Novel design concepts for unconventional antenna array architecutres in next generation communications systems

International Do toral S hool in Information

and Communi ation Te hnology

DISI- University of Trento

Novel Design Con epts for Un onventional

Antenna Array Ar hite tures in Next

Generation Communi ations Systems

Giorgio Gottardi

Advisor:

PaoloRo a, Asso iate Professor

University of Trento

In this work, the formulationand the implementationof innovative

method-ologi alparadigmsforthedesignofun onventional arrayar hite turesforfuture

generation ommuni ation systems has been addressed. By exploiting the

po-tentialities of the odesign strategy for elementary radiators in an irregularly

lustered array ar hite tures and by introdu ing an innovative apa ity-driven

design paradigm, the proposed methodologiesallow toee tively design

un on-ventional arrayar hite tureswithoptimaltrade-osintermsofperforman eand

omplexity/ osts. The odesignsynthesisstrategyisproposedtosolvethearising

massive multi-obje tivedesign problem aimed at tting the multiple obje tives

and requirementson the free-spa e performan e of the array ar hite ture.

Af-terward, the apa ity-drivendesignparadigmisformulatedandimplementedfor

thedesignofMIMO arrayar hite turestomaximizethequalityofthe

ommuni- ationsystem inrstpla einsteadof onsideringfree-spa e gures-of-merit. A

setofnumeri alresultshasbeenprovided(i)tovalidatetheproposedparadigms

inreal-appli ations enarios and (ii)toprovide insightsonthe ee tiveness, the

limitationsand the potentialities ofproposed design methodologies.

Keywords

5G ommuni ations,5Gradiatingsystems,integer- odedgeneti algorithm(GA),

[R1℄ G. Gottardi, L. Poli, P. Ro a, A. Montanari, A. Aprile, and A.

Massa, Optimal monopulse beamforming for side-looking airborne

radars, IEEE Antennas Wireless Propag. Lett., vol. 16, pp.

1221-1224,2017.

[R2℄ G. Oliveri, G. Gottardi, F. Robol, A. Polo, L. Poli, M. Salu i, M.

Chuan, C. Massagrande, P. Vinetti, M. Mattivi, R. Lombardi, and

A. Massa, Co-design of un onventional array ar hite tures and

an-tennaelementsfor5Gbasestations, IEEETrans. AntennasPropag.

-Spe ialIssueon'AntennasandPropagationAspe tsof5G

Commu-ni ations,' vol. 65,no. 12,pp. 6752-6767, De ember 2017.

[R3℄ M.Salu i,G.Oliveri,N.Anselmi, G.Gottardi,andA. Massa,

Per-forman e enhan ement of linear a tive ele troni ally-s annedarrays

by means of MbD-synthesized metalenses, Journal of

Ele tromag-neti Waves and Appli ations, vol. 32, no. 8, pp. 927-955,2018.

[R4℄ M. Bertolli,M. Donelli, A. Massa, G. Oliveri, A. Polo, F. Robol,L.

Poli,A.Gelmini,G.Gottardi,M.A.Hannan,L.T.P.Bui,P.Ro a,

C. Sa hi, F. Viani, T. Moriyama, T. Takenaka, and M. Salu i,

"Computational methods for wireless stru tural health monitoring

of ultural heritages," Journal of Physi s: Conferen e Series, vol.

1131,pp. 1-7, 2018.

[R5℄ A. Massa, G. Gottardi, and E. Rajo-Iglesias, "CS-Based

omputa-tionalmethodsfor inverse problems arising inarrays pro essing and

design," Journal of Physi s: Conferen e Series, vol. 1131, pp. 1-7,

2018.

[R6℄ M. Salu i, L. Tenuti, G. Gottardi, A. Hannan, and A. Massa, A

System-by-Design method for e ient linear array miniaturization

throughlow- omplexityisotropi lenses, Ele troni sLetters,vol. 55,

no. 8,pp. 433-434, April2019.

[R7℄ G. Oliveri, G. Gottardi, and A. Massa, A new meta-paradigm for

the synthesis of antenna arrays for future wireless ommuni ations,

IEEE Trans. Antennas Propag., vol. 67, no. 6, pp. 3774-3788, June

2019.

