1

Reconfigurable Intelligent Surface-Aided WirelessPower Transfer Systems: Analysis and

ImplementationNguyen Minh Tran, Student Member, IEEE, Muhammad Miftahul Amri, Student Member, IEEE,

Je Hyeon Park, Student Member, IEEE, Dong In Kim, Fellow, IEEE, and Kae Won Choi, Senior Member, IEEE

Abstract—Reconfigurable intelligent surface (RIS) is a promis-ing technology for RF wireless power transfer (WPT) as it iscapable of beamforming and beam focusing without using activeand power-hungry components. In this paper, we propose amulti-tile RIS beam scanning (MTBS) algorithm for poweringup internet-of-things (IoT) devices. Considering the hardwarelimitations of the IoT devices, the proposed algorithm requiresonly power information to enable the beam focusing capabilityof the RIS. Specifically, we first divide the RIS into smallerRIS tiles. Then, all RIS tiles and the phased array transmitterare iteratively scanned and optimized to maximize the receivepower. We elaborately analyze the proposed algorithm and builda simulator to verify it. Furthermore, we have built a real-lifetestbed of RIS-aided WPT systems to validate the algorithm. Theexperimental results show that the proposed MTBS algorithmcan properly control the transmission phase of the transmitterand the reflection phase of the RIS to focus the power at thereceiver. Consequently, after executing the algorithm, about 20dB improvement of the receive power is achieved compared tothe case that all unit cells of the RIS are in OFF state. Byexperiments, we confirm that the RIS with the MTBS algorithmcan greatly enhance the power transfer efficiency.

Index Terms—Reconfigurable intelligent surface (RIS), RFwireless power transfer (WPT), beam focusing, energy harvestingefficiency.

I. INTRODUCTION

IN the near future, a massive number of internet-of-things(IoT) devices are expected to be deployed [1]. Powering

these billions of IoT devices is challenging. A surging mainte-nance cost makes the traditional methods with power cords andremovable batteries not suitable anymore [2]. Recently, the ra-dio frequency (RF) wireless power transfer (WPT) is emergingas a potential technology for resolving this difficulty [3], [4].In contrast to inductive or magnetic resonance coupling, RFWPT has the advantage of long charging distance. However, itstransfer efficiency degrades quickly as the distance increases.Recently, much higher efficiency can be achieved with RFWPT by beamforming technology. Utilizing the phased array

The authors are with the Department of Electrical and ComputerEngineering, School of Information and Communication Engineering,Sungkyunkwan University (SKKU), Suwon, Korea (email: nmtran@skku.edu,miftahulamri@skku.edu, pjw8251@skku.edu, dikim@skku.edu, kaewon-choi@skku.edu).

This work was partly supported by Institute of Information & commu-nications Technology Planning & Evaluation (IITP) grant funded by theKorea government(MSIT) (No.2021-0-00746, Development of Tbps wirelesscommunication technology, 50%), and in part by the Korea Electric PowerCorporation under Grant R18XA06-15 (50%).

antenna (PAA), one can perform beamforming to focus theelectromagnetic (EM) wave at the receiver. Nonetheless, inthe PAA system, each radiating element should be equippedwith various RF components such as amplifiers, phase shifters,and attenuators. This results in very high complexity, highimplementation cost, and higher power consumption in thesystem, especially in a large-scale system.

Recently, reconfigurable intelligent surface (RIS) is emergedas a promising technology for RF WPT since it is capableof beamforming and beam focusing without using activecomponents. The RIS is also known as other alternativenames such as intelligent reflecting surface (IRS) [5], largeintelligent surface (LIS) [6], software-controlled metasurface[7], or programmable coding metasurface [8], [9]. An RISconsists of hundreds to thousands of passive reflecting unitcells with a special design structure. With a control element(e.g., a PIN diode) integrated, one can electronically controland change the characteristics (e.g., phase, magnitude) of theincoming wave upon each unit cell in the RIS. By intelligentlycontrolling the reflection phase of each unit cell in the RIS,power beams can be focused to the desired positions.

The RIS enables beamforming and beam focusing withoutusing active and power-hungry components. In other words,the RIS ensures lower loss in RF wireless energy transferas compared to the existing technologies only using PAA.Additionally, RISs can be massively manufactured at a verylow cost. Then, one can easily deploy a very large scale ofRISs in the walls of a building or a room to boost up the powertransfer efficiency. These features make it preferable for RFwireless power transfer applications. One potential applicationscenario of the RIS-aided WPT system is given in Fig. 1. Inthis scenario, the RIS is installed in the ceiling of a smart-automated factory for assisting the WPT system. The RISreflects the EM beam from a power beacon, then it focusesthe reflected wave at the devices on the ground. Accordingly,the RIS helps the WPT system to enhance the power transferefficiency and extend the power transfer range.

Although the RIS offers considerable benefits comparedto conventional PAA systems, several challenges need to beaddressed when it comes to practice. The channel estimationis one of the challenging tasks that needs to be tackled forrealizing the RIS-aided WPT. To perform beamforming andbeam focusing, one should estimate the channel between thetransmitter, receiver, and the RIS.

Some recent works have proposed effective channel training

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Fig. 1: RIS-aided WPT system conceptual application sce-nario.

strategies for RIS channel estimation. The authors of [10]have proposed a channel estimation protocol that turns oneach single element while keeping others off. This approachis practically difficult to realize for the following reasons. Thecost and complexity of the system increase if we control boththe phase and magnitude of the unit cells separately. Moreover,the reflection from only one unit cell is not noticeable sinceit is submerged in the other strong signals. Similar channeltraining method is introduced in [11], [12]. The authors of[13] proposed a more practical training method called DFT-Hadamard-based basis training reflection matrix. The authorsconsidered practical discrete phase shifts and demonstratedthat the proposed method operates effectively. Another ef-ficient channel estimation protocol is proposed in [14] fororthogonal frequency division multiplexing (OFDM) systems.A pre-design RIS reflection pattern is obtained by using a two-dimensional discrete Fourier transform (2D-DFT) matrix. Thiswork is further extended in [15], [16].

The potential use of RIS in RF WPT systems has beenanalyzed and demonstrated in [17]–[22]. The work [17]considered and analyzed an RIS-aided simultaneous wirelessinformation and power transfer (SWIPT) system. The authorsjointly optimized the transmit precoding matrices of the basestation and the passive phase shift matrix of the RIS. Theresults show that employing RISs in SWIPT greatly enhancesthe system performance. Another work on using RIS for WPTis proposed in [18]. The authors maximize the receive powerby jointly optimizing the beamformer at the transmitter andthe phase shifts at the RIS. However, this work assumesperfect channel state information (CSI) for simplifying theproblem. Similar work has been done in [19] with perfectchannel estimation assumption. Practical beamforming for theRIS is demonstrated in [21], [22] by experiments. In ourprevious work [21], the experimental results with real-lifetestbeds have proven that RIS can greatly enhance the powertransfer efficiency. The work [21] has reported at most 20 dBenhancement in signal-to-noise radio (SNR) by RIS for thewireless communications systems.

The above-mentioned works are done under the strongassumption that both the phase and magnitude of the receivedsignal are known at the receiver. However, in practice, it is veryhard to obtain the accurate phase information at the receiver

because of the frequency drift and phase noise of the carrierfrequency sources. Due to a low switching speed of RIS unitcells, stabilizing the phase of the carrier frequency sourcewithin one RIS state or tracking it over multiple RIS statesis almost impossible. Then, the channel estimation should bedone only based on the magnitude or power of the receivesignal. One may come up with a typical beam scanning methodwith a known codebook for the entire RIS. This method maywork if the receiver is in the far-field region of the RIS.However, with a typical scanning method, the energy transferefficiency dramatically deteriorates in the radiative near-fieldregion, which is a common situation in the large-scale RISsystem. We have to come up with a solution for enabling thebeam focusing capability of the RIS to handle this situation.

Therefore, in this paper, we propose a multi-tile RIS beamscanning (MTBS) algorithm to overcome this challenge. Wedivide the whole RIS into smaller RIS tiles to ensure thatthe transmitter and receiver are in the far-field region ofeach individual RIS tile. Moreover, instead of controlling eachunit cell separately, we introduce high-level direction controland phase control parameters to efficiently control an RIStile. Subsequently, based only on the receive power level,we iteratively optimize the control parameters of the RIStiles and transmitter to maximize the receive power. We haveelaborately analyzed the proposed model and derived a closed-form expression for the receive power with respect to thecontrol parameters. The MTBS algorithm is designed basedon the findings from the analysis.

