Automatic Calibration Using a Modified Genetic Algorithm...

Research ArticleAutomatic Calibration Using a Modified Genetic Algorithm forMillimeter-Wave Antenna Modules in MIMO Systems

Cheng-Nan Hu 1 Philip Lo2 Chien-Peng Ho1 and Dau-Chyrh Chang1

1Communication Engineering Department of OIT New Taipei City 22061 Taiwan2FIH Limited FTC Division No 4 Minsheng Street Tucheng District New Taipei City Taiwan

Correspondence should be addressed to Cheng-Nan Hu fo011mailoitedutw

Received 25 November 2019 Revised 24 February 2020 Accepted 10 April 2020 Published 3 June 2020

Academic Editor Giuseppe Castaldi

Copyright copy 2020 Cheng-Nan Hu et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

is study proposes a method for designing and calibrating a millimeter-wave (mm-wave) multiple-input multiple-output(MIMO) antenna module Herein we adopt a design example involving a 64-element MIMO antenna array arranged in atriangular lattice (instead of the commonly used rectangular lattice) to achieve a 3degdB enhancement in effective isotropic radiatedpower Analyzing a grating lobe diagram indicates a scan volume of plusmn60degplusmn45deg in the azimuthelevation direction To calibrate themassive mm-wave MIMO antenna module we propose a modified genetic algorithm to align the amplitudephase of thetransmittingreceiving signal of the module to reduce the time required for the calibration process Finally we conducted a simpleexperiment to validate the proposed method

1 Introduction

Fifth-generation mobile communication technology is ex-pected to introduce an advanced air interface in new radio-frequency bands Millimeter-wave (mm-wave) frequencybands (ie ge26GHz) can provide a channel bandwidth ofapproximately 1GHz (or higher) to enhance mobilebroadband function with a throughput of up to 10Gb cansupport ultrareliable and low-latency communication ca-pability with submillisecond latency under required packetloss and can enable massive machine-type communicationto connect billions of devices (ie Internet of ings (IoT))[1] Large-scale antenna arrays (also called multiple-inputmultiple-output (MIMO) arrays) with beam-formingtechnology for single-user MIMO or multiple-user MIMOcommunication between a base station and mobile devicescan provide high antenna gain to overcome radiationpropagation path losses at the aforementioned frequenciesMoreover sustaining an effective radio link budget canengender high-data-rate communications and high-capacityoperation in networkse effective isotropic radiated power(EIRP) is a crucial measure of transmitter performance

Herein we adopt a design example involving a 64-elementMIMO array arranged in a triangular lattice to increase theantenna gain by 3 dB

To equip a massive large MIMO system with beam-steering capability the system must be adequately calibratedto generate the desired phase front to steer a dynamic three-dimensional pencil beam in a specified direction Considerfor example MIMO antennas After the radiating signals ofthe MIMO antennas are adequately calibrated and aligneduniformly across the antenna aperture the antennas cangenerate a pencil beam pattern with a very high EIRP in theboresight direction thus the signal quality can be improvedfor high-data-rate applications

Massive MIMO arrays can be calibrated through eitherover-the-air (OTA) field tests including those that involvefar-field [2ndash5] and near-field [6ndash8] test ranges or built-inself-calibration tests [9] Near-field techniques are advan-tageous for calibrating large-scale phased array systems [6]because the techniques provide useful information to an-tenna designers specifically the techniques provide infor-mation that is useful for diagnosing antenna illuminationthrough the back-transformation of the computed far-field

HindawiInternational Journal of Antennas and PropagationVolume 2020 Article ID 4286026 9 pageshttpsdoiorg10115520204286026

value to the aperture of the AUTusing an inverse fast Fouriertransform However the signal level detected in the near-field range is susceptible to noise interference especially inmm-wave systems In built-in self-calibration tests phasetoggling is applied to implement a closed-loop transmittingreceiving coupler near the radiating element for signal de-tection Although detected signals can be used for moni-toring calibration and fault isolation in phased antennaarray systems [9] signal deviations caused by parasiticcircuit effects of the radiated structure feeding network andradome (ie housing of the system) cannot be considered inmm-wave systems Moreover the array systems must have asufficient built-in circuit design for closed-loop testing andcalibration to ensure adequate operation is can beachieved using radio-frequency integrated circuit (RFIC)technology for a medium-sized array system with low-poweroperation However such an arrangement is complex for anarray with large antenna elements and high-poweroperation

To solve the aforementioned MIMO calibration prob-lems this study proposes a calibration method that entailsfirst applying a modified genetic algorithm (GA) in the far-field test range to calibrate an mm-wave massive MIMOsystem e advantages of the proposed calibration methodare as follows

(1) No additional closed-loop built-in circuits are re-quired thus reducing system design complexity

(2) e overall system calibration is considered to en-sure accuracy

(3) e modified GA with machine learning capabilitybased on big data can be easily applied to a massproduction line for automatically calibrating 5Gmassive MIMO systems

e remainder of this paper is organized as followsSection 2 presents the theoretical approach of the proposedmethod and the numerical investigation of the simulatedresults In Section 3 a simple experimental study is reportedSection 4 provides the study conclusion

2 Theory and Numerical Results

21 System Configuration Figure 1 illustrates the designconcept of an mm-wave massive MIMO antenna modulethat can automatically undergo self-calibration through themodified GA e MIMO antenna module comprises thefollowing components (1) 64-element microstrip patchantenna array (2) 16 front-end modules each of which hasfour-channel transmitreceive (TR) devices (3) a powerdistribution network and (4) a test antenna in the far-fieldrange is study adopted a four-element TRX half-duplexsilicon front-end IC (F5280 IDT Inc) [10] operating at25ndash31GHz As presented in Figure 1(b) the antenna arraycomprises a set of polarized elements with position vectorD [d1 d2 dm dM] where dm is the location of themth antenna element

e far-field pattern of the simultaneously excitedMIMO antenna array is expressed as follows

f(θ φ) WH

middot eminus jKT middotDξ(θφ) W

Hmiddot E(θφ) (1)

where

W w1 w2 wM1113858 1113859T (2)