[R8℄ N.Anselmi,G.Gottardi,G.Oliveri,andA.Massa,Atotal-variation

sparseness-promoting method for the synthesis of ontiguously

lus-tered linear ar hite tures, IEEE Trans. Antennas Propag., vol. 67,

row., Antennas Propag.,vol. 11,no. 13,pp. 1841-1845, O t. 2017.

[R10℄ A.Gelmini,G.Gottardi,andT. Moriyama,"A ompressive

sensing-based omputational method for the inversion of wide-band ground

penetratingradar data," Journal of Physi s: Conferen e Series, vol.

904, pp. 1-7, 2017.

[R11℄ G. Gottardi and T. Moriyama, "Indoor dete tion of passive targets

re ast as an inverse s attering problem," Journal of Physi s:

Con-feren e Series, vol. 904, pp. 1-7, 2017.

[R12℄ M.Salu iandG.Gottardi,"Advan esonmulti-s aleMbDsynthesis

ofWAIMs foradvan ed phasedarrays,"Journal of Physi s:

Confer-en e Series, vol. 963, pp. 1-4, 2018.

[R13℄ N. Anselmi and G. Gottardi, Re ent advan es and urrent trends

inmetamaterials-by-design, Journal of Physi s: Conferen e Series,

vol. 963, pp. 1-3, 2018.

[R14℄ P. Ro a, G. Gottardi, M. Bertolli,F. Robol, T. Moriyama, and T.

Takenaka,"Pro essingGPRdatawithinverses atteringapproa hes,"

Journal of Physi s: Conferen e Series, vol. 1131, pp. 1-7, 2018.

[R15℄ G.GottardiandL.Poli,"Human hestimagingbyreal-time

pro ess-ing of ele tri al impedan e data tomography," Journal of Physi s:

[C1℄ F. Viani,N.Anselmi, M. Donelli,P.Garofalo, G.Gottardi,G.

Oliv-eri, L.Poli,A. Polo, P. Ro a, M. Salu i,L. Tenuti, and A. Massa,

On the role of information in inversion and synthesis & hallenges,

tools,andtrends,"2015IEEEMediterraneanMi rowaveSymposium

(MMS'2015),Le e,Italy,pp. 1-4, November30-De ember2,2015.

[C2℄ L. Poli, P. Ro a, G. Gottardi, and A. Massa, Design of simplied

largearray stru tures for preliminaryexperimentalvalidation, 10th

European Conferen eonAntennasand Propagation(EUCAP2016),

Davos,Switzerland, pp. 1-4, April 11-15,2016.

[C3℄ L. Poli, N. Anselmi, G. Gottardi, P. Ro a, and A. Massa,

"Proba-bilisti interval method for phased array sensitivity analysis," 2016

IEEE AP-S International Symposium and USNC-URSI Radio

S i-en e Meeting, Fajardo, Puerto Ri o, pp. 919-920, June 26 - July 1,

2016.

[C4℄ G.Oliveri,E.Bekele,M.Salu i,L.Tenuti,G.Gottardi,T.Moriyama,

T. Takenaka, F. Bilotti, A. Tos ano,A. Massa, A system-by-design

approa h to the synthesis of mantle loaks for large diele tri

ylin-ders, PIERS 2016, Shangai, China, August 8-11, pp. 3144-3145,

2016.

[C5℄ A.Massa, N.Anselmi,G.Gottardi,G.Oliveri,L.Poli,P.Ro a,M.

Salu i,and L. Tenuti, Un onventional te hniques for the synthesis

of modern antenna arrays, 11th European Conferen e on

Anten-nas and Propagation (EUCAP 2017), Paris, Fran e, pp. 2843-2845,

Mar h 19-24, 2017.

[C6℄ G.Gottardi,N.Ebrahimi,P.Ro a,andA.Massa,Optimal

synthe-sisof monopulse beamforming weights for airborne radards through

onvexoptimization,2017InternationalAppliedComputational

Ele -tromagneti sSo iety Symposium, ACES 2017, Firenze, Italy, pp.

1-2,Mar h 26-30,2017.

