when a person was walkingin an area (referred to as the candidate person), and the WiFimeasurements when multiple people are walking behind thewall in another area (test area), our system can separate thegait information of each person in the test area and determineif he/she (referred to as the query person) is the same as thecandidate person. Both query and candidate people were notseen during training. In this part, we describe the details of ourevaluation setup, including the test subjects, the data collectionof the candidate spectrograms, and the test experiments.Test Subjects: Our test set has 6 subjects (5 male subjectsand 1 female subject), none of whom is part of the trainingset. Their heights range from 162 cm to 186 cm. They have anaverage speed of 1.31 m/s (standard deviation: 0.27 m/s) andan average gait cycle of 1.01 s (standard deviation: 0.15 s).Candidate Spectrograms: We collect 10 WiFi measurementsfor each test subject in the area of Fig. 7 (c) in a line-of-sight(non-through-wall) setting to serve as candidate spectrograms.For each measurement, one test subject walks away from thelink for about 10 m. The WiFi measurements are transformedinto spectrograms, which then serve as the candidate spectro-grams for identification. As a WiFi measurement in this settingonly involves one person walking away from the link, eachcandidate spectrogram translates into one valid segment thatcontinuously spans the entire walking duration. Thus, insteadof using the term “candidate spectrogram segment”, we usethe shortened form “candidate spectrogram” in this paper.


Fig. 7. (a)–(b) WiFi training areas: We collect the WiFi measurements of the training subjects in a line-of-sight setting in these two areas.(c) Test candidate area: We collect the measurements of the test subjects in this hallway area, in a line-of-sight setting, to be used for thecandidate spectrograms. (d)–(g) Test areas: We conduct the test experiments in these 4 behind-wall areas (lounge, conference room, parkinglot, and outdoor area), which represent a variety of real-world scenarios. The WiFi transmitter and receiver are placed behind the wall ineach area, as shown by the black arrow.

Test Experiments: We conduct the test experiments in 4different test areas, as shown in Fig. 7 (d)–(g), which aredisjoint from both the training areas of Fig. 7 (a)–(b) and thearea where the candidate spectrogram was generated. Thesetest areas represent several real-world scenarios with a varietyof area size, geometry, and clutterness. More specifically, thearea of Fig. 7 (d) is a lounge area with couches and coffeetables. The area of Fig. 7 (e) is a conference room with severaltables and chairs.The area of Fig. 7 (f) is located inside aparking structure. The area of Fig. 7 (g) is a roofed outdoorarea near a building. We conduct a total of 92 test experimentsin these test areas, where the WiFi Tx and Rx are placedbehind walls, with no direct view of the walking subjects.The walls consist of wooden panels that attenuate the wirelesssignals by 4 to 5 dB, which is similar to or larger than those ofcommon non-concrete and non-metal building materials [24].It is worth noting that wood is used for the walls of 90% of theresidential and small commercial buildings in the U.S. [25].

First, consider the test experiments with 2 people (total of 80experiments). In each such experiment, 2 of the 6 test subjectsare randomly selected to walk simultaneously in the area.Each subject then walks casually on general paths. Duringthe experiment, the AoAs of the walking subjects are trackedat the receiver, and their respective individual spectrogramsare separated and extracted from the aggregate WiFi signalas described in Sec. IV. The informative and valid segmentsof the spectrograms of the tracks are automatically detectedas discussed in Sec. IV-C, which are then used as the querysegments. In the test experiments with 3 people, 3 of the 6 testsubjects are randomly selected in a total of 12 experiments.The AoAs of the 3 walking people are then tracked to extractindividual spectrograms, whose valid segments then serve asthe query segments.

Test Dataset for the Case of 2 People: This test set consistsof the test subjects’ candidate spectrograms and the queryspectrogram segments from the test experiments when twopeople were present, in the form of query-candidate pairs.More specifically, each test pair consists of a candidate spec-trogram and a query spectrogram segment, and is assigned apositive label if they belong to the same person and a negative

one otherwise. Our test set has in total 15,792 such test pairs.Since there can be more than one query spectrogram seg-

ment obtained from the same person’s track in an experiment,we also look at the test cases where the system identifieswhether the person of a track is the same as the person ofa candidate spectrogram, by fusing the decisions of all thevalid segments from this track as discussed in Sec. V-C. Inthis setting, we have a total of 4,892 pairs of a query trackand a candidate spectrogram. We refer to the first setting whereeach query is one single segment as the segment-based settingand the second setting where the query consists of all the validsegments from a track of a person as the track-based setting.Test Dataset for the Case of 3 People: For the test experi-ments with 3 people walking simultaneously, the correspond-ing test set has 2,416 query-candidate test pairs in the segment-based setting and 1,512 test pairs in the track-based setting.