E(θφ) eminus jKT middotDξ(θ φ)

K 2πλ

[sin θ cosφ sin θ sinφ cos θ]T

(3)

where λ is the wavelength at frequency f θ and ϕ are theazimuthal angle and angle of elevation of the far-field sourcerespectively and T is the matrix transpose

ξ(θφ) is a function of the polarized pattern of an in-dividual element and wi(wi cie

jψi ) is the complexweighting coefficient at the ith element of weight vector We Hermitian transpose which combines transposition andconjugation is denoted byH and the radiation pattern of thearray is denoted by f(θ φ) To satisfy the scan volume re-quirement the spacing arrangement of the antenna elementsin the system should be specified that is either a rectangularor triangular lattice For a rectangular lattice the spacings inthe x-axis y-axis and dxdy can be expressed as follows

dxleλ

1 + sin θaz( 1113857 (4)

dyleλ

1 + sin θel( 1113857 (5)

where θazθel is the scan volume specification in the azi-muthelevation direction

rough (4) and (5) the dx and dy values for elementsarranged in a rectangular lattice can be derived as 0536λ and0586λ respectively satisfying the scan coverage require-ment of az 60deg and el 45deg Moreover for elementsarranged in a triangular lattice the dx and dy values can bederived as 10733λ and 06066λ respectively by analyzing agrating lobe diagram [11] as shown in Figure 1(c) where thesolid and dashed lines represent the boundary of the scanvolume and grating lobe respectively Since the aperture sizeis increased by arranging array elements in a triangularlattice the MIMO provides relatively high antenna gainunder the same scan volume requirement nevertheless suchan increase is not suitable for miniaturization On the basisof the derived spacing values the maximum element gain(Ge 4πdx dyλ2) corresponding to the rectangular andtriangular lattice arrangements can theoretically be com-puted to be 596 and 913 dBi respectively is thus indi-cates that the EIRP is theoretically improved byapproximately 3 dB is improvement is crucial to MIMOdesign because power amplification results in poor efficiencyin mm-wave systemse use of additional power amplifiersfor a 3 dB output power gain will increase power con-sumption levels and engender heat sink problems in suchsystems According to the preceding theoretical calculationsthe design of massive MIMO systems requires high EIRP insmall-cell applications which reduces volume constraints inspace

2 International Journal of Antennas and Propagation

When the excitation coefficient vector W is calibrateduniformly with equal amplitude and phase distribution themaximum antenna gain (Gmax) can be derived to be2719 dBi in the boresight direction (θ 0deg and ϕ 0deg)Calibration is a complex process that involves testing allstates of both the phase shifter and the attenuator of eachradiating element at various operational frequencies Con-sider for example a front-end RFIC with 6-bit phase shiftersand 4-bit attenuators calibrating a 64-element MIMO an-tenna array with 10 frequencies would require approxi-mately 655360 (64times 64times16times10 655360) iterations ofmanual testing per each antenna element

Accordingly because of the lack of a built-in closed-loopcalibration circuit in front-end RFICs (IDT F5280) forprecise phase and amplitude control of the excitation co-efficient vectors an artificial intelligence calibration methodis essential for the automatic calibration of mass-producedmassive MIMO systems

22 GA for Far-Field Calibration On the basis of assump-tions or simplifications engineering problems can bemathematically modeled by imitating real-world principlesSubsequently mathematical problems can be solved nu-merically Finally the derived problem solution can used toaddress a broader class of real problems Several algorithmsor systems have been demonstrated to be extremely helpfulin addressing problems in various fields including artificialneural networks [12 13] fuzzy control [14] simulatedannealing [15 16] and GAs Studies have successfully usedGAs for antenna pattern synthesis and autocalibration[17 18] to obtain the optimum excitation coefficient vector(Wopt) for achieving high antenna performance (ie max-imum antenna gain with a specified sidelobe level) Figure 2presents the general design flow of a GA for the far-fieldcalibration of a massive MIMO in an anechoic chamber thisprocedure is used to mathematically imitate the evolution ofthe excitation coefficient vector (W) iteratively until the

TX InputRX Output

16

4-channel front-end ICs

1

16

(a)

Patch antenna dx

Y

Z

X

Test antenna

dy

θφ

(b)

ndash1 ndash08 ndash06 ndash04 ndash02 0 02 04 06 08 1Tx - Sin (TH)lowastCos (PH)

ndash1

ndash05

0

05

1

Ty-S

in (T

H)lowast

Sin

(PH

)

Solid-line Scan covorageDashed-line Grating lobes

Freq = 28GHzdx = 115mmdy = 65mmE1 = ndash45degE2 = 45degAz1 = ndash60degAz2 = 60deg

(c)

ndash80 ndash60 ndash40 ndash20 0 20 40 60 80THETA (DEG)

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

Relat

ive p

ower

(dB)

Far-Field (SUM)

H-plane (X-Z plane cut)E-plane (Y-Z plan cut)

(d)

Figure 1 (a) Schematic of mm-wave active massive MIMO system (b) 8times 8 element microstrip array (dx 115mm dy 65mm)associated with a test antenna in the far-field range for calibration (c) grating lobe diagram analysis (solid line scan volume dashed linegrating lobes) of the array with a triangular array lattice of dx 115mm and dy 65mm (d) two-dimensional far-field patterns (E-Hplane)