We have built a real-life testbed of the RIS-aided WPTand performed experiments to verify the effectiveness of theproposed method. The prototype system consists of a trans-mitter, a receiver, and an RIS. The RIS comprises 16×16 one-bit guided-wave unit cells. The transmitter is a phased arrayantenna that is capable of beam steering. Multiple rectennasare incorporated into the receiver to efficiently harvest the EMwave power. By experiments, we have shown that the MTBSalgorithm works well with different RIS tile sizes in the testscenarios. Almost 20 dB gain in the receive power can beachieved by the MTBS algorithm compared to the case thatall unit cells of the RIS are in OFF state. Furthermore, wehave measured the power transfer efficiency according to thedistance between the transmitter and receiver. To the best ofour knowledge, the analysis and experiments on RIS-aidedWPT systems with multi-tile RIS beam scanning method havenot been done in any previous work.

In summary, the contributions of this paper are threefold.• We elaborately analyze the multi-tile RIS-aided WPT

scheme. Specifically, we divide the RIS into smallerRIS tiles. Moreover, we suggest high-level direction andphase control parameters to handle each RIS tile and thetransmitter. Consequently, the closed-form formula forthe receive power with respect to the control parametershas been derived.

• We propose a multi-tile RIS beam scanning (MTBS)algorithm for enhancing the performance of the RIS-aidedWPT system. With only receive power information at thetransmitter, the proposed algorithm can realize the beamfocusing capability of the RIS.

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• A real-life testbed of the RIS-aided WPT system isbuilt to verify the proposed algorithm. We have shownexperimental results to demonstrate the effectiveness ofthe MTBS algorithm. No previous works have conductedsuch comprehensive experiments.

The rest of the paper is organized as follows. Section IIpresents the overall multi-tile RIS-aided RF-WPT systemmodel and the control model of the RIS tile and transmitter. InSection III, we provide an intuitive analysis on the end-to-endWPT performance given the beam steering control parameters.The multi-tile RIS beam scanning algorithm is presented inSection IV. The RIS design, system implementation, andexperimental setups are given in Section V. Simulation andexperimental results are presented in Section VI, and the paperis concluded with Section VII.

II. SYSTEM MODEL

A. RIS-Aided Wireless Power Transfer System Spatial ModelThe RF-WPT system in consideration consists of one multi-

antenna transmitter, one multi-antenna receiver, and K RIStiles as presented in Fig. 2. The EM wave conveying thewireless power is transmitted from the transmitter, reflectedby the RIS tiles, and received by the receiver. The frequencyof the EM wave is denoted by f , and the free-space wavelengthof the EM wave is denoted by λ.

,

Reconfigurable Intelligent Surface

Transmitter Receiver

RIS Tile k

Fig. 2: RIS-aided WPT system.

The transmitter and receiver are rectangular planar antennaarrays with MTx × NTx antenna elements and MRx × NRx

antenna elements, respectively. The transmitter and receiverhave their own local coordinate system, in which the antennaelements are placed along the x-axis and y-axis on the x-y plane. Each antenna element in the transmitter or receiveris indexed by a tuple (m,n). The antenna spacing betweenadjacent antenna elements in the transmitter is given by δTx,x

and δTx,y in x and y directions, respectively. The antennaspacing is denoted by δRx,x and δRx,y for the receiver. Theposition of antenna element (m,n) of the transmitter in thex-y plane of the local coordinate system is

uTxm,n = (δTx,xκM

Tx

m , δTx,yκNTx

n )T (1)

where κJj is the jth grid point in the uniform grid with sizeJ centered at the origin, that is

κJj = j − J/2− 1/2. (2)

Similarly, the position of antenna element (m,n) of thereceiver is given by

uRxm,n = (δRx,xκM

Rx

m , δRx,yκNRx

n )T . (3)

In the RF-WPT system, there are K rectangular-shaped RIStiles, each of which is indexed by k = 1, . . . ,K. RIS tile khas MRIS

k ×NRISk unit cells. In the local coordinate system for

each RIS tile, the unit cells are placed along the x-axis and y-axis on the x-y plane. The unit cell spacing is δRIS,x and δRIS,y

in x and y directions, respectively. The position of unit cell(m,n) of RIS tile k in the x-y plane of the local coordinatesystem is given by

uRISk,m,n = (δRIS,xκ

MRISk

m , δRIS,yκNRIS

kn )T . (4)

The distance between the origin of the local coordinatesystems (i.e., the center points) of the transmitter and RIStile k is denoted by rTx-RIS

k . Similarly, rRIS-Rxk is the distance

between the origin of the local coordinate systems of RIS tilek and the receiver. We assume that the transmitter and receiverare located within the far-field region of each RIS tile. Thatis, the size of an RIS tile is sufficiently small compared to thedistances rTx-RIS

k and rRIS-Rxk . If this condition is not met, the

RIS tile can be further divided into smaller RIS tiles.The direction from the transmitter to RIS tile k is rep-

resented by elevation θTx-RISk and azimuth φTx-RIS

k from theviewpoint of the local coordinate system of the transmitter. Onthe other hand, the direction from RIS tile k to the transmitterin the local coordinate system of RIS tile k is represented byelevation θRIS-Tx

k and azimuth φRIS-Txk . In the same way, the

directional relationship between the receiver and RIS tile k isdefined by θRx-RIS

k , φRx-RISk , θRIS-Rx

k , and φRIS-Rxk .

In this paper, we prefer to use the u-v coordinates forrepresenting the direction. The u-v coordinate of elevation θand azimuth φ is s = (sin θ cosφ, sin θ sinφ)T . For example,the u-v coordinates of the directions from the transmitter toRIS tile k is given by

sTx-RISk = (sin θTx-RIS

k cosφTx-RISk , sin θTx-RIS

k sinφTx-RISk )T . (5)

The u-v coordinates for other directions, denoted by sRIS-Txk ,

sRx-RISk , and sRIS-Rx

k , can be defined in the same manner.The spatial relationship between the transmitter and RIS

tile k is fully determined by three parameters rTx-RISk , sTx-RIS

k ,and sRIS-Tx

k , and that between the receiver and RIS tile k isdetermined by rRx-RIS

k , sRx-RISk , and sRIS-Rx

k . We can describethe power transfer from the transmitter to the receiver throughthe RIS tiles based on these spatial relationship. In this paper,we assume that the RIS tiles are positioned in such a way thatno power is transferred between the RIS tiles.

The gains of the antenna elements in the transmitter andreceiver towards RIS tile k are denoted by GTx-RIS

k and GRx-RISk ,

respectively. Similarly, the gains of a unit cell of RIS tile ktowards the transmitter and receiver are denoted by GRIS-Tx

k

and GRIS-Rxk , respectively.

B. RIS Tile Control Model

In this subsection, we model the unit cells in the RIS tiles,and explain the control mechanism of each RIS tile. The

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incident free space wave is converted into a guided wave inthe unit cell. The incident guided wave is reflected by thecontrollable load with the normalized impedance of zL, andthe reflected guided wave is radiated to the air as the reflectedfree space wave.

The guided wave is reflected according to the followingequation.

y = Γx, (6)

where x and y are the power waves of the incident andreflected guided wave of a unit cell and Γ is the reflectioncoefficient such that

Γ =zL − 1

zL + 1. (7)

The unit cell and the controllable load are designed in such away that the phase of the reflected wave is controlled by vary-ing the reflection coefficient. Then, the reflection coefficient isgiven by

Γ = exp(jξ), (8)

where ξ is the phase shift. The phase shift can be continuous,for example, if the varactor is used as a controllable load. Onthe other hand, if a PIN diode is used as a controllable load,the phase shift is discrete. Let Ψ denote the number of thecontrol states of the unit cell. Then, the ψth state of a unitcell corresponds to the phase shift of

ξ =2π(ψ − 1)

Ψ, (9)

for ψ = 1, . . . ,Ψ.We define Γk,m,n as the reflection coefficient of unit cell

(m,n) of RIS tile k. Since there are a large number of unitcells, it is difficult to find out the optimal reflection coefficientfor each unit cell individually. Instead, we introduce high-level control parameters for each RIS tile. The direction ofthe reflected wave from RIS tile k is controlled by elevationθRISk and azimuth φRIS

k . With these control parameters set, theincident wave coming from the normal direction of the RIS tileis reflected towards the direction of elevation θRIS

k and azimuthφRISk . The u-v coordinate of θRIS

k and φRISk is given by

ck = (sin θRISk cosφRIS

k , sin θRISk sinφRIS

k )T . (10)

We use ck as the direction control parameter of RIS tile k. Inaddition, the phase of the reflected wave is controlled by thephase control parameter wk for RIS tile k.

