Research ArticleBeam Synthesis with Low-Bit Reflective Coding MetamaterialAntenna: Theoretical and Experimental Results

Qinhao Wu , Yongqiang Cheng, Xiang Li, and Hongqiang Wang

College of Electronic Science, National University of Defense Technology, No. 109, Deya Road, Changsha, China

Correspondence should be addressed to Qinhao Wu; qinhaowu@hotmail.com

Received 1 November 2017; Revised 12 January 2018; Accepted 4 February 2018; Published 26 March 2018

Academic Editor: Giuseppe Castaldi

Copyright © 2018 Qinhao Wu et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Coding metamaterials are the new technology where the aperture coding provides the hardware foundation for the miniaturizationof the devices. As a synthetic 2-D plane, metamaterial antennas are composed of subwavelength resonant particles. It can realizereal-time control of electromagnetic wave and build multifunction radar array system. We make a detailed explanation of itsarray structure, working principle, and hardware system. However, it is usually difficult to synthesize flexible beams because thephase value is very limited in this antenna. Two methods are proposed in this paper to demonstrate the beam synthesis basedon repetitive coding and convolution, and the distribution of beam pointings is analysed on the basis of this mechanism.Experiments that measure the radiation pattern of this antenna are carried out to verify the simulated results using only 1-bitcoding metasurface in a radar system, whose phase value is controlled by pin diode on the surface.

1. Introduction

Phased array radar is extensively adopted into detection invirtue of its flexible properties in beam scanning. Its phaseshift properties are constrained by the properties of the phaseshifter, which can be easily affected by the temperature andthe nature of the device itself. Conventional phased arrayradar is generally bulky and complex in structure. Althoughit overcomes the limitations of mechanical scanning for radarperformance, there are some new techniques such as printedantenna, conformal array, solid T/R components, time delaydevice, optical and digital beamforming being applied thesedays. The huge cost of T/R components, large size, weight,and manufacturability always push the innovation and prog-ress of the whole technology. The metamaterial particles anddigital codes are incorporated with each other in the wake ofthe proposed coding metamaterial, which have aroused wideconcern recently [1–3]. Based on coding metamaterial, it canrealize the real-time control of EM wave, which is directlyrelated to the information domain to physical domain [4, 5].

In 2013, Lipworth et al. in Duke University proposed thataperture made by metamaterial could be used to realize

compressive microwave imaging, and the whole systemwould require only a microwave detector [6, 7]. Resonanceunits with different resonant frequencies are randomly dis-tributed on metamaterial surfaces [8]. With the change ofthe frequency of the excitation source, the radiation patternof the antenna has been changed and many different mea-surement modes can be obtained by frequency scanning inthe operating bandwidth.

The research of artificial electromagnetic material wascarried out in the National Key Laboratory of MillimetreWave in the Southeast University in China several yearsago. Their team has designed a series of metasurfaces withultralow profiles and used them in the fields of beam synthe-sis, microwave imaging, and holographic surfaces [9]. Theyalso proposed a millimetre-wave active imaging methodbased on the combination of metamaterial and machinelearning imaging algorithm. They use the FPGA (field-pro-grammable gate array) to control the working state of theartificial electromagnetic material and use machine learningalgorithms to get the high-resolution image of the target.The system requires only a single millimetre-wave transmit-ter and receiver, so it has extremely low hardware cost. The

HindawiInternational Journal of Antennas and PropagationVolume 2018, Article ID 5058789, 9 pageshttps://doi.org/10.1155/2018/5058789

system does not require a mechanical scan, so it can image inreal time [10].

In this paper, a radar system with a coding metamater-ial antenna is introduced. Its performance in beam synthe-sis and target detection where the number of coded bits foreach element in the coding metasurface may not be sub-stantial subject to hardware conditions. The wavefronts ofEM waves can be steered via the discontinued phase intro-duced at a subwavelength scale superficially on substratesin virtue of this system. The focus of this paper is mainlyto analyse how to synthesize flexible beams and to verifyit with experiment when a very confined phase value isemployed in a metamaterial antenna, which is called“low-bit coding metasurface”. For conventional phasedarray antennas, it can achieve continuous beam synthesisbecause of its flexible and continuous phase shifters, wherethe phase difference between the adjacent elements isrelated to the beam deviation. Another difference is thatthe phase difference between every adjacent element isalways a fixed value in order to obtain the maximumcoherence stack of the distant field in the direction of beamsynthesis. However, in metamaterial antenna, the phase dif-ference which can be selected is very limited. So, the codingrules can no longer be simply set according to the mappingrelationship between the beam pointing and the phase dif-ference. We also set up an experimental system to proveour theory.