International Journal of Antennas and Propagation 3

optimal Wopt is obtained e stages in the iterative loop ofthe GA (Figure 2) are described as follows

221 Evaluation is stage is also called initialization Itentails generating an initial population and its offspring andthen ranking genes

222 Selection is stage represents the mechanism forselecting individuals (populations) for reproductionaccording to their fitness (objective function) values

223 Crossover is stage involves merging the geneticpopulation of two individuals Two carefully selected parentscan produce excellent children

224 Mutation is stage entails making random alter-ations to gene values In real evolution genetic informationcan be varied randomly by erroneous reproduction or otherdeformations of genes In a GAmutation can be realized as arandom deformation of strings with a specified probability

If the excitation coefficient vector of a MIMO system isadequately calibrated the maximum measured EIRP wouldbe attained in the boresight direction this can be approx-imated as follows

EIRP GA + 10 log10(N) + Pelem + L + Lscan + SP (6)

GA 20 log10(|f(θ ϕ)|) (7)

where GA is the antenna gain Pelem (13 dBm) is the trans-mitter power per element N is the total number of antennaelements SP (simminus6491 dB) is the space loss at a 15m rangeand 28-GHz frequency Lscan is the scan loss (0 dB atboresight) and L (simminus2 dB) is the total power loss in theantenna When the weighting vector (W) is adequatelycalibrated with a uniform distribution the maximum an-tenna gain Gmax is close to the antennarsquos area gain(10 log10((4πAλ2)) sim2719 dBi A is the area of the antenna)in theoryus according to (6) EIRPopt corresponding to arange R of 0 and 15m can be estimated to be 5626 andminus865 dBm respectively

During calibration the measured EIRP value should beless than the EIRPopt value because of random amplitudephase errors ofW caused by factors such as device variationunequal transmission line trace lengths and radome effectsus the cost function (f (Wi)) at the ith iteration of the GAoptimization loop can be defined as follows

fc Wi( 1113857 min EIRP(i) minus EIRPopt1113966 1113967 (8)

where EIRP (i) represents the EIRP measured in the ithiteration of the GA optimization loop for a test antenna inthe boresight direction in the far-field range (R 15m inthis case) When (2) is substituted into (6) and (7) costfunction (8) in a root-mean-square sense can be summarizedas follows for numerical analysis

fc Wi( 1113857 min

1113936Ni1 wi

111386811138681113868111386811138681113868111386811138681113936

Ni1 wi

111386811138681113868111386811138681113868111386811138682

minus N1113966 11139672

N

11139741113972

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

⎫⎪⎪⎪⎬

⎪⎪⎪⎭

(9)

Accordingly the GA design flow (Figure 2) can be ap-plied to calibrate the massive MIMO system in order toachieve maximum EIRP and tune the phase and amplitudeof W until the optimal excitation coefficient (Wopt) isattained e error of the excitation weighting vector (δW

Wopt minus W) can be computed and written in the internalmemory of the front-end ICs to correct the amplitudephaseerror of the excitation weighting vectors Phase errors en-gendered by the deviation of signal traces connecting fromchips to antennas can be considered the determinant errorsbut signal errors caused by chip-to-chip variations can beconsidered random errors which is the major considerationin the following numerical analysis

e phaseamplitude of W is assumed to be randomlydistributed uniformly around the interval (0 2π)(005 02)e excitation coefficient of each radiating element (Wii 1 2 64) should be calibrated to the normalized valueof 0125 (1

N

radic) in order to achieve maximum EIRP or

antenna gain Before the GA iterative loop (Figure 2) isexecuted for calibration the excitation coefficient (Wi i 12 64) of each element to the binary code should beencoded to represent each population of the generation Inthis study a 6-bit phase shifter associated with three LSBs ofthe attenuator was used for coding W

In each population the phaseamplitude error of theweighting vector (Wi) is also generated uniformly in theinterval (0 2π)(005 02) to compute the EIRP (or antennagain) of each generation using (6) and (8) to rank genesSubsequently the inferior genes (poor EIRP) are discardedand superior genes (better EIRP) are crossed over to producethe next generation Random mutation ensures the evolu-tion of the generation to successfully attain the specifiedgoal After the GA iterative loop is executed the massive

Selection

Crossover

Evaluation

x x

Mutation

∆φ [i] ∆ω [i]

Peak power error RMS power error

x x

Figure 2 Setup of GA for far-field calibration of massive MIMOsystem in an anechoic chamber


MIMO system can be calibrated automatically to attain themaximum EIRP and Wopt simultaneously

Figure 3 illustrates numerical simulation results re-garding the autocalibration of the 64-element MIMO systemthrough a GA with a population (M) of 20000 and 600 it-erative loops (Ic) Figure 3(a) presents plots from a con-vergence analysis with respect to the iterative numberindicating the amplitudephase standard deviation error ofW to be less than 05 and antenna gain to be higher than2718 dBi after 300 iterative loops In Figure 3(a) the solidline dashed line and dashed line with circles represent thesimulated antenna gain amplitude error () and phaseerror () respectively Figure 3(b) shows a plot of thecomputed EIRP against the observation angle (θ) under Wbefore and after calibration revealing that the computedEIRP can be improved from minus30 to minus86 dBm in theboresight direction after the GA-based calibration ecorresponding phase and normalized magnitude of W usedin the EIRP computation (Figure 3(b)) are plotted inFigure 3(c) e marginal deviation in the phaseamplitudeof the excitation coefficient can be attributed to the quan-tization error

