battery-less location tracking for internet of things

IEEE INTERNET OF THINGS JOURNAL, VOL. 6, NO. 5, OCTOBER 2019 9147

Battery-Less Location Tracking for Internet ofThings: Simultaneous Wireless Power

Transfer and PositioningArif Abdul Aziz, Lorenz Ginting, Dedi Setiawan, Je Hyeon Park, Nguyen Minh Tran , Gyu Yang Yeon,

Dong In Kim , Fellow, IEEE, and Kae Won Choi , Senior Member, IEEE

Abstract—We propose a battery-less location tracking systemthat enables 3-D positioning of an Internet of Things (IoT) devicepowered by the radio frequency (RF) wireless power transfer(WPT). In the proposed system, a power beacon is equippedwith a phased antenna array that has the dual purposes of high-efficiency WPT and phase-based accurate positioning. In order toenhance the efficiency of the RF WPT, we propose a beam focus-ing algorithm that dynamically controls the respective phases ofantenna elements to place the focal point of the electro-magnetic(EM) wave onto the target IoT device. We also propose a phase-based positioning algorithm that requires only one multiantennaanchor point for determining the distance as well as the directionfrom the anchor point. We analyze the Cramer–Rao lower bound(CRLB) of the phase-based positioning with a single multiantennaanchor point, and show that the distance from the anchor pointcan be estimated as long as the IoT device lies within the radia-tive near-field region. We propose a joint location tracking andWPT algorithm that performs 3-D positioning and beam-focusedWPT in a unified way. We have built a real-life testbed witha large-scale antenna array with 64 antenna elements for test-ing the proposed algorithm. The experimental results show theeffectiveness of the proposed algorithm in a real environment.

Index Terms—Beam focusing, Cramer–Rao lower bound(CRLB), Internet of Things (IoT), location tracking, phasedantenna array, positioning, wireless power transfer (WPT).

I. INTRODUCTION

RECENTLY, the radio frequency (RF) wireless powertransfer (WPT) technique has gained great attention from

research communities and industries [1]. The RF WPT makesuse of the electro-magnetic (EM) wave to wirelessly deliverpower to remote targets. Since the EM wave is radiated froman antenna and propagates over space, the RF WPT techniqueenjoys much longer power transfer distance than the nonra-diative magnetic WPT techniques (e.g., inductive or magneticresonant coupling) do [2]. Despite of this advantage, the RF

Manuscript received January 1, 2019; revised May 29, 2019; acceptedJuly 8, 2019. Date of publication July 12, 2019; date of current versionOctober 8, 2019. This work was supported in part by the National ResearchFoundation of Korea through the Korean Government (MSIP) under Grant2014R1A5A1011478, and in part by the Korea Electric Power Corporationunder Grant R18XA06-15. (Corresponding author: Kae Won Choi.)

The authors are with the Department of Electronic, Electrical, and ComputerEngineering, Sungkyunkwan University, Suwon 16419, South Korea (e-mail:[email protected]; [email protected]; [email protected];[email protected]; [email protected]; [email protected]; [email protected]; [email protected]).

Digital Object Identifier 10.1109/JIOT.2019.2928313

Fig. 1. Concept of the proposed battery-less location tracking system.

WPT technique typically has lower power transfer efficiencythan other techniques due to the difficulty in focusing the radi-ated EM wave onto a small receiving spot. Therefore, it is ofparamount importance to enhance the RF power transfer effi-ciency as well as to find appropriate application areas withlow power supply requirements.

In near future, it is envisioned that a massive numberof Internet of Things (IoT) devices will be deployed tointerconnect cyber and physical spaces. A foremost challengeof this large-scale IoT deployment is to supply sufficient powerto IoT devices for their uninterrupted operation [3]. Powersupplies with wired power cords or battery replacement areundesirable options because of excessive installation and main-tenance costs. One viable solution to this problem is the WPT,especially the RF WPT technique is the most suitable for thefollowing two reasons. First, the RF WPT can supply wirelesspower to IoT devices scattered over a wide area thanks to itslong-range power transfer capability. Second, IoT devices suchas sensor nodes and identification tags have very low powerconsumption in the microwatt to milliwatt range, which can besupplied by the RF WPT technique with relatively low powertransfer efficiency. Therefore, the RF WPT technique can real-ize a battery-less IoT system that perpetually operates withoutbattery replacement.

In this paper, we propose a battery-less location trackingsystem as given in Fig. 1. This figure shows the concept ofthe proposed system, which consists of a power beacon andan IoT device. The power beacon supplies wireless power to

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9148 IEEE INTERNET OF THINGS JOURNAL, VOL. 6, NO. 5, OCTOBER 2019

the IoT device and tracks the location of the IoT device atthe same time. In the proposed system, the 3-D position of anIoT device, which perpetually operates without a battery, canbe tracked by only a single anchor point (i.e., power beacon).Therefore, the proposed system potentially has wide applica-tion areas, for example, indoor positioning for tracking assetsand people, indoor navigation, and motion tracking, free ofpower cords or battery replacement.

One of the most promising applications of the proposedsystem is the asset tracking. The localization tags are attachedto equipments or assets in a warehouse for inventory monitor-ing. In a smart factory, parts or accessaries on a production linecan be tracked by the proposed system for automating the pro-cess of storage, transportation, or assembly. Tracking portableequipments in a factory or hospital increases the utilizationand prevents their loss. The proposed system can remotelyreplenish the batteries of a large quantity of the lightweightlocalization tags attached to assets.

The power beacon is equipped with a phased antenna arrayconsisting of multiple antenna elements as seen in Fig. 1.The power beacon is able to control the phase and magnitudeof the EM wave from each antenna element to synthesize amicrowave beam. The purpose of the phased antenna arrayis twofold: 1) beam focusing for high-efficiency WPT and 2)3-D positioning. In this paper, we design a simultaneous WPTand positioning algorithm for the phased antenna array-basedsystem.

When transferring power to the IoT device, the phasedantenna array can focuses the EM wave onto the IoT devicelike a convex lens does as long as the IoT device lies withina radiated near-field region of the antenna array [4], [5]. This“beam focusing” can greatly enhance the power transfer effi-ciency. For the beam focusing, it is essential for the powerbeacon to estimate the transfer coefficient from each antennaelement to the IoT device. The proposed algorithm estimatesthe transfer coefficients only based on the receive power mea-surements at the IoT device. Based on these estimates, anoptimal beam focusing algorithm dynamically controls thephase of each antenna element so that the focal point of theEM wave is precisely placed at the IoT device.

There have been quite a few studies that have attempted toremotely charge IoT devices by the RF WPT (e.g., [6]–[9]).For example, Popovic et al. [6] proposed a receiver-sidedesign such as a rectenna and a power management circuit,Costanzo et al. [7] analyzed a system power transfer efficiency,Maehara et al. [8] suggested a multipoint power transmissiontechnique, and Sangare et al. [9] tested a mobile chargingplatform. However, these works do not make use of antennaarrays, and as a result, show very low power transfer effi-ciency. There are numerous wireless communication-theoreticworks that extend a multiple-input multiple-output (MIMO)concept to the multiantenna WPT [10]. For example, thewireless powered sensor network (WPSN) with multiantennapower beacons is studied in [11], the performance of thedirected microwave power transfer (MPT) is analyzed by thestochastic geometry in [12], and the optimal resource allo-cation in the multiantenna wireless powered communicationnetwork (WPCN) is investigated in [13]. However, these works

highlight only signal processing aspects without any practicalsystem consideration or any experimental validation.

Only a handful of works have implemented an antennaarray-based RF WPT system (e.g., [14] and [15]).Gowda et al. [14] have designed a Fresnel region antennaarray of 64 antenna elements for generating a focusedEM field. However, the array in [14] does not have phaseshifting components, only producing a fixedly focusedbeam. Yedavalli et al. [15] have proposed a blind adaptivebeamforming algorithm that searches for antenna phases withbetter receive power in a greedy manner, and have testedthe proposed algorithm on a four antenna software-definedradio (SDR) testbed. However, the algorithm in [15] isexpected to have a very slow convergence speed if applied toa massive antenna array. In our previous works [16], [17], wehave proposed a receive power-based adaptive beamformingalgorithm, and shown its performance on a multiantenna WPTtestbed with centralized and distributed antenna deploymentscenarios in [16] and [17], respectively. In this paper, wepropose a more advanced algorithm for beam focusing withhigher accuracy and lower complexity.