VII. SYSTEM EVALUATION

In this section, we present extensive experimental evalua-tions of our proposed system in 4 different through-wall areas(see Fig. 7), and for both cases of 2 and 3 people in the area.Furthermore, the subjects and areas in the test experimentshave never been seen during the training phase.

A. Evaluation CriteriaWe evaluate our proposed system by using pairs of a query

spectrogram segment and a candidate spectrogram. Givensuch a test pair, the system identifies whether they belongto the same person or not. The resulting binary classificationaccuracy is used as the evaluation metric. As we have differ-ent numbers of test pairs with positive (same-person) labelsand negative (different-people) labels, we report the balancedclassification accuracy, i.e., the average of the respectiveaccuracies over the same-person and different-people pairs.

B. Evaluation with Two Walking PeopleWe evaluate our proposed system on our extensive test set,

as described in Sec. VI-C, which contains only areas andsubjects not seen during training. The results are summarizedin Table I. For the track-based metric, our proposed systemachieves identification accuracies of 81%, 82%, 86%, and


Two people Three peopleSegment Track Segment TrackArea

based based based basedArea of Fig. 7 (d) 79% 81% 79% 73%Area of Fig. 7 (e) 83% 82% 79% 83%Area of Fig. 7 (f) 84% 86% 81% 87%Area of Fig. 7 (g) 77% 78% 79% 83%

Average 81% 82% 80% 83%

TABLE ITHE SEGMENT-BASED AND TRACK-BASED IDENTIFICATION

ACCURACIES OF OUR PROPOSED SYSTEM ON THE TEST SET, IN 4DIFFERENT THROUGH-WALL AREAS. THE LAST ROW SHOWS THE

AVERAGE PERFORMANCE OVER ALL THE AREAS.

78% for the 4 areas, respectively, with an overall averageaccuracy of 82%. This indicates that given the spectrogramsegments of a person’s track in an experiment, our system isable to correctly identify whether this person is the same asthe test subject of a candidate spectrogram for 82% of thetime. As for the segment-based setting, our system achievesidentification accuracies of 79%, 83%, 84%, and 77% for the4 areas, respectively, with an overall average of 81%.

Finally, we show the Receiver Operating Characteristic(ROC) curve for the track-based identification in Fig. 8. Itcan be seen that the ROC curve is significantly above the45-degree line. In particular, the Area Under Curve (AUC)is 0.89 in the track-based setting (and 0.88 in the segment-based setting), indicating a good performance. The AUC isequal to the probability that a randomly-drawn positive samplehas a higher score (e.g., the LLR(s) in Sec. V-B) than arandomly-drawn negative sample.2 It should be noted ourthreshold is automatically given by the neural network asdescribed in Sec. V-B and V-C. These results further confirmthe performance of our system.

C. Angular SeparationWe analyze the system’s performance with respect to the

angular separation between two walking people (differencebetween their AoAs) in the test areas. Fig. 9 shows the averageidentification accuracy as a function of the angle. It can be seenthat even when the angle between the two people is as smallas 20,3 our system still performs robustly with an accuracysimilar to those when the angular separation is larger.

D. Evaluation with Three Walking PeopleFor the three-people test experiments, our proposed system

achieves overall segment-based and track-based identificationaccuracies of 80% and 83%, respectively, averaged over the 4through-wall test areas. It can be seen that even with 3 peoplesimultaneously walking in the area, our system still achievesa good identification accuracy.

Overall, these extensive test results show that our proposedsystem can successfully perform identification when multiplepeople are simultaneously walking in the area, even though thepeople and areas have never been seen during training, and ina through-wall setting. They thus demonstrate the efficacy andapplicability of our system in various real-world scenarios.

2See [26] for more details on ROC and AUC.3Note that the minimum angular separation resolvable by the system

depends on the length of the Rx array. For instance, given our current hardwaresetup, the system will not be able to fully resolve two angles that are 10 (orless) apart. See Sec. VIII for a detailed discussion on AoA resolution.

0 0.2 0.4 0.6 0.8 1

False Positive Rate

0

0.2

0.4

0.6

0.8

1

Tru

e P

osit

ive R

ate

Fig. 8. Receiver OperatingCharacteristic (ROC) curvefor identification in the track-based setting.

20 30 40 50 60 70

Angular Separation

60

70

80

90

100

Acc

ura

cy (

%)

Fig. 9. Track-based identification ac-curacy as a function of the angu-lar separation between the subjects’tracks in the two-people experiments.