With the direction control parameter c and phase controlparameter w, the reflection coefficient of each unit cell in thecase of the continuous phase shift is set as follows.

Γk,m,n(c, w) = exp(jw)

exp(− j 2π

λcTuRIS

k,m,n

). (11)

If the phase shift is discrete, the reflection coefficient isquantized as follows.

Γk,m,n(c, w) = ΩΨ

(exp

(jw)

exp(− j 2π

λcTuRIS

k,m,n

)),

(12)

where ΩΨ is the phase quantization function. For a complexnumber z, the phase quantization function is defined as

ΩΨ(z) = |z| exp

(j

2π

Ψ

⌊Ψ

2π∠z + 0.5

⌋), (13)

where |z| and ∠z is the magnitude and phase of z.

C. Antenna Array Transmitter and Receiver Model

The transmitter is a phased antenna array, each antennaelement of which has a phase shifter to control the phase of thetransmitted wave. The transmitter sends out equal power fromall antenna elements. Let pTx denote the transmit power fromone antenna element. Similar to the RIS control, the trans-mitter is also controlled by high-level control parameters. Thedirection of the transmitted wave is represented by elevationθTx and azimuth φTx. The direction control parameter of thetransmitter is the u-v coordinate of θTx and φTx such that

q = (sin θTx cosφTx, sin θTx sinφTx)T . (14)

Let xi,j denote the transmitted power wave from antennaelement (i, j) of the transmitter. In addition, the transmitterexcitation vector is defined as the vector of the transmittedpower waves such that

x = (xi,j) i=1,...,MTx

j=1,...,NTx. (15)

When the direction control parameter q is given, the transmit-ted power wave from antenna element (i, j) of the transmitter,which is denoted by xi,j(q), is

xi,j(q) =√

2pTx · exp(− j 2π

λqTuTx

i,j

). (16)

We define the directional transmitter excitation vector as

x(q) = (xi,j(q)) i=1,...,MTx

j=1,...,NTx. (17)

The receiver is an antenna array in which each antennaelement receives the RF power. We assume the DC combiningtechnique for combining power from antenna elements. In theDC combining technique, a rectifier attached to each antennaelement performs RF-to-DC conversion, and then the DCpower from each rectifier is summed together. We define ζas the RF-to-DC conversion function that maps the receivedRF power to the rectified DC power. If ya,b denote the receivedpower wave from antenna array (a, b) of the receiver, the totalreceived DC power pRx

DC is given by

pRxDC =

MRx∑a=1

NRx∑b=1

ζ

(|ya,b|2

2

). (18)

III. WIRELESS POWER TRANSFER ANALYSIS

A. End-to-End Wireless Power Transfer Analysis

In this section, we analyze the whole RIS-aided RF-WPTsystem based on the system model in the previous section.We start with analyzing the channel gain between an antennaelement of the transmitter or receiver to a unit cell of an RIS

5

tile. In general, the channel gain between two antennas aregiven by

h =λ

4πd

√GAGB exp

(− j 2π

λd

), (19)

where d is the distance between two antennas and GA and GB

are the antenna gains of two antennas.Based on (19), we first derive the channel gain between

antenna element (i, j) of the transmitter to unit cell (m,n)of RIS tile k. Under the far-field assumption, the distancebetween the antenna element and unit cell is given by

d = rTx-RISk − (sTx-RIS

k )TuTxi,j − (sRIS-Tx

k )TuRISk,m,n. (20)

If we plug (20) into (19) and replace the antenna gains withGTx-RISk and GRIS-Tx

k , we derive the channel gain from antennaelement (i, j) of the transmitter to unit cell (m,n) of RIS tilek as

hTx-RIS(i,j),(k,m,n)

=λ

4πrTx-RISk

√GTx-RISk GRIS-Tx

k exp

(− j 2π

λrTx-RISk

)× exp

(j

2π

λ

((sTx-RISk )TuTx

i,j + (sRIS-Txk )TuRIS

k,m,n

)).

(21)

In a similar way, we derive the channel gain from unit cell(m,n) of RIS tile k to antenna element (a, b) of the receiveras

hRIS-Rx(k,m,n),(a,b)

=λ

4πrRIS-Rxk

√GRx-RISk GRIS-Rx

k exp

(− j 2π

λrRIS-Rxk

)× exp

(j

2π

λ

((sRIS-Rxk )TuRIS

k,m,n + (sRx-RISk )TuRx

a,b

)).

(22)

From (11), (21), and (22), the channel gain from antennaelement (i, j) of the transmitter to antenna element (a, b) ofthe receiver through unit cell (m,n) of RIS tile k is derivedas

hTx-RIS-Rx(i,j),(k,m,n),(a,b) = hTx-RIS

(i,j),(k,m,n)Γk,m,n(ck, wk)hRIS-Rx(k,m,n),(a,b)

(23)

Finally, the received power wave at antenna element (a, b)of the receiver is given by

ya,b =

MTx∑i=1

NTx∑j=1

( K∑k=1

MRISk∑

m=1

NRISk∑

n=1

hTx-RIS-Rx(i,j),(k,m,n),(a,b) + hTx-Rx

(i,j),(a,b)

)xi,j(q),

(24)

where hTx-Rx(i,j),(a,b) is the direct channel gain from antenna

element (i, j) of the transmitter to antenna element (a, b) ofthe receiver.

B. Beam Steering Analysis

Although the RF-WPT equation in (24) fully describes theend-to-end WPT, this equation is not intuitive since it treats theWPT as the summation of individual EM waves propagatedvia numerous antenna elements and unit cells. Actually, the

power is efficiently transferred when the beam is formed bythe transmit antenna array and the RIS tiles. By using the highlevel control methods of the RIS tile in (11) and the transmitantenna array in (16), we can reformulate (24) to describe thebeam steering behavior from the transmitter and RIS tiles.

From (11), (16), (21), and (22), we can calculate thereceived power wave relayed by RIS tile k in (24) as

MTx∑i=1

NTx∑j=1

MRISk∑

m=1

NRISk∑

n=1

hTx-RIS-Rx(i,j),(k,m,n),(a,b)xi,j(q)

=

(λ

4π

)2

√GTx-RISk GRIS-Tx

k GRx-RISk GRIS-Rx

k (2pTx)

rTx-RISk rRIS-Rx

k

× exp

(− j 2π

λ

(rTx-RISk + rRIS-Rx

k − (sRx-RISk )TuRx

a,b

))× exp

(jwk

)×MRIS

k∑m=1

NRISk∑

n=1

exp

(j

2π

λ(sRIS-Txk + sRIS-Rx

k − ck)TuRISk,m,n

)

×MTx∑i=1

NTx∑j=1

exp

(j

2π

λ(sTx-RISk − q)TuTx

i,j

).

(25)

We can simplify (25) as

Rk,(a,b) exp(jwk

)URISk (sRIS-Tx

k + sRIS-Rxk − ck)

× UTx(sTx-RISk − q).

(26)

In (26), Rk,(a,b) represents the magnitude and phase of thereceived power wave related to the distance throughout thetransmitter, RIS tile k, and antenna element (a, b) of thereceiver, which is defined asRk,(a,b)

=

(λ

4π

)2

√GTx-RISk GRIS-Tx

k GRx-RISk GRIS-Rx

k (2pTx)

rTx-RISk rRIS-Rx

k

× exp

(− j 2π

λ

(rTx-RISk + rRIS-Rx

k − (sRx-RISk )TuRx

a,b

)).