In the proposed battery-less location tracking system, thephased antenna array not only supplies focused wireless powerbut also tracks the 3-D position of the IoT device. In this paper,we propose a novel antenna array-based positioning algorithmthat extracts phase information from the receive power mea-surements at the IoT device, and then tracks the location ofthe IoT device based on the extracted phase information. Theproposed positioning algorithm is unique in that it utilizes onlythe receive power measurements, but still has the accuracy ofthe phase-based positioning. Moreover, the proposed antennaarray-based positioning requires only one anchor point, and iseasier to install than other multianchor positioning systems.With only one multiantenna anchor point, the proposed posi-tioning system is able to estimate the distance as well as thedirection (i.e., azimuth and elevation) from the anchor point.

The phase-based positioning has been an active researcharea especially in the context of RF identification (RFID)(e.g., [18]–[24]). In the RFID communication, a reader sendsa query to a tag, and the tag replies with a reflected signalby using backscatter communications. The phase is estimatedat the reader by comparing the phases of a local oscilla-tor and the reflected signal. Since this phase informationhas an integer phase ambiguity in relation to the distanceto the tag [25], much efforts have been put into effec-tively solving this phase ambiguity problem. To tackle thephase ambiguity problem, Hekimian-Williams et al. [18] andLiu et al. [19] considered phase differences between multipleantennas, Scherhäufl et al. [20] used a 2-D grid search-ing algorithm, Yang et al. [21] exploited the tag’s mobility,and Wang et al. [22] proposed a multiresolution positioningtechnique. Wang and Katabi [23] have proposed an RFIDpositioning system robust to multipath and nonline-of-sightscenarios. In [24], the tag positioning in the bistatic RFIDscenario is studied. Since the proposed location trackingsystem does not use the backscatter communications, theseRFID positioning algorithms cannot be directly applied to oursystem.


AZIZ et al.: BATTERY-LESS LOCATION TRACKING FOR IoT: SIMULTANEOUS WPT AND POSITIONING 9149

On the other hand, some positioning schemes by a collo-cated antenna array have been studied in [26] and [27]. Inthe positioning schemes in [26] and [27], a single antennaarray can only estimate the direction of the target, and multipleantenna arrays are required to fix the 3-D position. The com-mon conception regarding the antenna array positioning is thatonly direction can be estimated by using a single antenna array.However, this is not true. The distance can also be estimated ifthe target is located not too far from the antenna array. In thispaper, we reveal the possibility of 3-D positioning by a sin-gle antenna array by analyzing the Cramer–Rao lower bound(CRLB). The analysis shows that the distance as well as thedirection can be estimated as long as the target lies in theradiative near-field region of the antenna array. We also pro-pose an antenna array-based positioning algorithm based onthe Levenberg–Marquardt method.

The most prominent feature of the proposed battery-lesslocation tracking system is that it performs simultaneousWPT and positioning in a unified way. Liu et al. [28] haveproposed the idea of combining RF WPT and indoor local-ization. However, the system in [28] simply places anchorpoints that emit EM waves and identification signals for charg-ing and room-level localization without any novel method toenhance charging efficiency or localization accuracy. In [29],the localization by a WPT system is proposed. However, thissystem is actually irrelevant to our proposed system sinceRanganathan et al. [29] considered magnetic coupling-basednear-field WPT. Therefore, we can claim that proposing RF-based joint WPT and positioning is a novel contribution ofthis paper.

We have built a battery-less location tracking testbed toshow the performance of the proposed algorithms in a realisticscenario. The power beacon in the testbed has a large-scaleantenna array with 64 antenna elements. We have designedand fabricated a phased array board to dynamically controlthe phase and magnitude of the EM wave emitted by eachantenna element. The testbed can conduct a real-time operationof simultaneous WPT and location tracking by the proposedalgorithms programmed into the testbed. The test results haveproven the effectiveness of the proposed algorithms. The demovideo clips for the RF WPT and the battery-less locationtracking experiments can be found in [30] and [31].

The rest of this paper is organized as follows. We presentthe system model for the battery-less location tracking systemin Section II. The joint location tracking and WPT algo-rithm is proposed in Section III. We explain the design andimplementation of the battery-less location tracking system inSection IV. Section V presents the experimental results, andthis paper is concluded by Section VI.

II. SYSTEM MODEL

A. Battery-Less Location Tracking System Architecture

In the proposed system, a power beacon is capable of wire-lessly supplying power to an IoT device and of tracking thelocation of the IoT device. The power beacon is equippedwith a phased antenna array, which consists of N antenna ele-ments. Henceforth, each antenna element will be indexed by

Fig. 2. Architecture of the proposed battery-less location tracking system.

n (= 1, . . . ,N), and the nth antenna element will be calledantenna n.

Each antenna element radiates an EM wave that is a continu-ous wave (CW) with frequency f . Let λ denote the wavelengthof the EM wave. As in Fig. 2, the power beacon uses an oscil-lator to generate a source RF signal, which is amplified by adrive amplifier. The amplified source RF signal is split into NRF paths by using a power splitter. Each RF path has a vari-able attenuator, a phase shifter, and an amplifier. The phaseand magnitude of the RF signal of each RF path can be con-trolled by the phase shifter and variable attenuator. The RFsignal is amplified at the end of each RF path before radiatedby the antenna element. Let RA denote the radiation resistanceof an antenna element. We denote by vn the transmit voltageof antenna n, which is a complex cosine phasor for the volt-age across the radiation resistance of antenna n. The powerbeacon can control the phase and magnitude of vn by usingthe phase shifter and variable attenuator. The transmit powerfrom antenna n is given by

pn = |vn|22RA

. (1)

We assume that the maximum transmit power of each antennaelement is limited to P. When an antenna element trans-mits with the maximum transmit power, the magnitude of thetransmit voltage is ν = √2RAP.

The IoT device operates only by making use of RF powerwirelessly supplied by the power beacon, without any wiredpower cord or any battery. The EM wave transmitted by thepower beacon is received by the receive antenna of the IoTdevice. From the point of view of the receive antenna, therest of the circuit in the IoT device is simplified to a loadresistance. We assume that the load resistance is matched tothe radiation resistance of the receive antenna. Therefore, theload resistance is RA. Let u denote the receive voltage of theIoT device, which is a complex cosine phasor for the voltageacross the load resistance. Then, the receive power from thereceive antenna is given by

ρ = |u|2

2RA. (2)



The receive voltage u is excited by the EM wave from eachantenna element of the power beacon. That is, the receivevoltage is given by

u =N∑

n=1

hnvn = hTv (3)

where hn is a transfer coefficient from antenna n of the powerbeacon to the IoT device. The transfer coefficient hn is a com-plex number, the magnitude and phase of which, respectively,reflect the attenuation and phase rotation of the EM wave whilepropagating through space. In (3), h and v are the transfercoefficient vector and transmit voltage vector, respectively, i.e.,h = (h1, . . . , hN)

T and v = (v1, . . . , vN)T.

The rectifier converts the received RF power to dc power,and the rectified dc power is stored in a supercapacitor or issupplied to active components. The IoT device has a superca-pacitor for temporarily storing extra energy to prevent blackoutcaused by momentary interruption in wireless power sup-ply. The active components in the IoT device include themicrocontroller unit (MCU) and the RF transceiver. Theseactive components use wirelessly supplied power or drainthe energy stored in the supercapacitor for their operations.The MCU includes a central processing unit (CPU) and otherperipherals, taking a role of controlling the whole IoT device.The RF transceiver is compliant with a low-power commu-nication technology such as IEEE 802.15.4, and is used forcommunicating with the power beacon.

The IoT device is equipped with a power meter that mea-sures the receive power ρ. From (2) and (3), the receive powermeasurement, denoted by ρ, is given as

ρ = ρ + η = 1

2RA|u|2 + η = 1

2RA|hTv|2 + η (4)

where η is the receive power measurement noise. TheMCU obtains the receive power measurement by usingthe power meter, and sends a feedback packet, enclosing thereceive power measurement, to the power beacon via the RFtransceiver.

B. Coordinate System and EM Wave Propagation Model

The coordinate system under consideration and the place-ment of the IoT device and the power beacon are shown inFig. 3. The antenna array of the power beacon is a planarantenna array with Nrow rows and Ncol columns. Each antennaelement is considered to be a microstrip patch antenna, radi-ating an EM wave toward a single direction. In our systemmodel, all the antenna elements in the planar antenna arrayare placed on the y-z plane, and radiate an EM wave towardthe positive direction along the x-axis.

We denote the position of antenna n in the Cartesian coor-dinate system by an = (ax

n, ayn, az

n)T. The antenna spacings

between two neighboring rows and columns are denoted byχrow and χcol, respectively. We assume that the antenna spac-ing is equal to or less than a half-wavelength of the EM wave,that is, χrow ≤ λ/2 and χcol ≤ λ/2. Then, the position ofantenna n is given by

axn = 0 (5)

Fig. 3. Coordinate system model.

ayn = {ςcol(n)− �Ncol/2�} · χcol (6)

azn = {ςrow(n)− �Nrow/2�} · χrow (7)

where ςcol(n) and ςrow(n) are, respectively, the column indexand the row index of antenna n such that

ςcol(n) = �(n− 1)/Nrow� (8)

ςrow(n) =

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(n− 1) mod Nrow

if ςcol(n) is an even number

Nrow − 1− ((n− 1) mod Nrow)

if ςcol(n) is an odd number.