The rest of the paper is organized as follows: Section 2presents the hardware of the antenna system. We demon-strate the mechanism of phase-controlled surface and itsworking parameters, which is the foundation for the beamsynthesis analysis (with very confined phase values) in thefollowing chapters. Then, analytical beam synthesis methodsare proposed in Section 3, where we give the equations andnumerical simulation of the radiation pattern of low-bit cod-ing material antenna. In Section 4, the concrete experimentand measurement based on the proposed theory are pre-sented to verify the simulation. Finally, conclusions are madein Section 5.

2. Hardware

The coding metasurface consists of different subwavelengthresonant particles where the phase shift is represented by dis-crete codes like “0” and “1”, which can be employed to repre-sent the phase value 0° and 180°. The surface that we use inthis experiment includes 20 × 20 elements made from sub-wavelength resonant particles, and the phase value is con-trolled by the pin diode. When the pin diode in eachelement is on, its voltage is 0.8V, which represents phasevalue 180°. When it is off, its voltage is 0V, which represents0°. When the EM wave emitted by the horn antenna isreflected by the metasurface, its phase changes accordingly.At present, the advanced metamaterial antenna can realizephase modulation by up to 2-bit code, which has two layersin a unit cell on the metasurface. There is a pin diode on eachlayer whose states (on or off) can represent 4 phase values(00, 01, 10, and 11, or 0°, 90°, 180°, and 270°, resp.). It meansthat the codes are not represented by effective medium

parameters and the metasurface can be digitally controlledto produce different radiation patterns, which is realizedby hardware such as FPGA. So, the binary codes can changethe diode states on the unit cells and result in the change ofthe transmission characteristics of the entire coding meta-surface [11].

The feed in this antenna is not realized by a feed networkbut by a horn antenna (shown in Figure 1), which means thatthe antenna surface is illuminated by the horn antenna.There is a code input port on the side. When the powerswitch is on, the RF signals are fed into the horn antennaand the coding scheme calculated previously is input viathe code input port, which provides the phase values in par-allel for each element on the antenna and controls the beampointing in real time. The feeder transmits the fixed power tothe horn antenna.

A schematic diagram of this detection system is pre-sented in Figure 2. DSP component provides the specificsignal parameters such as pulse width (100 ns), bandwidth(200MHz), pulse repetition interval (PRI, 10μs), and car-rier frequency (500MHz). The intermediate frequency(IF) signal whose frequency range is from 400MHz to600MHz is upconverted twice (2.4GHz and 6.6GHz, resp.)in the T/R components. So, the frequency range of the out-put signal from T/R is from 9.4 to 9.6GHz. Then, the sig-nal is transmitted to the horn antenna and then illuminatesthe reflective metasurface. Another path in this system isthe code input, which starts from DSP and to the smallFPGA component in the metamaterial antenna. The codescheme is designed based on the parameters of the antennaand signal based on the experimental demand, and thecode is input directly during the experiment to realize thebeam control.

3. Beam Synthesis

3.1. Repetitive Coding. For a uniform line array antenna, inthe case of all the elements equally coupled with amplitudeE, the radiation pattern of far field is defined as

E θ = E 〠N−1

k=0ejk ψ−φ , 1

where λ, θ, θ0, N , and d denote the wavelength, the angledeviated from the normal, the beam pointing, the amountof elements, and array spacing, respectively. ψ = 2π/λ dsin θ refers to the phase difference resulting from the differ-ence in wave path, and φ = 2π/λ d sin θ0 denotes the dif-ference in excitation current phase produced by adjacentelements. So, the range of the beam scan is affected by therange of φ, which suggests that there are only 4 beampointings when it is 2-bit coding and only 2 beam pointingwhen it is 1-bit coding. And because the wavelength cannotbe changed randomly, it makes sense to change the arrayspacing d.