(27)

Furthermore, in (26), URISk (v) denotes the beam steering

function of RIS tile k that maps a direction vector v =(vx, vy)T in the u-v coordinate to the gain of the beam. Wedefine URIS

k (v) as

URISk (v)

= MRISk NRIS

k ΞMRISk

(2πδRIS,x

λvx

)ΞNRIS

k

(2πδRIS,y

λvy

),

(28)

where ΞM (x) is the periodic sinc function such that

ΞM (x)

=1

M

M∑m=1

exp(jxκMm

)=

(−1)l(M−1), if x = 2πl for l = 0,±1,±2, . . .

sin(Mx/2)

M sin(x/2), otherwise.

(29)

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Since the periodic sinc function ΞM (x) is maximized when xequals to zero, URIS

k (v) has the maximum gain MRISk NRIS

k ifv is a zero vector. This means that the gain of the beam fromRIS tile k to the receiver (i.e., URIS

k (sRIS-Txk + sRIS-Rx

k − ck) in(26)) is maximized when the direction control parameter ofRIS tile k is set as ck = sRIS-Tx

k + sRIS-Rxk .

Similarly, UTx(v) denotes the beam steering function of thetransmitter, defined as as

UTx(v) = MTxNTxΞMTx

(2πδTx,x

λvx

)ΞNTx

(2πδTx,y

λvy

).

(30)

We can see that UTx(v) has the maximum gain MTxNTx ifv is a zero vector. Therefore, the gain of the beam fromthe transmitter to RIS tile k (i.e., UTx(sTx-RIS

k − q) in (26))is maximized when the direction control parameter of thetransmitter is q = sTx-RIS

k .We define the set of the phase and direction control

parameters for all RIS tiles as ω = (ω1, . . . , ωK) andC = (c1, . . . , cK). When the direction control is used forthe transmitter and all RIS tiles, from (26), the received waveat antenna element (a, b) in (24) is rewritten as

ya,b(ω,C,q)

=

K∑k=1

Rk,(a,b) exp(jwk

)URISk (sRIS-Tx

k + sRIS-Rxk − ck)

× UTx(sTx-RISk − q)

+ Φa,b(q),

(31)

where Φa,b(q) is the power directly transferred to antennaelement (a, b) of the receiver without going through any unitcell of any RIS tile. We define Φa,b(q) as

Φa,b(q) =

MTx∑i=1

NTx∑j=1

hTx-Rx(i,j),(a,b)xi,j(q). (32)

We can calculate the total received DC power at the receiverfrom (18) and (31).

The equation (31) can be intuitively interpreted as follows.The transmitter directs the beam to some selected RIS tilesby controlling the direction control parameter q. For theseselected RIS tiles, and the gains of the beams from thetransmitter to RIS tiles (i.e., UTx(sTx-RIS

k − q)) become high.RIS tile k reflects the beam from the transmitter towards somedirection according to the direction control parameter ck. RIStile k should set ck as ck = sRIS-Tx

k + sRIS-Rxk to direct the

reflected beam to the receiver. The receiver receives the beamsreflected from multiple RIS tiles as well as the wave directlytransferred from the transmitter. The phases of the beams fromRIS tiles vary according to Rk,(a,b), and they do not matchthe phase of the direct wave from the transmitter. Therefore,each RIS tile should control the phase control parameter wkto align the phases of the beams at the receiver so that all thewaves are optimally combined at the receiver.

IV. POWER-BASED BEAM SCANNING ALGORITHM

A. Beam Scanning of Transmitter and RIS TilesIn this subsection, we design the power-based beam scan-

ning algorithm that controls the transmitter and RIS tiles

to maximize the total receive power at the receiver. In thisalgorithm, the transmitter and RIS tiles perform the beamscanning, and the receiver measures the receive power ofeach beam. Then, the algorithm decides the best beam forthe transmitter and RIS tiles based on the receive powermeasurements in an iterative manner.

The set of scanning beams for the transmitter and RIS tilesare generated by a uniform grid in the u-v coordinate system.Each scanning beam is determined by a direction controlparameter, q for the transmitter and ck for RIS tile k. Letq(l) and c

(l)k as the direction control parameter for the lth

scanning beam of the transmitter and RIS tile k, respectively.Then, we define q(l) as

q(l) =

(∆Tx,u

ΥTx,u − 1κΥTx,u

lu ,∆Tx,v

ΥTx,v − 1κΥTx,v

lv

)T, (33)

where ∆Tx,u and ∆Tx,v are, respectively, the scan widths alongthe u and v axes, ΥTx,u and ΥTx,v are, respectively, the numbersof scanning beams along the u and v axes, and lu = ((l − 1)(mod ΥTx,u))+1 and lv = b(l−1)/ΥTx,uc+1 are respectivelythe indices of the scanning beam along the u and v axes.The number of scanning beams of the transmitter is LTx =

ΥTx,uΥTx,v. Similarly, we define c(l)k as

c(l)k =

(∆RIS,uk

ΥRIS,uk − 1

κΥRIS,u

k

lu ,∆RIS,vk

ΥRIS,vk − 1

κΥRIS,v

k

lv

)T, (34)

where ∆RIS,uk and ∆RIS,v

k are, respectively, the scan widthsalong the u and v axes for RIS tile k, ΥRIS,u

k and ΥRIS,vk are,

respectively, the number of scanning beams along the u andv axes for RIS tile k, and lu = ((l − 1) (mod ΥRIS,u

k )) + 1and lv = b(l − 1)/ΥRIS,v

k c + 1 are, respectively, the indicesof the scanning beam along the u and v axes. The number ofscanning beams of RIS tile k is LRIS

k = ΥRIS,uk ΥRIS,v

k .The receiver designates one antenna element at the center of

the antenna array as a sensor antenna, and measures the receivepower of the sensor antenna. Let antenna element (a, b) be thesensor antenna. Then, when the direction control is used for thetransmitter and all RIS tiles, the receive power measurementis given by

P =|ya,b|2

2=|∑Kk=1 exp(jωk)αk(ck)βk(q) + γ(q)|2

2,

(35)

where

αk(c) = Rk,(a,b)URISk (sRIS-Tx

k + sRIS-Rxk − c), (36)

βk(q) = UTx(sTx-RISk − q), (37)

γ(q) = Φa,b(q). (38)

To find out the best beam towards RIS tiles, the transmittercan generate a wide beam by turning on only one antennaelement (i, j) while turning off all other antenna elements.In this case, the following wide-beam transmitter excitationvector is used by the transmitter.

x = (xi,j) i=1,...,MTx

j=1,...,NTx, (39)

7

where xi,j =√

2pTx for antenna element (i, j) and xi,j = 0for all (i, j) except for (i, j). Then, the receive power mea-surement is simplified to

P =|∑Kk=1 exp(jωk)αk(ck)βk + γ|2

2, (40)

where

βk = exp

(j

2π

λ(sTx-RISk )TuTx

i,j

), (41)

γ = hTx-Rx(i,j),(a,b)

√2pTx. (42)

B. RIS Tile and Transmitter Scanning Method

In this subsection, we propose the RIS tile scanning methodthat finds the best phase and direction control parametersfor a specific RIS tile while the transmitter and other RIStiles are fixed. Let us suppose that the scanning for RIS tilek is performed. To focus on RIS tile k, the receive powermeasurement is rewritten as

P (ω, c) =|X + exp(jω)Y (c)|2

2, (43)

where ω and c are, respectively, the phase and direction controlparameters for RIS tile k, and

X =∑

k=1,...,Kk 6=k

exp(jωk)αk(ck)βk(q) + γ(q) (44)

Y (c) = αk(c)βk(q), (45)

if the direction control is used for the transmitter, and

X =∑

k=1,...,Kk 6=k

exp(jωk)αk(ck)βk + γ (46)

Y (c) = αk(c)βk, (47)

if only one antenna element of the transmitter is turned on.Fig. 3 shows the receive signal ya,b for three different phase

control parameters for RIS tile k. It is clear that the receivesignal relayed by RIS tile k (i.e., exp(jω)Y (c)) is rotated withrespect to the phase control parameter ω. In contrast, the signalX relayed from other RIS tiles and directly received from thetransmitter are fixed.

Re

Im

, = 0

,

, = /2 , =

Fig. 3: Receive signal with different phase control parameters.