(9)

In (9), “mod” is the modulo operator. Fig. 3 shows an exampleplanar antenna array configuration with 16 antenna elements,and we can see that each antenna is indexed in a zigzagmanner.

We designate one of the antenna elements at the center ofthe phased antenna array as an anchor antenna. The anchorantenna is placed at the origin of the coordinate system. Letn∗ denote the index of the anchor antenna. We set n∗ to theindex of the antenna element at the center as

n∗ =

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

�Ncol/2� · Nrow + �Nrow/2� + 1

if �Ncol/2� is an even number

�Ncol/2� · Nrow + Nrow − �Nrow/2�if �Ncol/2� is an odd number.

(10)

In (5)–(10), we can see that the anchor antenna is located atthe origin, i.e., an∗ = (0, 0, 0)T.

The 3-D position of the IoT device is denoted by s. Theposition of the IoT device can be specified in the Cartesiancoordinate system or the spherical coordinate system. The IoTdevice is located at s = (sx, sy, sz)T in the Cartesian coordi-nate system. With a slight abuse of notation, s also denotes theposition of the IoT device in the spherical coordinate system.That is, s = (r, θ, φ)T where r, θ , and φ denote the radius, ele-vation, and azimuth of the IoT device, respectively. Then, theposition of the IoT device in the Cartesian coordinate systemcan be given in terms of r, θ , and φ by

sx = r sin θ cosφ (11)



sy = r sin θ sinφ (12)

sz = r cos θ. (13)

The EM wave from the power beacon is radiated toward thepositive direction along the x-axis, that is, the azimuth ofthe radiation direction is limited between −π/2 and π/2. Weassume that −π/2 < φ < π/2 so that the IoT device is withinthe range of the EM wave radiation from the power beacon.

The distance between antenna n and the IoT device locatedat s is denoted by dn(s). This distance is calculated as

dn(s) = ‖s− an‖2=√(

sx − axn

)2 + (sy − ay

n)2 + (

sz − azn)2. (14)

Since the anchor antenna is placed at the origin, the distancefrom the anchor antenna to the IoT device is dn∗(s) = r.According to [32], the transfer coefficient hn is given in termsof the distance by

hn = λ

4πdn(s)

√GTx

n GRxn σn

× exp

(−j

(2π

λdn(s)+ ξ + 2π ln

))

= κn exp(jωn) (15)

where GTxn is the gain of antenna n of the power beacon, GRx

nis the gain of the receive antenna of the IoT device, σn isthe polarization loss factor, ξ is a fixed phase rotation, ln canbe any integer number, and κn and ωn are, respectively, themagnitude and phase of hn such that

κn = λ

4πdn(s)

√GTx

n GRxn σn (16)

ωn = −2π

λdn(s)− ξ − 2π ln. (17)

In (17), ln is introduced for representing the integer phaseambiguity. Note that the magnitude of the transfer coefficient(i.e., κn) is derived based on the Friis equation.

The antenna gains (i.e., GTxn and GRx

n ) and the polariza-tion loss factor (i.e., σn) are functions of the attitude of theIoT device as well as the position of the IoT device. Thus,it is impossible to determine the magnitude of the transfercoefficient (i.e., κn), which includes the antenna gain and thepolarization loss factor, only in terms of the position of the IoTdevice. Therefore, for tracking the location of the IoT device,we do not use the magnitude of the transfer coefficient, butonly use the phase of the transfer coefficient.

III. JOINT LOCATION TRACKING AND WIRELESS POWER

TRANSFER ALGORITHM

A. Overview of Joint Location Tracking and Wireless PowerTransfer Algorithm

In this section, we design the joint location tracking andWPT algorithm. This algorithm consists of three separatesteps: 1) phase estimation; 2) location tracking; and 3) optimalWPT.

The only input to the algorithm is the receive power mea-surement ρ in (4). The power beacon transmits an EM wavewith a number of different training transmit voltages. The IoT

device measures the receive power for each training trans-mit voltage, and feedbacks the receive power measurementsto the power beacon. In the first step, the algorithm calcu-lates the phases of the transfer coefficients for all antennaelements based only on the receive power measurements. Wewill explain the phase estimation algorithm in Section III-B.

The estimated phases are used both for the location track-ing and the optimal WPT. The location tracking algorithmtakes the estimated phases as inputs, and calculates the posi-tion of the IoT device. We will formulate the location trackingproblem, analyze the CRLB, and propose the location trackingalgorithm in Sections III-C–III-E, respectively.

For the optimal WPT, the power beacon has to focus thebeam of the EM wave onto the receive antenna of the IoTdevice. This beam focusing can be achieved by setting thetransmit voltage of each antenna element to the conjugate ofthe estimated phase. We will discuss the beam focusing forthe optimal WPT in Section III-F.

It is noted that the proposed phased array-based locationtracking algorithm can stand alone without the WPT, andcan be applied to other types of antenna array systems suchas massive MIMO communications system. Nevertheless, wehave combined the location tracking algorithm with the WPTbecause there are needs of augmenting the location trackingsystem with the WPT capability for charging a potentiallylarge number of localization tags. Moreover, the beam focus-ing for the WPT and the location tracking have fundamentalsimilarities in the mathematical aspects, and many parts ofthe hardware infrastructure and the software algorithm can beshared between them. The location tracking algorithm extractsthe location information embedded in the phase informationthat is utilized by the WPT for beam focusing.

B. Phase Estimation Based on Receive Power Measurement

In this section, we introduce a phase estimation algorithmthat calculates the phase of the transfer coefficient of eachantenna element. It is impossible to estimate the absolutephase of the transfer coefficient based on the receive powermeasurements. Thus, the proposed phase estimation algorithmestimates a relative phase of the transfer coefficient, whichis defined as follows. Let us define h0 as the summation oftransfer coefficients of all antennas such that

h0 = κ0 exp(jω0) =N∑

n=1

hn = 1Th (18)

where κ0 and ω0 are the magnitude and phase of h0, respec-tively, and 1 is the column vector of all ones. By usingh0, we define a relative transfer coefficient vector g =(g1, . . . , gN)

T as

g = hh∗0. (19)

Then, the relative transfer coefficient for antenna n is given by

gn = κnκ0 exp(j(ωn − ω0)) = κnκ0 exp(jω′n

)(20)

where ω′n is the relative phase of the transfer coefficient forantenna n such that

ω′n = ωn − ω0. (21)



The proposed phase estimation algorithm first estimates therelative transfer coefficient vector g, and then obtains therelative phase ω′n from the estimated g.

For the phase estimation, the power beacon transmits theEM wave with a number of different training transmit voltagevectors. Let us first design training transmit voltage vectors.Although there are many possible choices for training transmitvoltage vectors, we design them in consideration of the fol-lowing two criteria. First, the calculation of the phases basedon the receive power measurements should be computationallyefficient. Second, the receive power for a training transmit volt-age vector should be sufficiently high so that the power meterin the IoT device can correctly measure the receive power.

In order to satisfy the above conditions for training transmitvoltage vectors, we first design antenna activation patterns thatare independent of each other for efficient computation andactivate multiple antenna elements at the same time for suffi-ciently high receive power. Let B denote an N × N squarematrix that represents the antenna activation patterns. Wedenote by bn,k the (n, k)th entry of B, and the nth row vectorof B is given by bn = (bn,1, . . . , bn,N). Here, bn is the nthantenna activation pattern. For defining B, we first define asquare matrix �m with 2m columns and 2m rows. The matrix�m can be obtained by the following rules:

�1 =(

1 11 0

)(22)

�m =(

�m−1 �m−1

�m−1 1−�m−1

)(23)

where 1 is the matrix of all ones. From (22) and (23), we caniteratively construct �m for m = 2, 3, . . . For example, �2

and �3 are given by

�2 =

⎛

⎜⎜⎝

1 1 1 11 0 1 01 1 0 01 0 0 1

⎞

⎟⎟⎠

�3 =

⎛

⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

1 1 1 1 1 1 1 11 0 1 0 1 0 1 01 1 0 0 1 1 0 01 0 0 1 1 0 0 11 1 1 1 0 0 0 01 0 1 0 0 1 0 11 1 0 0 0 0 1 11 0 0 1 0 1 1 0

⎞

⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

. (24)