23 Modified GA for Far-Field Calibration Generally in-formation regarding the randomness of the error of theexcitation weighting vector is not available In the previoussection to ensure the accuracy of the calibration results weassume that the phaseamplitude of the error of weightingvectors is uniformly distributed in the interval (0 2π)(00502) moreover we use a large population and high numberof iterations in the GA optimization loops is is a time-consuming process and is unsuitable for mass production Ifthe randomness of the error of the vector can be adequatelycharacterized and set in advance for the GA iterative loopthe calibration time can be reduced considerably

Accordingly the modified GA proposed in this studysolves the aforementioned problem of high time complexityIn the modified GA a large historical database with a rewardmechanism is established for machine learning of thecharacteristics of random errors erefore in mass pro-duction the random behavior of each population can beestimated according to the parameters established in thehistorical database such that the calibration time can bereduced considerably Figure 4 displays the flowchart of themodified GA To assess the feasibility of the modified GA wecan use a preset Gaussian error of the vector (δWs) with anamplitude (vv) and phase (rad) meanstandard deviation ofm 0σ 005 and m 0σ 157 respectively

We intentionally ignore this background informationand set the population of random genes (M) with a uniformdistribution of the phaseamplitude of the error of the vectorin (0 2π)(0 02) to 20000 moreover we set number ofiterative loops (Ic) to 500 We execute the GA-based cali-bration process 60 times (NL 60) When the specified goalis achieved such thatWopt (i) (i 1 NL) the error of thevector can be simply computed using formula δW (i)Wopt(i)minusW (i) to produce 3840 (NLtimesN 64times 60) randomamplitudephase error numbers For 3840 random variables

we can fit the probability distribution function of this eventafter running 60 GA calibration procedures

e simulation of the historical database after the 60calibration runs indicates that the mean (micro) and standarddeviation (σ) of the amplitudephase of the error vector(δW) with a Gaussian distribution are minus00097minus000117 and00480151 respectively Hence we adaptively reset theestimation parameters (μ and σ) for use in the iterative loopsof our modified GA (Figure 4) to reduce the calibration time

e convergence analysis results obtained from thesimulation of our GA are plotted in Figure 5 and comparedwith those obtained using the conventional GA e solidlines with symbols represent the simulated results for ourmodified GA and the dashed lines with solid symbolsrepresent the results for the conventional GA

Figure 5 reveals that our modified GA reduces the re-quired number of iterative loops by 75 (from 275 to 200loops) representing a nearly 27 reduction compared withthe conventional GA A 3-byte SPI write operation for thetransmission of write commands would require 1200 ns onthe basis of a 20-MHz clock rate this would result in alatency of at least 768ms for one beam-steering commandas well as additional computation time erefore theproposed GA would require at least 1536 secs(768mstimes 200) to execute calibration processes

3 Experimental Study

Because of budget limitations we conducted a simple ex-perimental study (Figure 6(a)) using a 2times 2 subarray an-tenna module of the massive MIMO system (Figure 1(b)) Inthe experiment four microstrip antennas were printed onthe top-side and the front-end IC (IDT5280) associated withone IO and one power connector mounted on the back sideof the PCB

Considering the lack of the dedicated testing software tocommand the front-end IC we performed a bench test(Figure 6(b)) by using IDTrsquos testing software (TimingCommander) to generate the database for calibrationthrough the proposed method e database included theamplitudephase information of 64-phase shifter commandstates (6 bits) changing corresponding to each element atoperational frequencies On the basis of the bench test re-sults the signal vector error (W) engendered by changes inthe phase command states was simulated to calibrate thephase distribution of the 2times 2 MIMO system using theproposed method (Section 22) We performed the cali-bration at a frequency of 27GHz only because the chipsetvendor already provided the default setting of 28GHz Tosimplify the experiment we ensured that all channelsconstantly radiated at the maximum power gain level Ta-ble 1 lists the calibration data of phase shifter commandstates corresponding to the four-element system at 27 and28GHz Running a bench test would require 25 h never-theless our proposed calibration method could shorten theduration of this time-consuming process to a few secondssubject to the availability of dedicated testing softwareSubsequently as depicted in Figure 7 we applied the defaultsetting of the front-end IC (f 28GHz) for the experimental


study by conducting OTA measurements at a compactantenna test range at Oriental Institute of Technology

Figure 8 displays plots of the measured copolarizationradiation patterns at 2728GHz indicating a measured peakgain of 4424865 dBi e measured patterns indicate thesimultaneous achievement of both maximum peak gain andadequately calibrated phase distributions as illustrated bythe symmetrical radiation patterns in the boresight direction(Figure 9) We subsequently applied the data calibrated bythe proposed method (Table 1 at 27GHz) to the F5280 ICregister to perform OTA measurements again e

measurement results demonstrated that the gain could beimproved by 33 dB at 27GHz but degraded by 285 dB at28GHz indicating that excitation coefficient calibrationagainst operating frequencies is essential for MIMO systemperformance

Figure 9 illustrates plots of the measured EIRP and TRPagainst the input power level with the power being sweptfrom 0 to 10 dBm at VNA and being attenuated by ap-proximately 345 dB cable loss Finally we changed the phaseshifter states to be out of phase along the x-axis to formdifference patterns e measurement results (Figure 10)

50 100150200250300350400450500550600Iterative number

ndash1

0

1

2

3

4

5

Erro

r in

()

16

18

20

22

24

26

28

Ant

enna

gai

n (d

Bi)

Phase error (standard deviation in rad)Normalized amplitude error () (standard deviation)Antenna gain (dB)

(a)

ndash80 ndash60 ndash40 ndash20 0 20 40 60 80eta (deg)

ndash40

ndash30

ndash20

ndash10

EIRP

(dBm

)

Optimal pattern

Before auto-calAer calibration (ic =600)

(b)