Arising from the confined phase values in the foregoingsystem, each code shall be p times repeated to elevate the“equivalent array spacing” d and d = pd0. d0 denotes the

2 International Journal of Antennas and Propagation

actual physical spacing on the metasurface. For this reason,the beam pointing shall be determined by

sin θ0 =λ

pd02M, 2

where M is the code bit.

The simulation shows that this method is feasible (seeFigure 3). The coding matrix refers to the arrangementstate of the encoding value on the metasurface containing100 × 100elements, where the color in each element repre-sents its corresponding values. For 2-bit coding inFigure 3(a), its phase values 0°, 90°, 180°, and 270° are rep-resented by 00, 01, 10, and 11, respectively, which can alsobe denoted by 0, 1, 2, and 3 in the color bar. To explainthis process better, let λ = d0 × 2M , so the beam pointingis θ0 = arcsin 1/p .

To prove that the repetition of the code is indeed equiv-alent to increase the “equivalent spacing” of the element,the analytic and approximate radiation pattern are bothgiven for comparison. The analytic radiation expressionrefers to the actual pattern by repetitive coding, and theapproximate expression refers to the result got by replacingd with pd0 in the radiation pattern of the conventionalphased array.

For the analytic radiation expression, the codes are gener-ally arranged in the following order (shown in Table 1) in auniform line array.

To facilitate the calculation, the element numberswho have the same phase are put into the same matrix.βi i = 0, 1,… , 2M − 1 contains the element numberswhose phase is 2πi/2M . On that basis, in line with theorder of arrangement exhibited in Table 1, it is able tobe defined as

Assuming that the amount of elements is exactlyN = 2M × p × l, the analytic radiation pattern can be acquiredas follows:

E θ = 1 − ejωp

1 − ejω× 1 − ejωpl×2

M

1 − ejωp×2M× 〠

2M−1

k=0e−j 2πk/2M−kpω , 4

where ω = 2πd0/λ sin θ.For approximate expression, simply use pd0 to replace d

in conventional phased array antenna radiation pattern:

E θ ≈sin N/2 2πpd0/λ sin θ − 2π/2Msin 1/2 2πpd0/λ sin θ − 2π/2M 5

The results are exhibited in Figure 4 with the simulationof the above two methods.

It can be seen from the simulated results that the approx-imate pattern is highly similar to the actual pattern in thebeam pointing although there is a difference between theirmain lobe width and side lobe level. It provides an importanttheoretical support for repetitive coding, where it can achievethe similar results of increasing the physical array spacing.Although this method is very straightforward, its syntheticbeampointing is very confined. If the appropriate wavelength,code bits, and other parameters are selected, it may producesin θ0 = 1/2p, sin θ0 = 1/p, sin θ0 = 2/p, sin θ0 = 3/p, and soon. The distribution of beam pointing is indicated in Figure 5.

Arising from the properties of the inverse trigonometricfunction itself, the beam pointing is centrally distributed atsmall angles (θ0 < 15°) in any case to adjust to other parame-ters. In practical applications, wavelength and code bits can-not be changed once determined in a real radar system madeby the metasurface. It is of great necessity to ascertain othersmethods of synthesizing more flexible beams.

βi =

p × i p × i + 1 ⋯ p × i + p − 1p × 2M + i p × 2M + i + 1 ⋯ p × 2M + i + p − 1

⋮ ⋮ ⋱ ⋮

p × 2M × l − 1 + i p × 2M × l − 1 + i + 1 ⋯ p × 2M × l − 1 + i + p − 1

3

Metasurface

Horn antennaCode inputfeeder

Power cord

RF input

Power supply

Figure 1: The experimental setup in a microwave anechoic chamber.

3International Journal of Antennas and Propagation

3.2. Beam Synthesis by Convolution.When the repetitive cod-ing method is adopted, the far field radiation pattern can bedecomposed from (1) as follows:

E θ = E 〠N−1

k=0ejkψ−jφk 6

It can be seen from (6) that if e−jφk is regarded as a time-domain sequence with k as a time variable, the radiation pat-tern E is like the Fourier transform of this time-domainsequence. Through the analysis of the antenna pattern, itcan be concluded that its shape is similar to a sinc function.The sinc function has similarities to the impulse function,which has a good convolution shift property. Combined withsome of the basic beam points of the repetitive foregoing cod-ing method, it can synthesize flexible beams.