Note that �m is a symmetric and invertible matrix. For msuch that 2m ≥ N, the matrix B is a submatrix of �m fromthe first row to the Nth row and from the first column to theNth column. Then, we have bn,k = ϕm

n,k for n, k = 1, . . . ,N,where ϕm

n,k is the (n, k)th entry of �m.Based on B, we construct (3N−2) different training transmit

voltage vectors as follows. We first define a training trans-mit voltage vector activating all antenna elements, which isdenoted by γ 0 = (γ 0

1 , . . . , γ0N)

T. If the power beacon usesγ 0, all antenna elements transmit with the maximum transmitpower P while all phases of the transmit voltages are set tozero. Then, γ 0

n = ν for n = 1, . . . ,N, where ν is the mag-nitude of the transmit voltage when the maximum transmit

power is used, i.e., ν = √2RAP. We can define γ 0 as

γ 0 = ν · 1. (25)

In addition to γ 0, we define three training transmit volt-age vectors for each antenna activation pattern bn. Letus denote these three training transmit voltage vectors byγ 1

n = (γ 1n,1, . . . , γ

1n,N)

T, γ 2n = (γ 2

n,1, . . . , γ2n,N)

T, and γ 3n =

(γ 3n,1, . . . , γ

3n,N)

T, which are defined as

γ 1n = ν · bT

n (26)

γ 2n = ν ·

(1− bT

n

)(27)

γ 3n = ν ·

{bT

n +(1− bT

n

)j}. (28)

As can be seen in (26), the power beacon transmits withantenna k’s for which bn,k is one if γ 1

n is used. On the otherhand, if γ 2

n is used, the power beacon transmits with antennak’s for which bn,k is zero as seen in (27). As in (28), if γ 3

n isused, the power beacon transmits with all antenna elements,but antenna k’s, for which bn,k is zero and one, have π/2 phasedifference.

The power beacon transmits an EM wave with (3N − 2)training transmit voltage vectors (i.e., γ 0, γ 1

n, γ 2n, and γ 3

n forn = 2, . . . ,N), and the receive power for each training transmitvoltage vector is measured by the IoT device. We denote byρ0, ρ1

n , ρ2n , and ρ3

n the receive power measurements when γ 0,γ 1

n, γ 2n, and γ 3

n are used as training transmit voltage vectors,respectively. The receive power measurements ρ0, ρ1

n , ρ2n , and

ρ3n are equal to the true receive powers, which are denoted byρ0, ρ1

n , ρ2n , and ρ3

n , plus the receive power measurement noises,which are denoted by η0, η1

n, η2n, and η3

n. Then, from (4), wehave

ρ0 = 1

2RA|hTγ 0|2 + η0 = P|1Th|2 + η0 (29)

ρ1n =

1

2RA|hTγ 1

n|2 + η1n = P|bnh|2 + η1

n (30)

ρ2n =

1

2RA|hTγ 2

n|2 + η2n = P|(1T − bn

)h|2 + η2

n (31)

ρ3n =

1

2RA|hTγ 3

n|2 + η3n = P|{bn +

(1T − bn

)j}h|2 + η3

n.

(32)

Now, the phase estimation problem is to obtain the relativephases ω′n for n = 1, . . . ,N based on the receive power mea-surements ρ0, ρ1

n , ρ2n , and ρ3

n for n = 1, . . . ,N. To this end,we first estimate the relative transfer coefficient vector g. Letg = (g1, . . . , gN)

T denote the estimator of g. We derive g inthe following theorem.

Theorem 1: The estimator of g is given by

g = 1

P· B−1ϒρ (33)

where ρ is the receive power measurement vector such that

ρ =(ρ0, ρ1

2 , ρ22 , ρ

32 , . . . , ρ

1N, ρ

2N, ρ

3N

)T. (34)



In (33), ϒ is a matrix with the size of N × (3N − 2), whichis defined as

ϒ =

⎛

⎜⎜⎜⎜⎜⎝

1 0 0 · · · 01/2 � 0 · · · 01/2 0 � · · · 0...

......

. . ....

1/2 0 0 · · · �

⎞

⎟⎟⎟⎟⎟⎠(35)

where

� = ((1− j)/2 −(1+ j)/2 j/2

). (36)

For such estimator, the error vector is given by

g− g = 1

P· B−1ϒη (37)

and the mean squared error matrix is

E[(g− g)(g− g)H

] = B−1ϒ�ϒH(

B−1)H

(38)

where η is the receive power measurement noise vector suchthat

η =(η0, η1

2, η22, η

32, . . . , η

1N, η

2N, η

3N

)T(39)

and � is the mean squared noise matrix normalized by thetransmit power such that

� = E[ηηH

]

P2. (40)

Proof: See the Appendix.In Theorem 1, we can see that the mean squared error matrix

vanishes as the mean squared noise matrix normalized by thetransmit power (i.e., �) goes to zero from (38). Therefore, theestimator g in (33) is a valid estimator of g. Moreover, g is anunbiased estimator under the condition that the expectation ofthe receive power measurement noise is zero (i.e., E [η] = 0)from (37).

From g, we can estimate the relative phase ω′n based on thefollowing equation:

gn = hnh∗0 = κnκ0 exp(jω′n

)

= κnκ0(cos ω′n + j sin ω′n

)(41)

where ω′n is the estimate of ω′n, and hn is the estimate of hn

such that

hn = κn exp(jωn). (42)

From (41), we can calculate the estimate of the relative phase,ω′n, as

ω′n = arctan2(Im(gn),Re(gn)) (43)

where arctan2(y, x) is the angle of a vector (x, y), and Re(x)and Im(x) are the real and imaginary parts of x, respectively.

C. Phased Array Location Tracking Problem Formulation

In this section, we formulate the phased array location track-ing problem for deriving the position of the IoT device basedon the estimate of the relative phase obtained in Section III-B.

The relative distance is defined as the distance betweenantenna n and the IoT device (i.e., dn(s)) subtracted by thedistance between the anchor antenna (i.e., antenna n∗) and theIoT device (i.e., dn∗(s) = r). Then, the relative distance ofantenna n when the IoT device is located at s is defined as

δn(s) = dn(s)− dn∗(s) = dn(s)− r. (44)

The estimate of the relative distance can be obtained fromthe relative phase estimated in Section III-B. From (17), therelative distance can be rewritten as

δn(s) = dn(s)− r = − λ

2π(ωn − ωn∗)− λ(ln − ln∗). (45)

Since we do not know the phase ambiguity term λ(ln − ln∗)in (45), it is difficult to obtain δn(s) in terms of ωn from (45).

To tackle this phase ambiguity problem, we make use ofthe property of the planar antenna array, that is, two neigh-boring antenna elements are spaced about a half-wavelengthapart. We focus on the phase difference between two neigh-boring antenna elements. In the antenna array configuration,two antenna elements with consecutive indices, i.e., antennas(n + 1) and n for any n = 1, . . . ,N − 1, are neighboring.From (17), the difference in the distance to the IoT devicebetween antennas (n+ 1) and n can be written as

dn+1(s)− dn(s) = − λ

2π(ωn+1 − ωn)− λ(ln+1 − ln). (46)

The distance between two neighboring antennas (n + 1) andn is less than a half-wavelength of the frequency of the EMwave (i.e., ‖an+1 − an‖2 ≤ λ/2). In addition, the azimuth ofthe IoT device is limited by −π/2 < φ < π/2. Therefore, thedifference in the distance to the IoT device between antennas(n+ 1) and n satisfies the following condition:

− λ/2 < dn+1(s)− dn(s) < λ/2. (47)

We can remove the phase ambiguity by using (47). That is,(ln+1− ln) in (46) should be an integer number that makes thecondition in (47) satisfied. Then, we can rewrite (46) as

dn+1(s)− dn(s)

={(− λ

2π(ωn+1 − ωn)+ λ

2

)mod λ

}− λ

2. (48)

From (44) and (48), we can rewrite δn(s) in terms of ωn as

δn(s) = dn(s)− dn∗(s)

=

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

∑n−1k=n∗

[{(− λ2π (ωk+1 − ωk)+ λ

2

)mod λ

}− λ2

]

if n > n∗

−∑n∗−1k=n

[{(− λ2π (ωk+1 − ωk)+ λ

2

)mod λ

}− λ2

]

if n < n∗

0, if n = n∗.(49)

Let us denote by δn the estimate of the relative distance ofantenna n, i.e., δn(s). We can obtain δn from the estimate of



the relative phase ω′k that is derived in (43). From (49), it isreasonable to calculate δn based on ω′k as

δn =

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

∑n−1k=n∗

[{(− λ2π

(ω′k+1 − ω′k

)+ λ2

)mod λ

}− λ2

]

if n > n∗

−∑n∗−1k=n

[{(− λ2π

(ω′k+1 − ω′k

)+ λ2

)mod λ

}− λ2

]

if n < n∗

0, if n = n∗.(50)

Finally, the phased array location tracking problem can bedefined. The position of the IoT device (i.e., s) is related tothe estimate of the relative distance in (50) by the followingformula:

δn = δn(s)+ μn = dn(s)− r + μn (51)

where μn is the relative distance measurement error. In avector form, (51) is written as

δ = δ(s)+ μ = d(s)− r · 1+ μ (52)

where δ = (δ1, . . . , δN)T, δ(s) = (δ1(s), . . . , δN(s))T, d(s) =

(d1(s), . . . , dN(s))T, and μ = (μ1, . . . , μN)T. The phased

array location tracking problem is to find the most likely posi-tion s for the given estimate of the relative distance δ basedon (52).