10 20 30 40 50 60Element number (N = 8 times 8)

ndash4

ndash2

0

2

4

6

Phas

e in

rad

00050101502025030350404505

Nor

mal

ized

mag

nitu

de (v

v)

Before calibration (phase)Aer calibration (phase)Before calibration (magnitude)Aer calibration (magnitude)

(c)

Figure 3 (a) Convergence analysis results regarding antenna gain and error of W against an iterative sequence number (b) Simulatedfar-field patterns obtained after the use of GA (M 20000 and Ie 600) (c) Corresponding phase and normalized magnitude of theweighting vector (W) used in EIRP computation

Design goalf (X) lt ε

No

Yes

Set parameters

Generate M random genes(Xi i = 1hellipM)

I = 1 to Ic loops

Rank genes from lowest tohighest measured gain

Discard inferior genes

Superior genes mate toproduce new generation

Random mutation

Next I

(Initialization)

(Selection)

(Crossover)

(Mutation)

DataBase(Wopt (j))

Stop

Data analysis

Figure 4 Flowchart of modified GA proposed in this study


50 100 150 200 250 300 350 400 450 500Iterative number

ndash1

0

1

2

3

4

5

Erro

r in

()

16

18

20

22

24

26

28

Ant

enna

gai

n (d

Bi)

Error estimation

Normalized mag error (GA)Phase error (GA)Normalized mag error (proposed)Phase error (proposed)Gain (GA)Gain (proposed)

Figure 5 Comparison of convergence analysis results between conventional and modified GAs (Figure 2)

4 microstrip patch antennas

Battery or

(a)

2 times 2 MIMO

Standard gain horn

(b)

Figure 6 (a) Illustration of 2times 2 MIMO antenna module (b) photograph of bench test conducted to generate calibration database

Table 1 Calibration results

Freq (GHz)Channel 1 Channel 2 Channel 3 Channel 4

Am (dB) Statephase Am (dB) Statephase Am (dB) Statephase Am (dB) Statephase28 minus178 0626deg minus157 0507deg minus155 0594deg minus161 0614deg27 minus174 2744deg minus154 2360deg minus182 2371deg minus183 2555deg

z

x

y

Figure 7 OTA measurements in CATR chamber at Oriental Institute of Technology


ndash36 ndash34 ndash32 ndash30 ndash28 ndash26 ndash24 Input power (dBm)

0

5

10

15

20

25

30

Mea

sure

d EI

RPT

RP (d

Bm)

Measure EIRP (f = 28GHz with calibration)Measured TRP (f = 27GHz with calibration)Measured TRP (f = 28GHz with calibration)Measured TRP (f = 27GHz without calibration)

Figure 9 Measured EIRP and TRP (in dBm)

90ndash90

0

180

0

ndash40

ndash30

ndash20

ndash10

(a)

90ndash90

0

180

0

ndash40

ndash30

ndash20

ndash10

(b)

Figure 10 Copolarized radiation pattern (DIF) in y-z plane at (a) f 27GHz and (b) f 28GHz

90ndash90

0

180

ndash40

ndash30

ndash20

ndash10

0

Far-field patternsfrequency 270000

(a)

90ndash90

0

180

ndash30

ndash20

ndash10

0

ndash40


(b)

Figure 8 Copolarized radiation patterns in y-z plane at (a) f 27GHz and (b) f 28GHz


confirmed the beam-steering capability of the MIMO an-tenna module that was adequately calibrated using theproposed method

4 Conclusion

e deployment of the mm-wave massive MIMO in theform of a small cell or customer-provided equipment isessential for 5G applications Reliable and time-efficientcalibration and test methods are crucial for developing mm-wave massive MIMO systems In this study we developed an8times 8 massive MIMO system with a triangular lattice toachieve a theoretical maximum EIRP of 5626 dBm We firstpropose a modified GA for the far-field calibration of themm-wave massive MIMO system We then present a nu-merical analysis to validate the effectiveness of the proposedGA Finally we executed a simple experiment to validate thata well-calibrated phase distribution can enable theachievement of maximum array gain in the boresight di-rection erefore our proposed method can enable auto-matic calibration of massive MIMO systems [19]

Data Availability

e figuresrsquo data used to support the findings of this studyare currently under embargo while the research findings arecommercialized Requests for data 12 months after publi-cation of this article will be considered by the correspondingauthor

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is study was financially supported by FIHMobile Limitede authors thank the FIH team for supporting the devel-opment of the design project

References

[1] 5G Vision White PapermdashSamsung (2015) httpswwwsamsungcomglobalbusinessnetworksinsights5g-vision

[2] C-N Hu ldquoA novel method for calibrating deployed activeantenna arraysrdquo IEEE Transactions on Antennas and Propa-gation vol 63 no 4 pp 1650ndash1657

[3] R Sorace ldquoPhased array calibrationrdquo IEEE Transactions onAntennas and Propagation vol 49 no 4 pp 517ndash525 2001

[4] R Long J Ouyang F Yang W Han and L Zhou ldquoFastamplitude-only measurement method for phased array cali-brationrdquo IEEE Transactions on Antennas and Propagationvol 65 no 4 pp 1815ndash1822 2017

[5] R Long J Ouyang F Yang W Han and L Zhou ldquoMulti-element phased array calibration method by solving linearequationsrdquo IEEE Transactions on Antennas and Propagationvol 65 no 6 pp 2931ndash2939 2017

[6] W T Patton and L H Yorinks ldquoNear-field alignment ofphased-array antennasrdquo IEEE Transactions on Antennas andPropagation vol 47 no 3 pp 584ndash591 1999

[7] H M Aumann A J Fenn and F GWillwerth ldquoPhased arrayantenna calibration and pattern prediction using mutual

coupling measurementsrdquo IEEE Transactions on Antennas andPropagation vol 37 no 7 pp 844ndash850 1989