Without loss of generality, the following sequence of timedomains shall be written as follows:

f k = e−jkφ, 7

where k = 0, 1,… ,N − 1. When ψ is replaced by −ω in (6),the following equation is proved:

f1 k f2 k ⇔ 12π F1 ω ∗ F2 ω , 8

where ∗ denotes the convolution operation. The frequencydomain function conforms to the following properties:

F ω − ω1 ∗ F ω − ω2 = F ω ∗δ ω − ω1∗ F ω ∗δ ω − ω2 ≈ F ω − ω1 − ω2

9

DSP FPGADDS

T/Rcomponents

RF out

MetasurfaceHorn antenna

A/D

Transmitted signalReceived signalCode input

FPGA

Figure 2: A schematic diagram of the metamaterial antenna detection system.

20 40 60 80 100

20

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100 0

0.5

1

1.5

2

2.5

3

(a)

−50 0 50−10

0

10

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30

40

Angle (°)

Mag

nitu

de (d

B)

(b)

Figure 3: Simulated results when λ = d0 × 2M , d0 = 1cm, N = 100,M = 2, and p = 2. (a) Coding matrix. (b) Radiation pattern: beam pointing:29 98° ≈ arcsin 1/2 ; 3 dB width: 2 41°; side lobe level: −13.10 dB.

Table 1: Coding arrangement in a uniform line array.

Uniform line array

Sum 2M × p× l

Sum 2M × p ……Code 0 … 0 1 … 1 … 2M − 1 … 2M − 1 ……Element number 0 …… p − 1 …… …… 2(p − 1) …… …… …… 2M(p−1) ……

4 International Journal of Antennas and Propagation

The approximation adopted above merely denotes theapproximation of the beam pointing. When two “timearrays,” namely, f1 k = e−jkφ1 and f2 k = e−jkφ2 , are multi-plied, their phase arrays (φ = φ1 + φ2) shall be added [12].Therefore, the synthesized angle shall be analyticallyexpressed as

sin θ0 = sin θ1 + sin θ2 10

In that the angle domain is projected to the frequencydomain (−ω = 2πd/λ sin θ), the Fourier transform men-tioned in this chapter shall be explicated as the spatialFourier transform.

3.3. 3-D Beam Synthesis.When it comes to 3-D beam synthe-sis, the metasurface contains m rows and n columns of ele-ments. The row and column spacing are denoted by d1 andd2, respectively. Through employing the foregoing approxi-mation, 3-D radiation pattern shall be defined as

E θ, φ = 〠n−1

i=0〠m−1

k=0exp j

2πid1λ

cos θ sin φ − ηik

+ 2πid2λ

sin θ − ζik ,11

where θ, φ, ηik, and ξik are elevation, azimuth, row phase dif-ference, and column phase difference. Using the approxima-tion method in (5), the radiation pattern in horizontal andvertical directions can be got, respectively:

E1 θ, ϕ ≈sin n/2 2πpd1/λ cos θ sin φ − 2π/2Msin 1/2 2πpd1/λ cos θ sin φ − 2π/2M ,

E2 θ ≈sin m/2 2πqd2/λ sin θ − 2π/2Msin 1/2 2πqd2/λ sin θ − 2π/2M

12

The total coding pattern is the modular addition ofsub coding patterns. p = p1, p2,… , pa means a sub cod-ing patterns which repeat p1, p2,… , pa times to controlthe azimuth. q = q1, q2,… , qb means b sub coding patternswhich repeat q1, q2,… , qb times to control the elevation.Then, sum up all the codes under the modular addition (2M).So, the analytical expressions for the designed elevation andazimuth are as follows:

sin θ0 =λ

d2 × 2M 〠b

i=1

1qi,

sin φ0 =λ

d1cos θ × 2M 〠a

k=1

1pk

13

To explain this process more vividly, the results of thesimulation experiment are given in Figure 6. The predesignedangles are θ0 = 4 78° and φ0 = 27 38°, respectively.