D. Cramer–Rao Lower Bound of Phased Array LocationTracking Problem

In the phased array location tracking problem, we attempt toestimate the position only based on the phase measurement inthe antenna array system. Although our proposed system is thetransmit antenna array coupled with a target node capable ofreceive power measurement, the proposed phased array loca-tion tracking problem formulation can be applied to a moregeneral class of antenna array systems, for example, a receiveantenna array system directly measuring the phase of the signalfrom a target node.

A common conception about the antenna array-based posi-tioning is that an antenna array can only estimate the direction(i.e., azimuth and elevation) of the target node with a direction-of-arrival (DOA) algorithm. This is true when the target nodelies in a far-field region of the antenna array. However, thedistance to the target node as well as the direction can beestimated if the target node is located in a radiative near-fieldregion (also known as Fresnel region) of the antenna array. Thetarget node is relatively close to the antenna array in compar-ison to the aperture of the antenna array if the target node isin the radiative near-field region.

In this section, we derive the CRLB to investigate the math-ematical properties of the 3-D location tracking only based ona single antenna array. For deriving the CRLB, we first cal-culate the Jacobian of the relative distance δ(s) with respectto r, θ , and φ. From (11), (12), (13), (14), and (44), we canrewrite δn(s) as

δn(s) = dn(s)− r

=((

r sin θ cosφ − axn

)2 + (r sin θ sinφ − ay

n

)2

+ (r cos θ − az

n

)2) 1

2 − r

=(

r2 − 2aynr sin θ sinφ − 2az

nr cos θ

+ (ay

n

)2 + (az

n

)2) 1

2 − r (53)

given axn = 0. From (53), the Jacobian of δ(s) is calculated as

Jδ(s) =

⎛

⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

∂δ1(s)∂r

∂δ1(s)∂θ

∂δ1(s)∂φ

∂δ2(s)∂r

∂δ2(s)∂θ

∂δ2(s)∂φ

......

...∂δn(s)∂r

∂δn(s)∂θ

∂δn(s)∂φ

......

...∂δN (s)∂r

∂δN (s)∂θ

∂δN (s)∂φ

⎞

⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(54)

where

∂δn(s)∂r= r − dn(s)− ay

n sin θ sinφ − azn cos θ

dn(s)(55)

∂δn(s)∂θ

= −aynr cos θ sinφ + az

nr sin θ

dn(s)(56)

∂δn(s)∂φ

= −aynr sin θ cosφ

dn(s). (57)

For the tractability of calculating the CRLB, we assume thatthe relative distance measurement error μn is a Gaussian noisewith the variance of σ 2

μ (i.e., E [μn] = 0 and E [μ2n] = σ 2

μ) andμn’s for different antennas are independent (i.e., E [μkμn] = 0for k �= n). Since the vector of the relative distance measure-ment error is a white Gaussian noise, the Fisher informationmatrix is calculated as

F(s) = 1

σ 2η

Jδ(s)TJδ(s). (58)

Let s = (r, θ , φ)T denote an unbiased estimator of the positionof the IoT device in the spherical coordinate system. The errorcovariance matrix of s is defined as

Cs = E[(s− s)(s− s)T

]. (59)

Now, we can give the CRLB as

Cs − F−1(s) � 0. (60)

where F−1(s) is the inverse of the Fisher information matrix,and “X � 0” means a matrix X is positive semidefinite. Itis difficult to directly get a useful insight from the CRLBin (60). Therefore, we derive the inequalities between thediagonal entries of the error covariance matrix and the Fisherinformation matrix as follows:

[Cs]ii ≥[F−1(s)

]

ii≥ ([F(s)]ii)

−1 (61)

where [X]ii denote the ith diagonal entry of the matrixX. In (61), the first inequality holds from (60) andthe second inequality holds since F(s) is a positivesemidefinite matrix. The following theorem is derivedfrom (61).



Theorem 2: The error variances of r, θ , and φ satisfy thefollowing lower bounds:

E

[(r − r)2

]

≥ σ 2μ

(∑Nn=1

((ay

n/dn(s))

sin θ sinφ + (az

n/dn(s))

cos θ

−αn(s)+ 1)2)−1

(62)

E

[(θ − θ)2

]

≥ σ 2μ

(∑Nn=1αn(s)2

(ay

n cos θ sinφ − azn sin θ

)2)−1

(63)

E

[(φ − φ)2

]≥ σ 2

μ

(∑Nn=1αn(s)2

(ay

n sin θ cosφ)2)−1

(64)

where

αn(s) = r/dn(s). (65)

In Theorem 2, we can investigate the characteristics of theerror variances according to the distance of the IoT devicefrom the antenna array. As the IoT device moves away fromthe antenna array (i.e., r → ∞), we have dn(s) → r andαn(s) → 1. Therefore, in (63) and (64), we can see thatthe lower bounds of the error variances for the elevation andazimuth are converged as r increases. This means that the esti-mation of the direction (i.e., elevation and azimuth) is possiblein the far-field region.

On the other hand, in (62), we can see that the lowerbound of the error variance for the radius goes to infinityas r increases. Therefore, the estimation of the radius is notpossible in the far-field region, which agrees with the com-mon conception about the antenna array-based positioning.However, the radius can be estimated in the radiative near-field region. The radiative near-field region is defined as theregion where the distance from the antenna array is relativelyshort compared to the size of the antenna array. Therefore, inthe radiative near-field region, we have relatively large valuesof ay

n/dn(s) and azn/dn(s) for some n in (62), which leads to

a small lower bound of the error variance for the radius.In Fig. 4, we show the graph for the CRLB of the radius esti-

mation. In this figure, we plot the simulation results and lowerbound of the error standard deviation of the radius, which isobtained by taking the square root of (62) in the paper. Theresults are derived as a function of the radius for various σμ.For this graph, we have used the same antenna configurationas the one for the experiment, which is the 4-by-8 antennaarray shown in Fig. 7(d). The azimuth and elevation of theIoT device are fixed to 0 and π/2, respectively. We can seethat the CRLB is quite tight, and is useful for predicting theerror standard deviation. We can also see that the radius esti-mation becomes less and less reliable as the IoT device movesaway from the power beacon, as predicted by the equation forthe CRLB.

E. Levenberg–Marquardt Method for Location Tracking

We find the least squares estimator of the position of the IoTdevice, which minimizes the sum of the squared deviationsfrom the measured relative distances. That is, the proposed

Fig. 4. CRLB for the radius estimation.

location tracking algorithm finds s that solves the followingnonlinear least squares problem:

minimizeN∑

n=1

{�n(s)}2 (66)

where �n(s) is the deviation from the measured relativedistance such that

�n(s) = δn(s)− δn = dn(s)− r − δn. (67)

We propose to use the Levenberg–Marquardt method [33]to solve the nonlinear least squares problem in (66). Let s (i)

denote the estimate of s at the ith iteration of the Levenberg–Marquardt method. The Levenberg–Marquardt method is aniterative algorithm that starts from an initial guess s (1) andupdates s (i) to s (i+1) in each iteration according to thefollowing rule:

s (i+1) = s (i) −(

A(

s (i))+ ψ(i)I

)−1q(

s (i))

(68)

where

A(s) = Jδ(s)TJδ(s) (69)

q(s) = Jδ(s)T�(s) (70)

�(s) = (�1(s), . . . ,�N(s))T = δ(s)− δ (71)

and I is the identity matrix and ψ(i) is the damping parameterfor the ith iteration. With the update rule in (68), the estimates (i) is expected to converge to the least squares solution.

The Levenberg–Marquardt method is actually a dampedGauss–Newton method. Each step of the Levenberg–Marquardt method is similar to that of the Gauss–Newtonmethod if the damping parameter ψ(i) is small, whereas itis close to that of the gradient method if ψ(i) is large. Whilethere are many variants of the methods for choosing ψ(i) ineach step, we use a constant damping parameter ψ to makesure that the location is continuously tracked. For the samereason, we do not specify the stopping criterion. We will dis-cuss the implementation of the Levenberg–Marquardt methodin Section IV.