[8] T Sato and R Konho ldquoNew calibration matrix calculationmethod for removing the effect of mutual coupling for uni-form linear arraysrdquo in Proceeedings of the IEEE 63rd Vehic-ular Technology Conferences pp 2686ndash2690 MelbourneAustralia May 2006

[9] K-M Lee R-S Chu and S-C Liu ldquoA built-in performance-monitoringfault isolation and correction (PMFIC) systemfor active phased-array antennasrdquo IEEE Transactions onAntennas and Propagation vol 41 no 11 pp 1530ndash15401993

[10] Transmitreceive half duplex IC 25GHz to 31GHz httpswwwidtcomusenproductsrf-productsphased-array-beamformersf5280-transmitreceive-half-duplex-ic-25ghz-31ghz

[11] W Von aulock ldquoProperties of phased arraysrdquo in Proceeedingsof the IRE 190 (Reprinted In Hansen R C Significant PhasedArray Papers Artech House Norwood MA USA October1973

[12] Q J Zhang K C Gupta and V K Devabhaktuni ldquoArtificialneural networks for RF and microwave design- from theory topracticerdquo IEEE International Microwave Symposium vol 51no 4 pp 1339ndash1350 2003

[13] Y Wang M Yu H Kabir and Q J Zhang ldquoEffective designof cross-coupled filter using neural networks and couplingmatrixrdquo in Proceedings of the IEEE International MicrowaveSymposium pp 1431ndash1434 San Francisco CA USA June2006

[14] F Farbiz and M B Menhaj ldquoA fizzy logic control basedapproach fop image filteringrdquo in Fuzzy Techniques In LmageProcessing E E Kerre and M Nachtegael Eds pp 194ndash221Springer-Verlag Berlin Germany 2000

[15] J Redvik ldquoSimulated annealing optimization applied to an-tenna arrays with failed elementsrdquoIEEE Antennas AndPropagation Society International Symposium Orlando FLUSA July 1999

[16] Y Yang Y Tan R Liang Q Wang and N Yuan ldquoA cali-bration algorithm of millimeter-wave sparse arrays based onsimulated annealingrdquo in Proceedings of the 2010 InternationalConference Microwave and Millimeter Wave Technologypp 1703ndash1705 Chengdu China May 2010

[17] S H Son S Y Eom S I Jeon and W Hwang ldquoAutomaticphase correction of phased array antennas by a genetic al-gorithmrdquo IEEE Transactions on Antennas and Propagationvol 56 no 8 pp 2751ndash2754 2008

[18] K N Sherman ldquoPhased array shaped multieam optimizationfor LEO satellite communications using a genetic algorithmrdquoin Proceedings 2000 IEEE International Conference on PhasedArray Systems and Technology Dana Point CA USA June2000

[19] K Chellapilla and A Hoorfar ldquoEvolutionary programmingan efficient alternative to genetic algorithms for electro-magnetic optimization problemsrdquo in Proceedings of the APSociety International Symposium Atlanta GA USA June1998


value to the aperture of the AUTusing an inverse fast Fouriertransform However the signal level detected in the near-field range is susceptible to noise interference especially inmm-wave systems In built-in self-calibration tests phasetoggling is applied to implement a closed-loop transmittingreceiving coupler near the radiating element for signal de-tection Although detected signals can be used for moni-toring calibration and fault isolation in phased antennaarray systems [9] signal deviations caused by parasiticcircuit effects of the radiated structure feeding network andradome (ie housing of the system) cannot be considered inmm-wave systems Moreover the array systems must have asufficient built-in circuit design for closed-loop testing andcalibration to ensure adequate operation is can beachieved using radio-frequency integrated circuit (RFIC)technology for a medium-sized array system with low-poweroperation However such an arrangement is complex for anarray with large antenna elements and high-poweroperation

To solve the aforementioned MIMO calibration prob-lems this study proposes a calibration method that entailsfirst applying a modified genetic algorithm (GA) in the far-field test range to calibrate an mm-wave massive MIMOsystem e advantages of the proposed calibration methodare as follows

(1) No additional closed-loop built-in circuits are re-quired thus reducing system design complexity

(2) e overall system calibration is considered to en-sure accuracy

(3) e modified GA with machine learning capabilitybased on big data can be easily applied to a massproduction line for automatically calibrating 5Gmassive MIMO systems

e remainder of this paper is organized as followsSection 2 presents the theoretical approach of the proposedmethod and the numerical investigation of the simulatedresults In Section 3 a simple experimental study is reportedSection 4 provides the study conclusion

2 Theory and Numerical Results

21 System Configuration Figure 1 illustrates the designconcept of an mm-wave massive MIMO antenna modulethat can automatically undergo self-calibration through themodified GA e MIMO antenna module comprises thefollowing components (1) 64-element microstrip patchantenna array (2) 16 front-end modules each of which hasfour-channel transmitreceive (TR) devices (3) a powerdistribution network and (4) a test antenna in the far-fieldrange is study adopted a four-element TRX half-duplexsilicon front-end IC (F5280 IDT Inc) [10] operating at25ndash31GHz As presented in Figure 1(b) the antenna arraycomprises a set of polarized elements with position vectorD [d1 d2 dm dM] where dm is the location of themth antenna element

e far-field pattern of the simultaneously excitedMIMO antenna array is expressed as follows

f(θ φ) WH

middot eminus jKT middotDξ(θφ) W

Hmiddot E(θφ) (1)

where

W w1 w2 wM1113858 1113859T (2)

E(θφ) eminus jKT middotDξ(θ φ)