For the given direction control parameter c, the optimalphase control parameter aligns the phases of X and Y . Theoptimal phase control parameter is given by

ωopt(c) = ∠(XY (c)∗), (48)

and the receive power for the optimal phase control parameteris

P (ωopt(c), c) =(|X|+ |Y (c)|)2

2

=|X|2 + |Y (c)|2

2+ |XY (c)∗|.

(49)

To compute the optimal phase control parameter ωopt(c),we need to measure the receive power with three differentphase control parameters, ω = 0, π, and π/2 as in Fig. 3.From (43), we have the receive power measurements for thesephase control parameters as

P (0, c) = (|X|2 + |Y (c)|2 +X∗Y (c) +XY (c)∗)/2, (50)

P (π, c) = (|X|2 + |Y (c)|2 −X∗Y (c)−XY (c)∗)/2, (51)

P (π/2, c) = (|X|2 + |Y (c)|2 + jX∗Y (c)− jXY (c)∗)/2.(52)

By solving these linear equations, we have

|X|2 + |Y (c)|2 = P (0, c) + P (π, c), (53)

XY (c)∗ =1− j

2P (0, c)− 1 + j

2P (π, c) + jP (π/2, c).

(54)

From (48), (49), (53), and (54), the optimal phase controlparameter and the corresponding receive power are calculatedbased on the receive power measurements as

ωopt(c) = ∠

(1− j

2P (0, c)− 1 + j

2P (π, c) + jP (π/2, c)

),

(55)

and

P (ωopt(c), c) =P (0, c) + P (π, c)

2

+

∣∣∣∣1− j2P (0, c)− 1 + j

2P (π, c) + jP (π/2, c)

∣∣∣∣, (56)

respectively.Now, we develop an algorithm that finds out the optimal

direction control parameter and the corresponding phase con-trol parameter that maximize the receive power P (ωopt(c), c)in (56). In Algorithm 1, we propose the RIS tile scanningalgorithm for a target RIS tile. Algorithm 1 scans the controlparameters of the target RIS tile while keeping those of otherRIS tiles and the transmitter unchanged. The index of the targetRIS tile is denoted by k. We denote by C−k and ω−k thevectors containing the direction and phase control parametersof the RIS tiles other than the target RIS tile, which is givenin Algorithm 1 as an input. In addition, x is the transmitterexcitation vector, which is also given in the algorithm as aninput. The algorithm starts by scanning the direction controlparameters of the target RIS tile with LRIS

kscanning beams

(line 3) while keeping the parameters of the other RIS tilesfixed to C−k and ω−k (line 1) and the parameters of the

8

transmitter fixed to x (line 2). For each scanning beam, thealgorithm changes the phase control parameter among threevalues (i.e., 0, π, and π/2) and measures the correspondingreceive power at line 4 of the algorithm. Then, the optimalphase control parameter ω(l) and the corresponding receivepower P (l) for the lth direction control parameter are com-puted at lines 5–7 according to (55) and (56). The index ofthe scanning beam with the highest receive power is figuredout at line 9. Then, the optimal direction and phase controlparameters resulting in the highest receive power are returnedat lines 10–12.

Algorithm 1: RIS Tile Scanning AlgorithmInput:Index of target RIS tile kDirection control parameters of other RIS tiles C−kPhase control parameters of other RIS tiles ω−kTransmitter excitation vector xOutput:Optimal direction control parameter copt

Optimal phase control parameter ωopt

1 Set the direction and phase control parameters of allRIS tiles except for the target RIS tile according toC−k and ω−k

2 Set the transmitter excitation vector x to the transmitter

3 for l← 1 to LRISk

do4 Measure P (0, c

(l)

k), P (π, c

(l)

k), and P (π2 , c

(l)

k)

5 ϑ← 1−j2 P (0, c

(l)

k)− 1+j

2 P (π, c(l)

k) + jP (π2 , c

(l)

k)

6 ω(l) ← ∠ϑ

7 P (l) ← P (0,c(l)

k)+P (π,c

(l)

k)

2 + |ϑ|8 end9 lopt ← arg maxl=1,...,LRIS

kP (l)

10 copt ← c(lopt)

k

11 ωopt ← ω(lopt)

12 return copt, ωopt

The transmitter should be optimized as well as the RIStiles. In Algorithm 2, we present a simple transmitter scanningalgorithm to find the optimal direction control parameter ofthe transmitter. The vectors of direction and phase controlparameters of all RIS tiles (i.e., C and ω) are given in thealgorithm as an input. The algorithm scans the beams of thetransmitter with LTx scanning beams (lines 2-5) while thewhole RIS is loaded with the RIS direction and phase controlparameter vectors C and ω (line 1). The optimal directioncontrol parameter with the maximum receive power is returnedat lines 6-8.

C. Multi-Tile RIS Beam Scanning Algorithm

In this subsection, we introduce the multi-tile RIS beamscanning (MTBS) algorithm to get the optimal control param-eters for all RIS tiles and the transmitter with only receivepower information. To reduce the scanning time, we proposea smart beam scanning algorithm that alternately scans andoptimizes the RIS tiles and transmitter by Algorithms 1 and

Algorithm 2: Transmitter Scanning AlgorithmInput:RIS direction control parameter vector CRIS phase control parameter vector ωOutput:Optimal transmitter direction control parameter qopt

1 Set the direction and phase control parameters of allRIS tiles to C and ω

2 for l← 1 to LTx do3 Set the transmitter excitation vector to x(q(l))4 Measure the receive power P (l)

5 end6 lopt ← arg maxl=1,...,LTx P (l)

7 qopt ← q(lopt)

8 return qopt

2. The overall operation of the MTBS algorithm is summarizedas follows. In the first iteration, only one antenna element ofthe transmitter is turned on for generating a wide beam fromthe transmitter. Then, all RIS tiles are scanned and optimizedone by one with the RIS tile scanning algorithm. After settingall RIS tiles with current optimal control parameters, thebeams for the transmitter are scanned to figure out the bestdirection control parameter of the transmitter. From the nextiteration, the transmitter activates all antenna elements anduses the best direction control parameter. Then, we repeatedlyperform the scanning and optimizing for all RIS tiles and thetransmitter to enhance the receive power over iterations.

Algorithm 3: Multi-tile RIS Beam Scanning (MTBS)AlgorithmInput:Number of scanning iterations ηOutput:Optimal RIS direction control parameter vector Copt

Optimal RIS phase control parameter vector ωopt

Optimal transmitter direction control parameter qopt

1 x← x2 for τ ← 1 to η do3 for k ← 1 to K do4 (ck, ωk)←

RIS tile scanning algorithm(k,C−k,ω−k,x)5 end6 q← Transmitter scanning algorithm(C,ω)7 x← x(q)8 end9 Copt ← C

10 ωopt ← ω11 qopt ← q12 return Copt, ωopt, qopt

The details of the MTBS algorithm is presented in Al-gorithm 3. This algorithm maintains and updates the RISdirection and phase control parameter vectors (i.e. C and ω)and the transmitter direction control parameter and excitation

9

vector (i.e., q and x). This algorithm starts by activatingone antenna element of the transmitter with the wide-beamtransmitter excitation vector x in (39) at line 1. Then, eachRIS tile is optimized by the RIS tile scanning algorithm inAlgorithms 1 at lines 3-5. Subsequently, the direction controlparameter of the transmitter is updated by the transmitter scan-ning algorithm in Algorithm 2 at line 7. The correspondingtransmitter excitation vector (i.e., x(q)) is updated to x at line6. This process is repeated η times, and the optimal controlparameters are obtained.

V. RIS-AIDED WPT SYSTEM IMPLEMENTATION

A. RIS Design and Fabrication

In this section, we present the design and fabrication ofthe RIS. We first design a 1-bit guided wave unit cell whichoperates at 5.8 GHz. The configuration of the unit cell isgiven in Fig. 4. The unit cell is designed on Rogers RO4350Bsubstrate (i.e., substrate 1 in Fig. 4(c)) with the relativepermittivity of 3.66 and thickness of 1.524 mm. Furthermore,an RF choke placed on the FR4-epoxy substrate (i.e., substrate2 in Fig. 4(c)) is incorporated into the unit cell.

PIN diode

(a) Unit cell (b) RF choke

(c) Layer stack-up

Unit cell layer

W

h

a

b

l1l2

Substrate 1

Substrate 2,3

RF Choke layer

Fig. 4: Unit cell configuration.