To better demonstrate the distribution of the beam point-ing synthesized by this method, the following simulationexperiment is carried out: assuming that N = 3, 1 ≤ a, b ≤ 4,and 1 ≤ qi, pk ≤ 10, then four different distributions areadopted to model the data, which are normal distribution,Rayleigh distribution, Weibull distribution, and Gammadistribution. The probability density functions (PDF) of fourmodels are shown in Figure 7.

As can be seen from the statistical distribution of thebeam, the beam pointings are intensive between 20° and50° while there is almost no distribution under 5°. Thisis because the number of the repetitions of a single codecannot be too high in the case of a finite number of ele-ments on the metasurface.

In terms of a fixed combination of designed elevation andazimuth, there may be more than one coding matrix. Differentperformances are indicated in beam pointing accuracy, main

−80 −60 −40 −20 0 20 40 60 80−10

−5

0

5

10

15

20

25

30

35

40

45

Angle (°)

Mag

nitu

de (d

B)

ApproximateAnalytic

Figure 4: Simulated results when N = 48, l = 6, M = 2, d0 = 1cm,f = 9 5GHz, and p = 2. (Blue curve) approximate radiation pattern:29 75° ≈ arcsin 1/2 ; 3 dB width: 2 87°; side lobe level: −13.34 dB.(Red curve) analytic radiation pattern: 29 75° ≈ arcsin 1/2 ; 3 dBwidth: 6 31°; side lobe level: −12.91 dB.

0 5 10 15 200

5

10

15

20

25

30

35

40

45

50

Parameters

Beam

poin

ting

(°)

1/2p1/p

2/p3/p

Figure 5: Beam pointing distribution with different parameters.

5International Journal of Antennas and Propagation

5 10(a1) (a2)

(a3)

(b)

(c) (d)

(a)

15 20 + +

=

5

10

15

205 10 15 20

5

10

15

20

5 10 15 20

5

10

15

205 10 15 20

5

10

15

20 0

0.5

1

1.5

2

2.5

3

-100-50

050

100

-100-50

050

100−50

0

50

Elevation (°)

x: 4.485y: 27.4z: 49.42

Azimuth (°)

Mag

nitu

de (d

B)

−40

−30

−20

−10

0

10

20

30

40

−50 0 5010

20

30

40

50

Elevation (°)

Mag

nitu

de (d

B)

−50 0 5025

30

35

40

45

50

55

Azimuth (°)

Mag

nitu

de (d

B)

Figure 6: Simulated results of modular addition when M = 2, f = 9 5GHz, m = n = 20, d1 = d2 = 1cm. (a) The modular addition of thecoding value in (a1), (a2), and (a3). The total modular addition is represented by q = 9 and p = 9, 2 . The radiation pattern in (a1)is q = 9 The radiation pattern in (a2) is p = 9 . The radiation pattern in (a3) is p = 2 . (b) 3-D radiation pattern. (c) Section viewwhen φ = φ0, beam pointing is 4 48°, 3 dB width is 10 29°, and side lobe level is −8.92 dB. (d) Section view when θ = θ0, beam pointing is26 83°, 3 dB width is 11 76°, and side lobe level is −9.04 dB.

6 International Journal of Antennas and Propagation

050

100

020

4060

8002468

1012

Elevation (°)Azimuth (°)

e1 (

°)

12345678910

502040

0

(a)

050

100

020

4060

800

10

20

30

40

Elevation (°)Azimuth (°)

e2 (

°)

10

15

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25

30

35

(b)

050

100

020

4060

80−40

−35

−30

−25

−20−15

Elevation (°)Azimuth (°)

e3 (

dB)

−36−34−32−30−28−26−24−22−20−18

(c)

Figure 8: The distribution of cost function for (a) beam pointing error, (b) main lobe width cost, and (c) side lobe level cost.

0 10 20 30 40 50 60 70 80 900

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Beampointing (°)

Prob

abili

ty

StatisticalStatisticalNormal

RayleighWeibullGamma

(a)

0 10 20 30 40 50 60 70 80 900

0.005

0.01

0.015

0.02

0.025

0.03

Beampointing (°)

Prob

abili

ty

StatisticalStatisticalNormal

RayleighWeibullGamma

(b)

Figure 7: Statistical result and distribution models of the beam pointing when M = 2, f = 9 5GHz, m = n = 20, and d1 = d2 = 1cm. (a) Forelevation and (b) for azimuth.