VIII. DISCUSSION AND FUTURE EXTENSIONS

In this section, we provide discussions on various aspects ofour proposed framework, as well as possible future extensions.Gait as a Unique Signature: While some studies suggest thatgait identification errors are inevitable for large groups (e.g.,100 people) [27], other studies have shown that RF-based gaitidentification can be effective for small to medium group sizes(e.g., up to 50 people) [7], [14]. It should be noted, however,that these papers have the same subjects in training and test,which makes the learning problem considerably simpler. Theynonetheless show that gait-based identification has a goodpotential for applications that involve a small to medium poolof subjects (e.g., in a residential or an office setting).Resolution of Peaks in the AoA Domain: The maximumnumber of people that the system can simultaneously detectis determined by the resolution (or width) of a peak in theAoA domain, which depends on length of the RX array. Inour experiments, we used an antenna array of total length 2λ,resulting in a first-null peak resolution of 0.23, i.e., two peaksare completely separated in the AoA domain if the differenceof their ψA values is greater than 0.23. This resolution canfurther be improved by extending the array, which does not addany synchronization/calibration overhead since we use only themagnitude of the received WiFi signal. Different processingtechniques (e.g., MUSIC) can also improve the resolution ofthe peaks, at the expense of much higher computational costs.Increasing the Number of People in the Area: While wehave tested our system for up to 3 people walking simulta-neously in an area, the proposed approach can be used for alarger number of people. The maximum number of people thatthe system can identify is determined by the resolution of apeak in the AoA domain, which depends on the length of theRX antenna array, as discussed above, as well as how crowdedthe area gets, how close to each other the people walk, andtheir walking directions. For instance, in our current setup, theAoA resolution is 10 degrees. This means that if two peopleconsistently walk with AoA separation of less than 10 degreesin the same direction, our current setup cannot separate them(if they walk in different directions, then it is still separable).As such, as long as the area is large enough such that eachperson’s AoA is not consistently less than 10 degrees fromsomeone else who is going in the same direction, then thecurrent system is able to identify all the people. As the areagets more crowded for its size, then one can increase thelength of the array to allow for a better AoA resolution, which


would allow our system to identify people even if they areconsistently walking close to each other in the same direction.One can also utilize more resources, such as positioning moretransceivers in different locations in the space in order tocapture different views of the people, and/or utilizing differentfrequency subcarriers to capture the time-of-flight data.Tracks of the Walking People: In Sec. IV-C, we have utilizedthe fact that when people move away/towards the link, ψT isconstant, excluding the need to directly estimate it via trackingpeople’s routes. In the rare case when no such segment isdetected in the entire spectrogram (e.g., if the person’s wholewalking path is parallel to the link), the constantly varyingvalue of ψT can be estimated by existing RF-based trackingsystems, and then incorporated in the proposed approach toidentify a person walking on any general track.Impact of Misalignment of the Rx Array: When the Rxarray is rotated by θe, the AoA of a person changes fromθ to θ + θe, where θ is the AoA before the rotation. Theseparability of the reflected signals from two people dependson the difference between their respective ψA values, whereψA = cos(θe) − cos(θ + θe). As such, given a small θe, theseparation between two people in the 2D spectrum can slightlyincrease or decrease due to the nonlinear cosine operation. Forinstance, consider two people whose original AoAs are 120

and 150. When the array is rotated by 5, the separationbetween their ψA values decreases from 0.37 to 0.33. Note thatgiven our current hardware setup, the two people’s signals arefully separable in the 2D spectrum as long as their ψA valuesare at least 0.23 apart. Our system is also robust to smallinter-antenna spacing errors, since they only slightly affect thewidth of the main beam and the side lobe levels, but not thelocation/AoA of the main beam [28].

IX. CONCLUSION

In this paper, we proposed a gait-based identification systemthat can, for the first time, identify multiple simultaneously-walking people through walls, using CSI magnitude measure-ments of a small number of off-the-shelf WiFi devices. Inorder to do so, our system first estimates the AoA of thereflected WiFi signals from the walking people, and usesthis information to separate their gait signatures. Given theextracted signal of an individual person’s walk, our systemgenerates a spectrogram to capture the frequency-time featuresof the gait for identification. We have extensively validated ourproposed system with 92 test experiments in 4 test areas. Ineach experiment, 2 or 3 test subjects walk simultaneously in anarea. Overall, our system achieves an overall average accuracyof 82% in identifying whether the person of a query datasample (extracted from a multi-person walking experiment)is the same as the person of a candidate spectrogram.

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