The principle of designing the unit cell is given in Fig. 5.Firstly, a rectangular patch is designed to resonate at 5.8 GHz.The EM wave at the resonant frequency is absorbed by thepath with the radiation impedance of ZR. Then, this wave isguided to a quarter wavelength transmission line in the formof a guided wave. The quarter wavelength transmission linewith characteristic impedance Z0 in combination with a stubis carefully designed to transform the radiation impedanceinto an appropriate value (e.g., transformed impedance Zt).The guided wave is reflected at the controllable load (i.e., aPIN diode) with the impedance ZL. Afterward, this reflectedguided wave propagates back to the patch and is re-radiatedto the air. The reflection coefficient at the PIN diode can beexpressed as

Γ =ZL − ZtZL + Zt

=zL − 1

zL + 1= |Γ| exp jξ, (57)

where

ZL =

R+ jωL ON state,

1jωC + jωL OFF state,

(58)

Zt = Z20/ZR is the transformed impedance, zL = ZL/Zt

is the normalized impedance, ξ is the phase shift. Ideally, themagnitude of the reflection coefficient (i.e., |Γ|) equals to 1. Toget a 180 phase difference, one should figure out the valuesof Zt and Z0 which satisfy

∆ξ = ξON − ξOFF = 180. (59)

PIN diode

ZRZR

Z0 ZL

C L

R LR L

OFF

ON

C L

R L

OFF

ON

l/4

EM wave

Lvia

Fig. 5: Equivalent circuit of the 1-bit guided wave unit cell.

In this design, we use a PIN diode (MACOM MADP-000907-14020) to control the reflection phase of the guidedwave. The PIN diode can be modeled as a series RL circuit(R = 5.2 Ω, L = 30 pH) in ON state, and as a series LCcircuit (L = 30 pH, C = 30 fF) in OFF state. To ensure thePIN diode operation, a biasing circuit with an RF choke isincorporated (see Fig. 4(b)). The RF choke is designed with abutterfly stub to prevent high-frequency signals from travelingto the DC source. To minimize the biasing circuit loss, wedesign the biasing point at the center of the patch, which is azero electric field point. Consequently, good isolation and noadditional loss from the DC biasing circuit to the main patchis achieved. The geometry parameters of the unit cell are listedin Table I.

TABLE I: Geometry parameters of the unit cell (unit: mm).

Parameter Value Parameter ValueW 36.2 l1 7.5a 16.61 l2 12b 12.88 h 1.524

The unit cell performance is validated by simulating inan EM simulator with periodic boundary and Floquet portexcitation. Fig. 6 indicates the magnitude and phase of thesimulated reflection coefficient. It is evident that a nearly 180

phase shift between ON and OFF state is achieved within 100MHz bandwidth around the center frequency. The reflectionamplitude is almost uniform between the two states. A smallamount of loss can be observed due to the lossy substrate andthe heat generated by the resistance of the PIN diode in ONstate.

10

5 . 6 5 . 7 5 . 8 5 . 9 6 . 0- 5

- 4

- 3

- 2

- 1

0

1

O N _ M a g n i t u d e O F F _ M a g n i t u d e O N _ P h a s e O F F _ P h a s e

F r e q u e n c y ( G H z )

Refle

ction M

agnitu

de |S 1

1|

- 2 4 0- 1 8 0- 1 2 0- 6 006 01 2 01 8 02 4 0

Refle

ction P

hase (D

egree)

Fig. 6: Simulation result of the unit cell in ON/OFF states.

Subsequently, we fabricated a 16 × 16 RIS as shown inFig. 7. The RIS is comprised of four sub-arrays, each ofwhich consists of 8× 8 unit cells. Additionally, four identicalcontrol boards are designed and fabricated to independentlycontrol each unit cell of these sub-arrays. The block diagramof the control board is shown in Fig. 8. In each control board,we use a 8-bit shift register (SN74HC595), a 3-to-8 decoder(74HC238), and eight 8-bit D-type flip flops (74AC16374). Adata acquisition equipment (DAQ) or a FPGA device is used togenerate the ON/OFF signals of the unit cells. These ON/OFFsignals are conveyed to the shift register, then forwarded toall D-type flip flops. Next, the flip flops load the ON/OFFsignals when they are selected by the decoder. As a result,the desired state of every unit cell is loaded with the controlsignal. Finally, we combine the control board with the RISas a sandwich structure. This facilitates extending the RIS toa larger scale. A LabVIEW code is programmed to properlycontrol the board.

Unit Cell

Reconfigurable Intelligent Surface

Fig. 7: 16× 16 RIS prototype.

DAQ/FPGA

SR DC

DFF DFF DFF DFF DFF DFF DFF DFF DFF DFF DFF DFF DFF DFF DFF DFF

DFF DFF DFF DFF DFF DFF DFF DFF DFF DFF DFF DFF DFF DFF DFF DFF

SR DC

SR DC SR DC

SR Shift register DecoderDC DFF D – flip flop

IN CLK CLR Q’ IN CLK CLR Q’

IN CLK CLR Q’IN CLK CLR Q’ 1 2 3 EN 1 2 3 EN

1 2 3 EN1 2 3 EN

Fig. 8: RIS control block diagram.

B. Testbed Setup

The complete real-life testbed of RIS-aided WPT system isdeployed as given in Fig. 9. Specifically, we aim to transferthe energy wirelessly from the transmitter to the receiver withrelaying by the designed RIS. The experiment system consistsof the fabricated RIS with its controller, a transmitter with itscontroller, and a receiver. An FPGA device (NI USRP 2944R)serves as the RIS controller.

Receiver

RISTransmitterRIS

Controller

TransmitterController

Z position

X position

Y position

Fig. 9: Experiment set-up.

An 8 × 8 phased array antenna is used as a transmitter ofthe system. The transmitter array comprises four 4 × 4 unitmodules which are made by stacking up a phased array board,an amplifier board, and an antenna board with a sandwichstructure (Fig. 10(a)). We have designed and fabricated asupplemental board to combine four modules in one 8 × 8transmitter. The board for combining modules consists of DC-DC converters, control signal lines, and two-stage Wilkinsondividers so that the transmitter can operate with only one

11

DC input, one control signal input, and one RF input. EachRF path consists of a phase shifter, an RF switch, a poweramplifier, and a shift register to control the phase shifter andthe RF switch. A data acquisition equipment (NI USB-6351)is utilized to control the excitation phase of the transmitter.To provide the RF source to the transmitter, we employ amicrowave signal generator (R&S SMB 100A) in combinationwith an RF amplifier.

Fig. 10(b) shows 4 × 4 rectenna array receiver. To harvestthe energy from the EM wave, multiple rectennas with highRF-to-DC conversion efficiency are integrated. Each rectifieris designed as a one-stage Dickson charge pump structurewith one series pair diode and two capacitors. RF switchescontrolled by a multiplexer and a decoder are connected torectifiers. By controlling these switches, we can measure theopen-circuit voltage of each rectenna, which is an indicatorof the receive power. The converted DC current from eachrectenna is combined in parallel.

Phased array board

Amplifier board

Antenna board

(a) Transmitter board

DC-DC Converter

Rectifier

Control Circuit

Front view Back view

(b) Receiver

Fig. 10: Transmitter and receiver prototype.

VI. NUMERICAL RESULTS

In this section, we present several simulation and experi-mental results for demonstrating the operation of the proposedalgorithm.

A. Simulation Results

To verify the proposed MTBS algorithm, we first showseveral simulation results with different RIS tile sizes. Fortesting the effectiveness of the proposed algorithm, we sim-ulate the system with a larger RIS compared to the one inexperiment. Specifically, we consider an 1-bit RIS with 40×40unit cells in this simulation. The RIS is divided into 400tiles and 100 tiles with the corresponding RIS tile sizes of2 × 2 and 4 × 4. The RIS is assumed to be located at theorigin of the global Cartesian coordinate system. The phasedarray transmitter consists of 8 × 8 antenna elements and ispositioned at (-0.5 m, 0 m, 2 m). The receiver is equippedwith 4 × 4 antenna array and is located at (2 m, 1 m, 2 m).The antenna element (2, 2) is selected as the sensor antennain the receiver. In the first iteration of the MTBS algorithm,the antenna element (4, 4) of the transmitter is turned on. Inthis simulation, the scanning beams over u-v coordinate ofthe transmitter/RIS tile are generated according to (33) and(34) given in Subsection IV-A. Specifically, for a M × N

planar array, we generate 2M ×2N scanning beams with 2Mscanning points in the u-axis and 2N scanning points in thev-axis. Therefore, 256 scanning beams are generated for the8×8 phased array transmitter. The number of scanning beamsfor RIS tile with 2 × 2 and 4 × 4 unit cells are 16 and 64,respectively.