7International Journal of Antennas and Propagation

lobe width, and side lobe level. To seek out the optimal codingmatrix, the normalized errors or costs of them shall be overallreckoned with to comprise the following cost function:

c = α e21e + e21a + β e22e + e22a + γ e23e + e23a , 14

where c is the total cost and e1, e2, and e3 are normalized costfor beam pointing accuracy, main lobe width, and side lobelevel, respectively. The subscripts e and a are for elevationand azimuth, respectively. The distribution of cost functionsis shown in Figure 8.

4. Experimental Results and Discussions

The experiment was carried out in a microwave anechoicchamber using the metamaterial antenna in the radar systemdescribed in Figure 2. The metasurface was illuminated by anoffset-fed horn antenna to avoid the shielding of the mainradiation as shown in Figure 1. The radar system is designedby Southeast University in China.

By using vector network analyzer, we got the radiationpattern and compared it with the simulated results. The sim-ulated and experimental results are compared in Figure 9,which suggest that the main lobe of the experimental resultsbasically conforms to the simulated results. It shows thatthis coding metasurface has the ability to control the beampointing, but it has relatively high side lobes and wide mainlobe (nearly 10°), which may affect the performance of tar-get detection. A finite number of elements leads to the wid-ening of the main lobe while the relative flat feeding modeon the metasurface leads to the increase of the side lobe.It is also clear from the results that insufficient code bits(only 1-bit) in this antenna leads to the presence of twosymmetrical main lobes. This can be improved if 2-bit cod-ing is implemented, but it cannot be realized due to the lim-itation of hardware conditions in this experiment. Another

issue is the quality of the antenna itself, which means thewelding and package level influence and the performanceof the antenna.

5. Conclusions

In this paper, we propose a metamaterial antenna with 400elements on the surface and the phase values are controlledby the pin diodes. It is made without a very large feed net-work but by only a horn antenna, which illuminates the cod-ing surface and makes the antenna more miniaturized andflexible. We present the beam synthesis methods with regardto this kind of antenna, where the code bits are limited to 1or 2 bit. Through employing repetitive coding and convolu-tion properties, the number of beam pointing that can besynthesized on the metasurface is greatly increased. We ana-lyze the distributions of the predesigned beam pointingsproduced by these two methods. This not only achievesbeam synthesis using metamaterial antennas but also pro-vides an approach to realize beam synthesis under specialconditions where phase values are confined in the conven-tional phased array antenna. We also use the experimentto verify this theory of beam synthesis by taking two azi-muths for the test. As the result shows, although the ampli-tude is different at every point, the position of the main andside lobe is basically accurate. There are two main problemsto be solved in the future work: First, beam synthesis underabout 5°(deviation from the normal of the metasurface) isdifficult for the two proposed methods since it needs largerepetition times (p). This is unrealistic in the case of a finitenumber of array elements. Second, optimization of the radi-ation pattern needs to be implemented because it is clearthat the side lobe level is very high for both experimentaland simulated results. Side lobe suppression is mainlyachieved by changing the distribution of radiation field on

−80 −60 −40 −20 0 20 40 60 80

−14

−12

−10

−8

−6

−4

−2

0

2

Azimuth (°)

Nor

mal

ized

mag

nitu

de (d

B)

SimulationExperiment

(a)

SimulationExperiment

−80 −60 −40 −20 0 20 40 60 80

−14

−12

−10

−8

−6

−4

−2

0

2

Azimuth (°)

Mag

nitu

de (d

B)

(b)

Figure 9: The comparison (section view and normalized magnitude) of simulated and experimental results when elevation is 0°. (a) Azimuthis 30°. (b) Azimuth is 42°.

8 International Journal of Antennas and Propagation

the metasurface, so the position, power, and radiationpattern of the horn antenna need to be further designed.

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper.

Acknowledgments

The paper is supported by the National Natural ScienceFoundation of China under Grant 61571011.

References

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