F. Beam Focusing for Optimal Wireless Power Transfer

In this section, we explain the beam focusing method formaximizing the receive power when the power beacon trans-mits wireless power to the IoT device. Recall that the transmitpower is |vn|2/(2RA), where vn is the transmit voltage ofantenna n. The transmit power from each antenna elementis limited to P. Under this transmit power constraint, thepower beacon maximizes the receive power of the IoT device,which is given by |hTv|2/(2RA). Therefore, the power beaconfinds the transmit voltage vector v that is the solution of thefollowing optimization problem:

maximize1

2RA|hTv|2 (72)

subject to|vn|22RA≤ P for all n = 1, . . . ,N. (73)

The solution of the optimization problem (72) and (73) isknown to be the phase conjugate of the voltage transfer coef-ficient. The magnitude of the transmit voltage of each antennais set to ν = √2RAP so that the maximum transmit power isused. If we denote by βn the phase of the transmit voltage ofantenna n, we can rewrite vn as

vn = ν exp(jβn). (74)

Then, the optimization problem (72) and (73) is rewritten as

maximize1

2RA

∣∣∣∣N∑

n=1

κnν exp(j(ω′n + ω0 + βn

))∣∣∣∣2

. (75)

where ω′n = ωn − ω0, ωn is the phase of hn, and ω0 is thephase of h0 =∑N

n=1 hn.The optimization target (75) is maximized when the phases

(ω′n + ω0 + βn) are aligned for all n = 1, . . . ,N. InSection III-B, we have obtained the estimate of the relativephase ω′n in (43). Therefore, we can maximize (75) by settingβn to the conjugate of the estimate of the relative phase. Then,the optimal transmit voltage of antenna n is

v∗n = ν exp(−jω′n

). (76)

IV. DESIGN AND IMPLEMENTATION OF BATTERY-LESS

LOCATION TRACKING SYSTEMS

A. Protocol Design and Algorithm Implementation

In this section, we design a protocol that implements thejoint location tracking and WPT algorithm in Section III. Thetime-domain structure of the proposed protocol is shown inFig. 5. Time is divided into frames, each of which is indexedby t. The former part of a frame consists of a number of train-ing slots. During the training slots, the power beacon transmitswith the training transmit voltage vectors, and the IoT deviceobtains the receive power measurements. On the other hand,the latter part of a frame is a power transfer slot, during whichthe optimal WPT is performed by beam focusing.

In each frame, there are (3M + 1) training slots and thereceive powers for M antenna activation patterns are mea-sured. Suppose that the index of the first antenna activationpattern measured in frame t is m. Then, the first training slotis allocated for measuring ρ0 while the other 3M training

Fig. 5. Time-domain structure of the proposed protocol.

slots are used for measuring ρ1n , ρ2

n , and ρ3n from n = m to

n = ((m+M−3) mod (N−1))+2. Here, the modulus oper-ator is used since the index of the antenna activation patternwraps around within the range of n = 2, . . . ,N. In the nextframe [i.e., frame (t+1)], the first antenna activation pattern isthe next one to the last antenna activation pattern measured inframe t, that is, the index of the first antenna activation patternin frame (t+1) is n = ((m+M−2) mod (N−1))+2. Fig. 5shows an example frame structure when N = 6 and M = 3.

The power beacon maintains the moving-averaged receivepower measurement for each training transmit voltage vec-tor, and updates it when a new receive power measurementis obtained. Let �0, �1

n , �2n , and �3

n for all n = 2, . . . ,Ndenote the moving-averaged receive power measurements. Atframe t, the IoT device obtains the receive power measure-ments and sends a feedback packet, which contains thesemeasurements, to the power beacon via the RF transceiver.Upon receiving the feedback packet, the power beacon updatesthe moving-averaged receive power measurements by using anexponentially weighted moving average as follows:

�0 ← ζ�0 + (1− ζ )ρ0 (77)

� in ← ζ� i

n + (1− ζ )ρin (78)

for i = 1, 2, 3 and for all antenna activation patterns used inframe t, that is, for all n from n = m to n = ((m + M − 1)mod (N−1))+2. In (77) and (78), ζ is a smoothing coefficientbetween 0 and 1.

At each frame, after updating the moving-averaged receivepower measurement, the power beacon performs the locationtracking and the WPT as follows. First, the power beacon cal-culates the relative transfer coefficient vector g by using (33)based on the moving-averaged receive power measurements.That is,

g = 1

P· B−1ϒ (79)

where = (�0, �12 , �

22 , �

32 , . . . , �

1N, �

2N, �

3N)

T. Then, therelative phases, ω′n, for all n are calculated by using (43) basedon the relative transfer coefficient vector g. For the locationtracking, the relative distances, δn, for all n are calculatedfrom the relative phases ω′n by using (50). The Levenberg–Marquardt method in Section III-E updates the position ofthe IoT device (i.e., s(i)) based on the relative distances by



Fig. 6. Algorithm flowchart for battery-less location tracking system.

using (68). This update in (68) can be done just one time ateach frame, or several times to enhance the convergence speed.Note that we use a fixed damping parameter ψ(i) = ψ in (68).Finally, the optimal WPT is performed during the power trans-fer slot by using the optimal transmit voltage v∗n. The optimaltransmit voltage is calculated based on the relative phases, ω′n,by using (76).

We summarize the algorithm flowchart for the proposedbattery-less location tracking system in Fig. 6.

B. Testbed Setup

A proof-of-concept (PoC) testbed is built for evaluatingthe performance of the proposed battery-less location trackingsystem, as shown in Fig. 7. This PoC testbed is implementedaccording to the architecture given Fig. 2, consisting of apower beacon and an IoT device. The frequency of the EMwave is f = 920 MHz, and all the components in the testbedare designed to operate on that frequency.

The main component of the power beacon in our testbed isthe phased array board in Fig. 7(a). We have designed andfabricated the phased array board with 16 RF paths. Eachphased array board has one RF input port that receives an RFsource signal. The RF source signal is split into 16 RF pathsby a power splitter chip (i.e., Mini-Circuits JEPS-16-1W+).On each RF path, a variable attenuator chip (i.e., Mini-Circuits SVA-2000+), a phase shifter chip (i.e., Mini-CircuitsSPHSA-152+), and a power amplifier chip (i.e., Mini-CircuitsGVA-92+) are installed to control and amplify an RF signal.The variable attenuator and phase shifter chips are controlledby the voltage from the digital-to-analog (DAC) chip (i.e.,Analog Devices AD5371).

In the power beacon, we use four phased antenna arrayboards which make 64 RF paths in total. The source signalis generated by a signal generator (i.e., Tektronix TSG4100A)and a drive amplifier (i.e., Ophir 5291E), and is divided bya four-way power splitter to be fed into four phased antenna

Fig. 7. PoC testbed for battery-less location tracking system. (a) Phasedarray board. (b) IoT device. Testbed (c) picture and (d) coordinate system.

array boards. The output signals from 16 RF paths of eachphased array board are radiated by a four-by-four microstrippatch antenna array, which is fabricated for our testbed. Theantenna gain of a single antenna element is 8 dB, and theantenna spacings between two neighboring rows and columnsare both 0.21 m. We use four microstrip patch antenna arrays,each of which has 16 antenna elements, and the total numberof antenna elements is 64. The maximum transmit power ofeach antenna element (i.e., P) is set to 5 mW. A computer anda field programmable gate array (FPGA) device (i.e., NI PXI-7841R) are used to control the phased array boards throughthe DAC chips. The battery-less location tracking algorithmsare implemented by using a Labview software that operateson both the computer and the FPGA.

The IoT device consists of the Powercast P1110 board,the energy storage, and the Zolertia Z1 mote, as shown in



Fig. 7(b). The Powercast P1110 board receives and measuresRF power from the power beacon, and consists of rectifier,power management, and power meter circuits. A supercapaci-tor (i.e., Samxon DDL series) with the capacitance of 0.1 F isused as an energy storage. The Zolertia Z1 mote is a sensorboard that adopts TI MSP430 as an MCU and TI CC2420 as anRF transceiver. The RF transceiver (i.e., TI CC2420) is com-pliant with the 802.15.4 protocol on the 2.4-GHz frequencyband, and is used to communicate with the power beacon. Inthe Zolertia Z1 mote, we use a Contiki operating system (OS)as a software platform.

We show the picture and the coordinate system of the wholetestbed in Fig. 7(c) and (d), respectively. The antenna array of64 antenna elements is placed at the origin, and the IoT devicecan be located within 6 m from the antenna array. Throughoutthe experiments, we have fixed the z-coordinate of the IoTdevice in the Cartesian coordinate system to 0 m. Then, theposition of the IoT device is represented by a 2-D Cartesiancoordinate (x, y), where x and y are the x- and y-coordinate inmeters, respectively. In our testbed, a camera-based positioningsystem (i.e., OptiTrack Flex 13) is used to find out the trueposition of the IoT device.