K 2πλ

[sin θ cosφ sin θ sinφ cos θ]T

(3)

where λ is the wavelength at frequency f θ and ϕ are theazimuthal angle and angle of elevation of the far-field sourcerespectively and T is the matrix transpose

ξ(θφ) is a function of the polarized pattern of an in-dividual element and wi(wi cie

jψi ) is the complexweighting coefficient at the ith element of weight vector We Hermitian transpose which combines transposition andconjugation is denoted byH and the radiation pattern of thearray is denoted by f(θ φ) To satisfy the scan volume re-quirement the spacing arrangement of the antenna elementsin the system should be specified that is either a rectangularor triangular lattice For a rectangular lattice the spacings inthe x-axis y-axis and dxdy can be expressed as follows

dxleλ

1 + sin θaz( 1113857 (4)

dyleλ

1 + sin θel( 1113857 (5)

where θazθel is the scan volume specification in the azi-muthelevation direction

rough (4) and (5) the dx and dy values for elementsarranged in a rectangular lattice can be derived as 0536λ and0586λ respectively satisfying the scan coverage require-ment of az 60deg and el 45deg Moreover for elementsarranged in a triangular lattice the dx and dy values can bederived as 10733λ and 06066λ respectively by analyzing agrating lobe diagram [11] as shown in Figure 1(c) where thesolid and dashed lines represent the boundary of the scanvolume and grating lobe respectively Since the aperture sizeis increased by arranging array elements in a triangularlattice the MIMO provides relatively high antenna gainunder the same scan volume requirement nevertheless suchan increase is not suitable for miniaturization On the basisof the derived spacing values the maximum element gain(Ge 4πdx dyλ2) corresponding to the rectangular andtriangular lattice arrangements can theoretically be com-puted to be 596 and 913 dBi respectively is thus indi-cates that the EIRP is theoretically improved byapproximately 3 dB is improvement is crucial to MIMOdesign because power amplification results in poor efficiencyin mm-wave systemse use of additional power amplifiersfor a 3 dB output power gain will increase power con-sumption levels and engender heat sink problems in suchsystems According to the preceding theoretical calculationsthe design of massive MIMO systems requires high EIRP insmall-cell applications which reduces volume constraints inspace





TX InputRX Output

16


1

16

(a)

Patch antenna dx

Y

Z

X

Test antenna

dy

θφ

(b)


ndash1

ndash05

0

05

1

Ty-S

in (T

H)lowast

Sin

(PH

)



(c)


ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

Relat

ive p

ower

(dB)

Far-Field (SUM)


(d)










GA 20 log10(|f(θ ϕ)|) (7)





fc Wi( 1113857 min

1113936Ni1 wi

111386811138681113868111386811138681113868111386811138681113936

Ni1 wi

111386811138681113868111386811138681113868111386811138682

minus N1113966 11139672

N

11139741113972

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

⎫⎪⎪⎪⎬

⎪⎪⎪⎭

(9)




N




Selection

Crossover

Evaluation

x x

Mutation

∆φ [i] ∆ω [i]


x x





















ndash1

0

1

2

3

4

5

Erro

r in

()

16

18

20

22

24

26

28

Ant

enna

gai

n (d

Bi)


(a)


ndash40

ndash30

ndash20

ndash10

EIRP

(dBm

)

Optimal pattern


(b)


ndash4

ndash2

0

2

4

6

Phas

e in

rad

00050101502025030350404505

Nor

mal

ized

mag

nitu

de (v

v)


(c)



No

Yes

Set parameters


I = 1 to Ic loops




Random mutation

Next I

(Initialization)

(Selection)

(Crossover)

(Mutation)

DataBase(Wopt (j))

Stop

Data analysis




ndash1

0

1

2

3

4

5

Erro

r in

()

16

18

20

22

24

26

28

Ant

enna

gai

n (d

Bi)

Error estimation




Battery or

(a)

2 times 2 MIMO

Standard gain horn

(b)





z

x

y




0

5

10

15

20

25

30

Mea

sure

d EI

RPT

RP (d

Bm)



90ndash90

0

180

0

ndash40

ndash30

ndash20

ndash10

(a)

90ndash90

0

180

0

ndash40

ndash30

ndash20

ndash10

(b)


90ndash90

0

180

ndash40

ndash30

ndash20

ndash10

0


(a)

90ndash90

0

180

ndash30

ndash20

ndash10

0

ndash40


(b)




4 Conclusion


Data Availability




Acknowledgments


References

























TX InputRX Output

16


1

16

(a)

Patch antenna dx

Y

Z

X

Test antenna

dy

θφ

(b)


ndash1

ndash05

0

05

1

Ty-S

in (T

H)lowast

Sin

(PH

)



(c)


ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

Relat

ive p

ower

(dB)

Far-Field (SUM)


(d)










GA 20 log10(|f(θ ϕ)|) (7)





fc Wi( 1113857 min

1113936Ni1 wi

111386811138681113868111386811138681113868111386811138681113936

Ni1 wi

111386811138681113868111386811138681113868111386811138682

minus N1113966 11139672

N

11139741113972

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

⎫⎪⎪⎪⎬

⎪⎪⎪⎭

(9)




N




Selection

Crossover

Evaluation

x x

Mutation

∆φ [i] ∆ω [i]


x x





















ndash1

0

1

2

3

4

5

Erro

r in

()

16

18

20

22

24

26

28

Ant

enna

gai

n (d

Bi)


(a)


ndash40

ndash30

ndash20

ndash10

EIRP

(dBm

)

Optimal pattern


(b)


ndash4

ndash2

0

2

4

6

Phas

e in

rad

00050101502025030350404505

Nor

mal

ized

mag

nitu

de (v

v)


(c)