(a) RIS tile size 2× 2

(b) RIS tile size 4× 4

Fig. 11: Simulation receive power over scanning iterations.

Fig. 11 shows the normalized receive power of the sensorantenna and the whole antenna array of the receiver over thescanning iterations with the RIS tile size of 2× 2 and 4× 4.The receive power of the sensor antenna and whole antennaarray are indicated by “MTBS - sensor power” and “MTBS- total power”. The “RIS OFF” represents the receive powerwhen all unit cells of the RIS in OFF state. We can see thatthe RIS is effectively trained by the proposed algorithm. In thefirst iteration, the RIS tiles are well trained with about 45 dBimprovement in the first case (i.e., RIS tile size of 2× 2) andalmost 28 dB gain in the second case (i.e., RIS tile size of 4×4)for both sensor antenna and whole antenna array. In the secondscanning iteration, all antenna elements of the transmitter areturned on to transmit with the best beam. Therefore, there is

12

a big jump in the receive power as shown in Fig. 11 at theend of the first iteration. The RIS tiles are re-trained in thesecond iteration. There is around 5 dB improvement in thereceive power that can be observed in both cases. The receivepower in both cases remain stable in the third iteration. Afterexecuting the algorithm, about 35 dB gain in the total receivepower (i.e., “MTBS - total power”) is obtained compared tothe “RIS OFF” case.

0 32 64 96 128 160 192 224 256Scanning beam index

-70

-60

-50

-40

-30

-20

-10

0

Nor

mal

ized

rec

eive

pow

er (

dB)

(a) Receive power according toscanning beams

1 2 3 4 5 6 7 8Antenna index - X axis

1

2

3

4

5

6

7

8

Ant

enna

inde

x -

Y a

xis

-150

-100

-50

0

50

100

150

Phase (Deg)

(b) Transmitter optimal phase ex-citation

Fig. 12: Transmitter scanning process.

The transmitter scanning results in the first iteration are pre-sented in Fig. 12. The normalized receive power correspondingto each scanning beam is given in Fig. 12(a). It is noted thatthe 140th scanning beam results in the highest receive power.Fig. 12(b) indicates the corresponding phase distribution ofthat scanning beam. The RIS optimal phase distributions ofthe two cases are given in Fig. 13. We can see that a convexlens-like pattern is formed in both cases to focus the powerbeam to the receiver. This cannot be done by a conventionalfar-field scanning algorithm.

0∘ 180∘

(a) RIS tile size 2× 2

0∘ 180∘

(b) RIS tile size 4× 4

Fig. 13: RIS optimal phase distribution.

B. Experimental Results

In this subsection, we present experimental results obtainedby performing the wireless power transfer experiments in thereal test scenarios with the fabricated RIS.

1) Algorithm Validation: We first verify the beam focusingcapability of the proposed system. The coordinate system ofthe testbed in Fig. 9 is given in Fig. 14. The RIS is set atthe origin of the coordinate system. In this test scenario, thetransmitter is located at (-0.5 m, 0 m, 1.5 m), and the receiver

is placed at (1.5 m, 0.5 m, 2 m). Similar to the simulation,the scanning beams over u-v coordinate of the transmitter/RIStile are generated in the same way. Thus, 256 scanning beamsare used for the 8 × 8 phased array transmitter. The numberof scanning beams for RIS tile sizes of 2 × 2, 4 × 4, and8 × 8 are 16, 64, and 256, respectively. In the first iteration,

Reconfigurable Intelligent Surface

Transmitter

Receiver

Z

X

Y

With Obstacle

Without Obstacle

Fig. 14: Testbed coordinate system.

one antenna element of the transmitter (i.e., antenna element(4, 4)) is turned on and transmits with the power of 23 dBm. Inthe next iteration, the whole phased array transmitter is activeand the transmit power of each element is 15 dBm. Highertransmit power in the first iteration ensures a sufficientlyhigh receive power for operating the algorithm correctly. Thereceiver measures the receive power at the sensor antennawhich is the antenna element (2, 2). It is noted that the receivepower of Figs. 15–21 is the receive RF power measured by asingle sensor antenna at the receiver.

To demonstrate the benefit of the RIS, we insert the obstaclebetween the transmitter and receiver to block the direct channel(see Fig. 14). The receive power for this case is presentedby “MTBS: with obstacle”, and the one without the obstaclecorresponds to “MTBS: without obstacle”. In addition, afterexecuting the proposed algorithm, we remove the RIS toclearly show the RIS effect. The corresponding result isindicated by “Without RIS”.

Fig. 15 presents the receive power of the sensor antennaover the iterations when the RIS tile size 4 × 4 is used inthe scanning. We can observe from Fig. 15 that very goodmeasured results are obtained. After the first iteration, whilearound 9 dB improvement is seen in the case without obstacle,7 dB gain is achieved when an obstacle is inserted. In the nextscanning iteration, we can see a great enhancement of thereceive power in the latter case (i.e. MTBS: with obstacle).Subsequently, the same performance is obtained for the twocases after executing the algorithm. It is clear that a fractionof the transmit power to some RIS tiles is blocked by theobstacle when one antenna element is active. As a result,these RIS tiles are not well trained in the first iteration.Hence, better optimal control parameters for the RIS tiles areupdated in the next iteration. Finally, we can see that around20 dB gain in the receive power is achieved with the proposed

13

Fig. 15: Receive power over the iteration (RIS tile size 4×4).

algorithm in comparison with the “RIS OFF” case. The receivepower degrades almost 35 dB when the RIS is removed (i.e.,“Without RIS” case).

0 8 16 24 32 40 48 56 64Scanning beam index

-23.5

-23

-22.5

-22

-21.5

Rec

eive

pow

er (

dBm

)

(a) Receive power with different phase control

0 8 1 6 2 4 3 2 4 0 4 8 5 6 6 4- 2 5 . 0- 2 4 . 5- 2 4 . 0- 2 3 . 5- 2 3 . 0- 2 2 . 5- 2 2 . 0- 2 1 . 5

R e c e i v e p o w e r

S c a n n i n g b e a m i n d e x

Recei

ve pow

er (dB

m)

- 3- 2- 1012345

O p t i m a l p h a s e

Optim

al phas

e (rad

)

O p i t m a l b e a m i n d e x

(b) Optimal phase control and corresponding receive power

Fig. 16: RIS tile scanning process in experiments.

The measured data while scanning the 12th RIS tile in thefirst iteration of “MTBS: without obstacle” case is shown in

Fig. 16(a). The receive power with respect to three differentphases of each scanning beam is measured. Using thesemeasured data, the optimal phase control of each scanningbeam is calculated by using (55). According to (56), the cor-responding receive power is obtained. The calculated optimalphase control and the corresponding receive power for allscanning beams are given in Fig. 16(b). We can observe thatthe 22th scanning beam is the optimal one with the highestreceive power of about -21.7 dBm.

0 32 64 96 128 160 192 224 256Scanning beam index

-30

-25

-20

-15

-10

-5

0

Rec

eive

pow

er (

dBm

) Optimal Beam

(a) Receive power according toscanning beam

1 2 3 4 5 6 7 8Antenna Index - X axis

1

2

3

4

5

6

7

8

Ant

enna

Ind

ex -

Y a

xis

0

50

100

150

200

250

300

350

Phase (Deg)

(b) Transmitter optimal phase con-trol

Fig. 17: Transmitter scanning process in experiment.

Fig. 17(a) presents the receive power with respect to thescanning beams when the transmitter is scanned in the firstiteration. We can see that the highest receive power is around-4 dBm at the 124th scanning beam. This scanning beamis selected as the optimal beam for transmitting in the nextiteration. The corresponding phase distribution of the optimalbeam of the transmitter is shown in Fig. 17(b).