We set the lengths of a frame and a training slot to 100and 1 ms, respectively, for the protocol in Section IV-A. Theparameters for the protocol are set to M = 4 and ζ = 0.1.

V. EXPERIMENTAL RESULT

A. Wireless Power Transfer Experiments

We have conducted the experiments to verify theperformance of the proposed WPT algorithm. Fig. 8 shows theoperation of the proposed phase estimation algorithm based onthe receive power measurements. For Fig. 8, we have put theIoT device at five different locations, (3, 0), (4, 1), (4,−1),(5, 0), and (3, 0), every 240 s. Fig. 8(a) shows the estimatedphases of the voltage transfer coefficients of all 64 antenna ele-ments over time. In this figure, we can see that the estimatedphase changes as the IoT device moves to a new position. Wecan also see that the estimated phases are the same for thefirst and last periods since the IoT device located at the samepositions (3, 0) for both periods. In Fig. 8(b), we can see thatthe receive power drops at the moment that the IoT deviceis moved, and recovers as the phases of the voltage transfercoefficients become correctly estimated.

In Fig. 8, we can see some delay until the phase estima-tion converges to the new one. The convergence speed of theproposed algorithm is mainly affected by the smoothing coeffi-cient ζ in (77) and (78) for the exponentially weighted movingaverage of the receive power measurement. The smoothingcoefficient ζ balances the tradeoff between the stability andthe convergence speed of the moving average. If the smooth-ing coefficient ζ is low, the algorithm gives more weights tothe history of previous measurements than the current mea-surement. Therefore, the low smoothing coefficient results inhigh stability and slow convergence. In our experiments, wehave conservatively set ζ to a rather low value (i.e., 0.1) tomake the receive power measurement accurate.

Fig. 9 shows the shape of the microwave beam created bythe proposed WPT algorithm when the IoT device is located

Fig. 8. Estimates of (a) voltage transfer coefficients and (b) receive powerover time.

along the center line. To construct the beam shape, we havefirst generated a beam by using the proposed algorithm andfixed the beam, and then we have moved the IoT device allover the testbed space to record the receive power. The IoTdevice is positioned at (2, 0), (4, 0), and (6, 0) in Fig. 9(a)–(c),respectively. The position of the IoT device is represented bya black X mark. We can see that the focal point of the beam isformed at the IoT device for various distances from the powerbeacon, which verifies that the proposed WPT algorithm workswell.

Fig. 10 shows the phases of the transmit voltages whenthe IoT device is positioned as in Fig. 9. We can see thatthe proposed WPT algorithm forms a convex lens-like phasedistribution to focus a beam onto the IoT device. It is also seenthat the curvature of the phase distribution becomes lower asthe IoT device moves away from the power beacon.

Fig. 11 shows the beam shape when the IoT device is offthe center line. We can see that the beam is steered towardthe IoT device if the IoT device is located at (4,−1) and(4, 1) as in Fig. 11(a) and (b), respectively. In these cases,the phases of the transmit voltages are shown in Fig. 12. The



Fig. 9. Beam shape when the IoT device is on the center line. (a) Coordinate:(2, 0). (b) Coordinate: (4, 0). (c) Coordinate: (6, 0).

phase distributions are inclined to one side to which the IoTdevice is offset.

Fig. 13 shows the receive power and the power transferefficiency according to the distance from the power beaconto the IoT device. The distance is actually the x-coordinate

Fig. 10. Phases of the transmit voltages when the IoT device is on the centerline. (a) Coordinate: (2, 0). (b) Coordinate: (4, 0). (c) Coordinate: (6, 0).

Fig. 11. Beam shape when the IoT device is off the center line.(a) Coordinate: (4, −1). (b) Coordinate: (4, 1).

of the IoT device, and the IoT device is on the center line(i.e., the y-coordinate is 0 m) or is offset by 1 m (i.e., they-coordinate is 1 m). For this experiment, we have used all



Fig. 12. Phases of the transmit voltages when the IoT device is off the centerline. (a) Coordinate: (4, −1). (b) Coordinate: (4, 1).

Fig. 13. (a) Receive power and (b) power transfer efficiency according tothe distance.

64 antenna elements or activated only 32 antenna elementsclose to the center line. In Fig. 13(a), we can see that thereceive power gradually decreases as the distance increases.The total transmit powers are 160 and 320 mW when 32 and

Fig. 14. (a) Receive power and (b) power transfer efficiency according tothe number of active transmit antennas.

64 antenna elements are activated, respectively. The powertransfer efficiency in Fig. 13(b) is obtained by dividing thereceive power by the total transmit power. We can see that thepower transfer efficiency reaches up to 18% at 2 m distancewhen 64 antenna elements are used.

The power transfer efficiency is affected by the number ofactive antenna elements. We show the receive power and thepower transfer efficiency as a function of the active antennanumber in Fig. 14. The active antenna elements are selectedfrom the ones close to the center line starting from the anchorantenna element. We can see that the power transfer efficiencyhas a linearly increasing tendency with the active antennanumber while the receive power increases quadratically. Thisis because more antenna elements can generate a sharpermicrowave beam, which is translated into a higher powertransfer efficiency.

B. Location Tracking Experiments

In this section, we show the performance of the proposedlocation tracking algorithm. The proposed location tracking



Fig. 15. Estimate of the relative distances of antenna elements when theIoT device is placed at six different positions. (a) Position 1. (b) Position 2.(c) Position 3. (d) Position 4. (e) Position 5. (f) Position 6.

algorithm first calculates the relative distances from antennaelements to the IoT device as explained in Section III-C. Then,the Levenberg–Marquardt method finds the position of theIoT device that best matches these relative distances. Fig. 15shows the estimates of the relative distances of all 64 antennaelements when the IoT device is located at six different posi-tions. The positions 1–6 are (2,−0.62), (2.65,−0.62), (2, 0),(2.65, 0), (2, 0.62), and (2.65, 0.62), respectively. In this fig-ure, we can see that the azimuth of the IoT device can clearlybe identified by the relative distance pattern, for example, if wecompare the relative distance patterns at positions 1, 3, and 5.Also, we can see that the change in the radius of the IoT deviceleads to slight differences in the relative distance pattern, as

Fig. 16. Estimated and true positions when the IoT device moves.(a) Estimated and true positions over time. (b) 3-D position tracking.

can be seen in the relative distance patterns at positions 3 and4, which makes it possible to estimate the radius.

Fig. 16(a) shows the estimated and true positions over timewhen the IoT device is relocated every 60 s. In the begin-ning, the IoT device is placed at position 3, and then, ismoved to positions 1, 2, 4, 6, and 5 in sequence, and isplaced back at position 3 at last. In this figure, we can seethat the proposed algorithm well tracks the true position. ForFig. 16(b), we slowly and continuously move the IoT devicealong a rectangular-shaped course going through positions 3,1, 2, 4, 6, and 5 in sequence. Fig. 16(b) plots the estimated andtrue positions in a 3-D space. Although we can observe somefluctuations in the estimated position, the estimation positiongenerally tracks the true one.

Fig. 17(a) shows the positioning error vectors measured overthe testbed space. The positioning error vector is defined asthe vector starting from the true position and ending at theestimated position. For the test, we have put the IoT deviceat each point of the 12-by-15 grid with the spacing of 0.2 m.The average error distance, which is defined as the average ofthe magnitudes of the position error vectors, is calculated to



Fig. 17. Positioning accuracy. (a) Positioning error vector. (b) Radiusaccuracy. (c) Azimuth accuracy.

be 0.24 m. We can see that the error tends to become larger asthe IoT device moves away from the antenna array, which isconsistent with the CRLB analysis in Section III-D. To clearlyshow this tendency, we plots the graph revealing the accuracyof the radius estimation in a spherical coordinate system inFig. 17(b). The graph in Fig. 17(b) plots the estimated versusthe true radius, and shows that the radius estimation becomes

less accurate as the radius increases. The mean absolute errorof the radius estimation is calculated to be 0.15 m. On the otherhand, the azimuth estimation is more accurate as shown inFig. 17(c), which plots the estimated versus true azimuth. Theazimuth estimation is fairly accurate, and the mean absoluteerror of the azimuth estimation is calculated to be only 0.56◦.In addition, we have calculated the mean absolute error of theelevation estimation, which is 2.35◦.