No

Yes

Set parameters


I = 1 to Ic loops




Random mutation

Next I

(Initialization)

(Selection)

(Crossover)

(Mutation)

DataBase(Wopt (j))

Stop

Data analysis




ndash1

0

1

2

3

4

5

Erro

r in

()

16

18

20

22

24

26

28

Ant

enna

gai

n (d

Bi)

Error estimation




Battery or

(a)

2 times 2 MIMO

Standard gain horn

(b)





z

x

y




0

5

10

15

20

25

30

Mea

sure

d EI

RPT

RP (d

Bm)



90ndash90

0

180

0

ndash40

ndash30

ndash20

ndash10

(a)

90ndash90

0

180

0

ndash40

ndash30

ndash20

ndash10

(b)


90ndash90

0

180

ndash40

ndash30

ndash20

ndash10

0


(a)

90ndash90

0

180

ndash30

ndash20

ndash10

0

ndash40


(b)




4 Conclusion


Data Availability




Acknowledgments


References





























GA 20 log10(|f(θ ϕ)|) (7)





fc Wi( 1113857 min

1113936Ni1 wi

111386811138681113868111386811138681113868111386811138681113936

Ni1 wi

111386811138681113868111386811138681113868111386811138682

minus N1113966 11139672

N

11139741113972

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

⎫⎪⎪⎪⎬

⎪⎪⎪⎭

(9)




N




Selection

Crossover

Evaluation

x x

Mutation

∆φ [i] ∆ω [i]


x x





















ndash1

0

1

2

3

4

5

Erro

r in

()

16

18

20

22

24

26

28

Ant

enna

gai

n (d

Bi)


(a)


ndash40

ndash30

ndash20

ndash10

EIRP

(dBm

)

Optimal pattern


(b)


ndash4

ndash2

0

2

4

6

Phas

e in

rad

00050101502025030350404505

Nor

mal

ized

mag

nitu

de (v

v)


(c)



No

Yes

Set parameters


I = 1 to Ic loops




Random mutation

Next I

(Initialization)

(Selection)

(Crossover)

(Mutation)

DataBase(Wopt (j))

Stop

Data analysis




ndash1

0

1

2

3

4

5

Erro

r in

()

16

18

20

22

24

26

28

Ant

enna

gai

n (d

Bi)

Error estimation




Battery or

(a)

2 times 2 MIMO

Standard gain horn

(b)





z

x

y




0

5

10

15

20

25

30

Mea

sure

d EI

RPT

RP (d

Bm)



90ndash90

0

180

0

ndash40

ndash30

ndash20

ndash10

(a)

90ndash90

0

180

0

ndash40

ndash30

ndash20

ndash10

(b)


90ndash90

0

180

ndash40

ndash30

ndash20

ndash10

0


(a)

90ndash90

0

180

ndash30

ndash20

ndash10

0

ndash40


(b)




4 Conclusion


Data Availability




Acknowledgments


References








































ndash1

0

1

2

3

4

5

Erro

r in

()

16

18

20

22

24

26

28

Ant

enna

gai

n (d

Bi)


(a)


ndash40

ndash30

ndash20

ndash10

EIRP

(dBm

)

Optimal pattern


(b)


ndash4

ndash2

0

2

4

6

Phas

e in

rad

00050101502025030350404505

Nor

mal

ized

mag

nitu

de (v

v)


(c)



No

Yes

Set parameters


I = 1 to Ic loops




Random mutation

Next I

(Initialization)

(Selection)

(Crossover)

(Mutation)

DataBase(Wopt (j))

Stop

Data analysis




ndash1

0

1

2

3

4

5

Erro

r in

()

16

18

20

22

24

26

28

Ant

enna

gai

n (d

Bi)

Error estimation




Battery or

(a)

2 times 2 MIMO

Standard gain horn

(b)





z

x

y




0

5

10

15

20

25

30

Mea

sure

d EI

RPT

RP (d

Bm)



90ndash90

0

180

0

ndash40

ndash30

ndash20

ndash10

(a)

90ndash90

0

180

0

ndash40

ndash30

ndash20

ndash10

(b)


90ndash90

0

180

ndash40

ndash30

ndash20

ndash10

0


(a)

90ndash90

0

180

ndash30

ndash20

ndash10

0

ndash40


(b)




4 Conclusion


Data Availability




Acknowledgments


References























ndash1

0

1

2

3

4

5

Erro

r in

()

16

18

20

22

24

26

28

Ant

enna

gai

n (d

Bi)

Error estimation




Battery or

(a)

2 times 2 MIMO

Standard gain horn

(b)





z

x

y




0

5

10

15

20

25

30

Mea

sure

d EI

RPT

RP (d

Bm)



90ndash90

0

180

0

ndash40

ndash30

ndash20

ndash10

(a)

90ndash90

0

180

0

ndash40

ndash30

ndash20

ndash10

(b)


90ndash90

0

180

ndash40

ndash30

ndash20

ndash10

0


(a)

90ndash90

0

180

ndash30

ndash20

ndash10

0

ndash40


(b)




4 Conclusion


Data Availability




Acknowledgments


References























0

5

10

15

20

25

30

Mea

sure

d EI

RPT

RP (d

Bm)



90ndash90

0

180

0

ndash40

ndash30

ndash20

ndash10

(a)

90ndash90

0

180

0

ndash40

ndash30

ndash20

ndash10

(b)


90ndash90

0

180

ndash40

ndash30

ndash20

ndash10

0


(a)

90ndash90

0

180

ndash30

ndash20

ndash10

0

ndash40


(b)




4 Conclusion


Data Availability




Acknowledgments


References























4 Conclusion


Data Availability




Acknowledgments


References






















Automatic Calibration Using a Modified Genetic Algorithm...

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