0

180

Phase (Deg)

(a) Without obstacle

0

180

Phase (Deg)

(b) With obstacle

Fig. 18: RIS optimal phase distribution (RIS tile size 4× 4).

The optimal phase distribution of the RIS for the two casesof with and without obstacles are given in Fig. 18. A very goodagreement between the two cases confirms the same receivepower given in Fig. 15. Up to this point, we can observe thatthe proposed algorithm operates effectively even an obstacleinserted between the transmitter and the receiver. It provesthat by deploying the proposed algorithm, RIS can greatlyenhance the receive power of WPT systems even when thedirect channel deteriorates.

Furthermore, the experiments with RIS tile sizes of 2 ×2 and 8 × 8 are conducted and the results are presented inFigs. 19, 20, 21, and 22. We can see that very good resultsare obtained. The almost same performance is given betweentwo cases (with and without obstacle) when scanning withboth RIS tile sizes. There are around 20 dB and 35 dB gain

14

Fig. 19: Receive power over the iteration (RIS tile 2× 2).

of the receive power in comparison with the “RIS OFF” caseand “Without RIS” case, respectively. It can be seen fromFig. 20 that some RIS tiles are not very well trained. This isbecause the RIS tile size (i.e., 2×2) is relatively small, whichleads to small receive power causing the error in calculatingthe optimal parameters. However, a convex lens-like phasedistribution can still be formed, and a good result is achievedafter the MTBS algorithm is executed. In addition, a very goodmatch between the two results of the RIS tile size 8× 8 casecan be observed in Fig. 22(a) and Fig. 22(b). This explains thesimilar trend over scanning iterations between “MTBS: withobstacle” and “MTBS: without obstacle” presented in Fig. 21.

0

180

(a) Without obstacle

0

180

Phase (Deg)

(b) With obstacle

Fig. 20: RIS optimal phase distribution (RIS tile size 2× 2).

2) Power Transfer Experiment: Finally, we perform wire-less power transfer with the fabricated testbed and measurethe power transfer efficiency over the distances. In this testscenario, the transmitter and receiver are located 2 meters awayfrom the RIS in the z-direction. The transmitter, receiver, andRIS are set at the same height. Fig. 23 shows the positions ofthe transmitter, receiver, and RIS in x-z plane.

Specifically, the RIS is located at the origin of the coordinatesystem. The transmitter is positioned at (-1 m, 2 m), and thereceiver is at (x, 2 m) with x ranging from 0 m to 2.5 m. Thedistance between the transmitter and the receiver is indicatedby dTx-Rx in Fig. 23. Henceforth, we will call this distance the

Fig. 21: Receive power over the iteration (RIS tile size 8×8).

0

180

(a) Without obstacle

0

180

Phase (Deg)

(b) With obstacle

Fig. 22: RIS optimal phase distribution (RIS tile size 8× 8).

0.5

1.0

1.5

Z-axis (meter)

-1 -0.5 0 0.5 1.0 1.5 2.0 2.5 X-axis(meter)

2.0

Transmitter RIS Receiver

P1 P2

Fig. 23: Transmitter, receiver, and RIS position.

Tx-Rx distance. Indeed, the receiver is moved along with thex-axis from position P1 to position P2 to vary Tx-Rx distancefrom 1 meter to 3.5 meters. It is noted that the obstacle isremoved for this test. Furthermore, for a real WPT, the RFsignal is rectified and stored in the energy storage device(e.g., super-capacitor). Therefore, in this test the rectified DCpower of the whole antenna array is measured as the receiveDC power. It is different from the RF receive power fromthe sensor antenna presented in the previous results. The totaltransmit power is 2.1 W. The corresponding receive DC power

15

of the receiver according to the Tx-Rx distance is recorded,and the power transfer efficiency is calculated accordingly.In this experiment, the results with three different RIS tilesizes are obtained and compared with that of “RIS OFF” case.Fig. 24 shows the obtained results (i.e., receive DC power andpower transfer efficiency) according to the Tx-Rx distance.

Fig. 24: Receive power and power transfer efficiency over Tx-Rx distance.

Fig. 24 demonstrates that for all RIS tile-size cases, thereceive DC power fluctuates around 18 mW while varyingthe Tx-Rx distance from 1 m to 1.9 m before dropping to 2mW at 2.5 m. It is because the steering angle (φRIS-Rx

k ) getswider when the test distance increases. When it approachesthe steering limit of the RIS, a part of the reflected powerfrom the RIS is directed to the other side of the steeringangle. It is similar to the grating lobe phenomenon whensteering the beam in the planar phased array antenna. Hence,the performance deteriorates. Moreover, we can notice that thereceive DC power of the “RIS OFF” case increases to nearly5 dBm as the Tx-Rx distance approaches 2 m. This is dueto the specular reflection appearing at that point. The receiveDC power for that case degrades instantly when the receivercontinues moving along with x-axis.

It is observed that around 22.5 mW is transferred to thereceiver at 1.3 m Tx-Rx distance when the RIS tile is scannedwith the RIS tile size of 2×2. It corresponds to almost 1.05%power transfer efficiency. The reason for this low efficiency isthat the actual channel distance (i.e., transmitter-RIS-receiver)is almost 4.25 m. This efficiency is comparable with thatpresented in [23]. We can expect that higher power transferefficiency can be achieved by deploying a larger RIS system.However, this receive DC power is sufficient for charging thelow-power IoT receiver and keeping it alive [24].

The RIS optimal phase distribution patterns according todifferent Tx-Rx distances are shown in Fig. 25. Convex lens-like patterns are formed for every case. There is a goodagreement between the patterns of different RIS tile sizes ateach Tx-Rx distance. It is noticed that the patterns with RIStile size of 2 × 2 and 4 × 4 get worse as the Tx-Rx distanceincreases (see Fig. 25(e)) while that of the RIS tile size of 8×8is fine. This is because the signal reflected from the smaller

RIS tile size becomes very small when the receiver movesfurther away from the RIS. This incurs errors in the calculationof the algorithm. This phenomenon can be observed in Fig. 24.The receive DC power with RIS tile size of 8 × 8 is higherthan those of the RIS tile sizes of 2× 2 and 4× 4 at 3 m Tx-Rx distance. It is observed that, in the near region (relativelyshorter range from the transmitter), the RIS tile size of 2× 2performs the best of all three cases. On the other hand, in themiddle region (medium range from the transmitter), the RIStile size of 4 × 4 outperforms the other cases. The RIS tilesize of 8 × 8 is superior to the other cases in the far region(relatively longer range from the transmitter).

VII. CONCLUSION

In this paper, we have implemented a real-life testbed ofRIS-aided WPT system. We have proposed a multi-tile RISbeam scanning algorithm to enable the beam focusing capa-bility of the RIS with only power information. In addition, themathematical analysis was elaborately presented. Specifically,the RIS tile scanning algorithm was introduced to find theoptimal phase and direction control parameters of the RIStile. Then, multi-tile RIS scanning algorithm was performedby iteratively scanning and optimizing all RIS tiles and thetransmitter. The simulation has been carried out to prove theeffectiveness of the proposed algorithm. The simulation resultsshowed that the RIS with the proposed MTBS algorithm cangreatly improve the receive power at the receiver.

We have built a real-life testbed of the RIS-aided WPTsystem and performed the experiment to verify the MTBSalgorithm. The experiments with different RIS tile sizes wereconducted. The experimented results showed that the proposedalgorithm works very well. All RIS tiles were well optimizedin every iteration. Especially, in the considered test scenario,an approximately 20 dB gain in the receive power has beenobserved for all RIS tile sizes in comparison with the “RISOFF” case. Even in the presence of the obstacle, the MTBSalgorithm still provided the same performance as the casewithout the obstacle. It demonstrated that the proposed algo-rithm provides a great improvement even with the non-light-of-sight (NLOS) channel. The power transfer efficiency has beenobtained according to the Tx-Rx distance. The experimentedresults showed that about 22.5 mW (1.05% of efficiency) istransferred to the receiver at the Tx-Rx distance of 1.3 mwhen RIS tile size of 2× 2 is adopted. We expect that highertransferred power will be achieved by deploying a large-scaleRIS.

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Phase (Deg)

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