There are many possible sources of positioning errors in thereal-world testbed, for example, the receive power measure-ment noise, the power and phase control errors of the phasedantenna array board in the power beacon, and the mismatchbetween the antenna array configuration model and the realantenna array configuration. One of the dominant sources ofpositioning errors in the current testbed is the control error ofthe phased antenna array board. The phase shifter and variableattenuator chips are all controlled by analog voltages generatedby the DAC chip, which is inherently vulnerable to the noiseand temperature variation. In the future testbed, we expect thatthe positioning error can greatly be reduced by eliminatingthese error sources.

VI. CONCLUSION

In this paper, we have investigated a battery-less locationtracking system. We have designed a joint location trackingand WPT algorithm that determines the 3-D position of theIoT device based on the phase information and focuses the EMwave at the IoT device for optimal RF WPT. The proposedalgorithm is extensively tested on the large-scale antenna arraytestbed with 64 antenna elements.

From the practical point of view, a smaller antenna arrayaperture size makes the proposed system more useful. However,the antenna array aperture size in the current testbed is ratherlarge (i.e., 0.84 m × 3.36 m) because the RF of the testbed isrelatively low (i.e., 920 MHz). With a higher RF, we can reducethe antenna array aperture size while keeping the power transferefficiency and the positioning accuracy the same. In the nearfuture, we expect to build a small form-factor multiantennapower beacon operating in a higher frequency range.

The proposed antenna array-based positioning algorithm canbe separately applied to other type of systems with minor mod-ification. For example, in 5G mobile communications, the basestations will be equipped with a massive antenna array forcommunicating on millimeter wave spectrum. The proposedpositioning algorithm can be adopted in such base stations torealize the 3-D positioning with a single multiantenna anchorpoint.

APPENDIX

PROOF OF THEOREM 1

From (18), (19), (29), and (30), we can obtain the truereceive power for the training transmit voltage vectors γ 0

and γ 1n as

ρ0 = P|h0|2 (80)

ρ1n = P|bng|2/|h0|2. (81)

From (31), (32), (80), and (81), we can calculate the truereceive power for the training transmit voltage vectors γ 2

n



and γ 3n as

ρ2n = P|1Tg− bng|2/|h0|2= P

{|1Tg|2 + |bng|2 − (

1Tg)∗

bng− 1Tg(bng)∗}/|h0|2

= ρ0 + ρ1n − Pbng− P(bng)∗ (82)

ρ3n = P|j1Tg+ (1− j)bng|2/|h0|2= P

{|1Tg|2 + 2|bng|2 − (1+ j)

(1Tg

)∗bng

− (1− j)1Tg(bng)∗}/|h0|2

= ρ0 + 2ρ1n − (1+ j)Pbng− (1− j)P(bng)∗. (83)

From (82) and (83), we can calculate bng for n = 2, . . . ,N as

bng = 1

2P

{ρ0 + (1− j)ρ1

n − (1+ j)ρ2n + jρ3

n

}. (84)

In addition, from (18), (19), and (80), we can calculate b1g as

b1g = 1Tg = |h0|2 = 1

Pρ0. (85)

From (84) and (85), we can formulate the followingequality:

Bg = ϒρ/P (86)

where ρ is the true receive power vector such that

ρ =(ρ0, ρ1

2 , ρ22 , ρ

32 , . . . , ρ

1N, ρ

2N, ρ

3N

)T. (87)

From (86), we can calculate g as

g = B−1ϒρ/P = B−1ϒ (ρ − η)/P

= B−1ϒρ/P− B−1ϒη/P. (88)

In (88), we can take B−1ϒρ/P as the estimator of g, and thenthe residual error vector becomes g− g = B−1ϒη/P.

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Arif Abdul Aziz received the B.S. degree in elec-tronics and instrumentation engineering from theUniversity of Gadjah Mada, Yogyakarta, Indonesia,in 2014, and the M.S. degree from the Department ofComputer Science and Engineering, Seoul NationalUniversity of Science and Technology, Seoul, SouthKorea, in 2017. He is currently pursuing thePh.D. degree with the College of Informationand Communication Engineering, SungkyunkwanUniversity, Suwon, South Korea.

His current research interests include radiofrequency (RF) energy transfer technique and RF circuit design.

Lorenz Ginting received the B.S. degree in telecom-munication engineering from Institut TeknologiBandung, Bandung, Indonesia, in 2014, and theM.S. degree from the Department of ComputerScience and Engineering, Seoul National Universityof Science and Technology, Seoul, South Korea, in2017. She is currently pursuing the Ph.D. degreewith the College of Information and CommunicationEngineering, Sungkyunkwan University, Suwon,South Korea.

Her current research interests include radiofrequency energy transfer and beamforming.

Dedi Setiawan received the B.S. degree in biomed-ical engineering and the M.S. degree in com-puter engineering from Institut Teknologi Bandung,Bandung, Indonesia, in 2006 and 2012, respectively,and the Ph.D. degree from the Convergence Instituteof Biomedical Engineering and Biomaterials, SeoulNational University of Science and Technology,Seoul, South Korea, in 2019.

His current research interests include wireless sen-sor networks, energy harvesting power management,radio frequency energy transfer, and beamforming.

Je Hyeon Park received the B.S. degree from theSchool of Electronic and Electronic and ElectricalEngineering, Sungkyunkwan University, Suwon,South Korea, in 2018, where he is currently pur-suing the Ph.D. degree.

His current research interests include radiofrequency circuit design and antenna array signalprocessing.

Nguyen Minh Tran received the B.S. and M.S.degrees in electronics and telecommunication tech-nology from the VNU University of Engineeringand Technology, Hanoi, Vietnam, in 2014 and2016, respectively. He is currently pursuing thePh.D. degree with the College of Informationand Communication Engineering, SungkyunkwanUniversity, Suwon, South Korea.

His current research interests include microstripantennas analysis and design, coding metamaterial,radio frequency (RF) circuit design, and RF powertransfer.

Gyu Yang Yeon received the B.S. degree inmechatronics engineering from Korea PolytechnicUniversity, Siheung-si, South Korea, in 2018. He iscurrently pursuing the M.S. degree with the Collegeof Information and Communication Engineering,Sungkyunkwan University, Suwon, South Korea.

His current research interests include wire-less power transfer and radio frequency energyharvesting.

Dong In Kim (S’89–M’91–SM’02–F’19) receivedthe Ph.D. degree in electrical engineering from theUniversity of Southern California, Los Angeles, CA,USA, in 1990.

He was a tenured Professor with the Schoolof Engineering Science, Simon Fraser University,Burnaby, BC, Canada. Since 2007, he has been withSungkyunkwan University, Suwon, South Korea,where he is currently a Professor with the Collegeof Information and Communication Engineering.

Prof. Kim was a recipient of the NRF of KoreaEngineering Research Center in Wireless Communications for RF EnergyHarvesting for the period 2014–2021. From 2001 to 2019, he served asan Editor of Spread Spectrum Transmission and Access and an Editor-at-Large of Wireless Communication I for the IEEE TRANSACTIONS ON

COMMUNICATIONS. From 2002 to 2011, he also served as an Editor anda Founding Area Editor of Cross-Layer Design and Optimization for theIEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS. From 2008 to2011, he served as the Co-Editor-in-Chief for the IEEE/KICS JOURNAL OF

COMMUNICATIONS AND NETWORKS. He served as the Founding Editor-in-Chief for the IEEE Wireless Communications Letters from 2012 to 2015. Heis the Executive Chair of the IEEE ICC 2022 in Seoul. He is a fellow of theKorean Academy of Science and Technology, and a member of the NationalAcademy of Engineering of Korea.

Kae Won Choi (M’08–SM’15) received the B.S.degree in civil, urban, and geosystem engineeringand the M.S. and Ph.D. degrees in electricalengineering and computer science from SeoulNational University, Seoul, South Korea, in 2001,2003, and 2007, respectively.

From 2008 to 2009, he was with theTelecommunication Business of SamsungElectronics Company, Ltd., Suwon, South Korea.From 2009 to 2010, he was a Post-DoctoralResearcher with the Department of Electrical and

Computer Engineering, University of Manitoba, Winnipeg, MB, Canada.From 2010 to 2016, he was an Assistant Professor with the Department ofComputer Science and Engineering, Seoul National University of Scienceand Technology, Seoul. In 2016, he joined the faculty of SungkyunkwanUniversity, Suwon, where he is currently an Associate Professor withthe College of Information and Communication Engineering. His currentresearch interests include radio frequency energy transfer, visible lightcommunication, cellular communication, cognitive radio, and radio resourcemanagement.

Dr. Choi has been serving as an Editor for the IEEE COMMUNICATIONS

SURVEYS AND TUTORIALS since 2014, the IEEE Wireless CommunicationsLetters since 2015, and the IEEE TRANSACTIONS ON WIRELESS

COMMUNICATIONS since 2017.


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