[C7℄ N. Anselmi, P. Ro a, M. Salu i, G. Gottardi, and A. Massa, A

mask mat hing tiling optimization method for lustered phased

ar-rays, 2017 IEEE AP-S International Symposium and USNC-URSI

Radio S ien e Meeting, San Diego, California, USA, pp. 1045-1046,

July9-15, 2017.

[C8℄ G. Oliveri, P. Ro a, L. Poli, G. Gottardi, N. Anselmi, M. Salu i,

R. Lombardi, M. Chuan, M. Mattivi, P. Vinetti, F. Morgia, and

9-15, 2017.

[C9℄ N.Anselmi,P.Ro a,G.Gottardi,M.Salu i,andA.Massa,Tiling

optimizationoforthogonal-polygonshaped apertureforphasedarray

antennas, 2017 IEEE AP-S International Symposium and

USNC-URSIRadioS ien e Meeting,San Diego,California,USA,pp.

2025-2026, July 9-15, 2017.

[C10℄ L. Tenuti, P. Ro a, M. Salu i, G. Gottardi, and A. Massa,

In-novative optimization-based design of UWB planar arrays for

grat-inglobesredu tion, 2017IEEE AP-SInternational Symposiumand

USNC-URSIRadioS ien eMeeting,SanDiego,California,USA,pp.

2017-2018,July 9-15, 2017.

[C11℄ P.Ro a,N.Anselmi,M.Salu i,G.Gottardi,L.Poli,andA.Massa,

A novel analyti beam steering approa h for lustered phased

ar-ray ar hite tures, 2017 IEEE AP-S International Symposium and

USNC-URSI Radio S ien e Meeting, San Diego, California, USA,

pp. 2013-2014,July 9-15, 2017.

[C12℄ F. Robol, G. Gottardi, M. Salu i, G. Oliveri, and A. Massa,

De-signofnot h-enhan ed ompa tprintedantennasfor5G

ommuni a-tions, 2017 IEEE AP-SInternational Symposium and USNC-URSI

Radio S ien e Meeting, San Diego, California, USA, pp. 2321-2322,

July9-15, 2017.

[C13℄ G.Gottardi,G.Oliveri, andA. Massa,New antenna design on ept

for future generation wireless ommuni ation systems, 12th

Euro-peanConferen eonAntennasandPropagation(EUCAP2018),

Lon-don, United Kingdom, pp. 1-4, April9-13, 2018.

[C14℄ A.Massa, M. Bertolli,G.Gottardi,A. Hannan, D. Mar antonio,G.

Oliveri, A. Polo, F. Robol, P. Ro a, and F. Viani, Compressive

sensing as applied to antenna arrays: synthesis, diagnosis, and

pro- essing,2018IEEEInternationalSymposiumonCir uits&Systems

(ISCAS 2018), Firenze, Italy, pp. 1-5, May 27-30, 2018.

[C15℄ M. Bertolli,M. Donelli, A. Massa, G. Oliveri, A. Polo, F. Robol, L.

Poli,A.Gelmini,G.Gottardi,M.A.Hannan,L.T.P.Bui,P.Ro a,

C. Sa hi, F. Viani, T. Moriyama, T. Takenaka, and M. Salu i,

"Computational methods for wireless stru tural health monitoring

of ultural heritages," 8th International Conferen e on New

Com-putational Methods for Inverse Problems (NCMIP 2018), Ca han,

tionalmethodsfor inverse problems arising inarrays pro essing and

design,"8th International Conferen e onNew Computational

Meth-ods for Inverse Problems (NCMIP 2018), Ca han, Fran e, May 25,

2018.

[C17℄ G. Gottardi, G. Oliveri, D. Cunial, and A. Massa, Designing new

generationantennasfor5GMiMosystems-A newperspe tivein

ar-raysynthesis,2018IEEEAP-SInternationalSymposiumand

USNC-URSIRadioS ien eMeeting,Boston,Massa hussets,USA,pp.

2175-2176,July 8-13, 2018.

[C18℄ N.Anselmi,M.Donelli,A.Gelmini,G.Gottardi,G.Oliveri,L.Poli,

P. Ro a, L.Tenuti, and A. Massa, Design and optimization of

ad-van edradarand ommuni ationssystemsandar hite tures

ELE-DIAResear h Center, AttiXXIRiunione Nazionaledi

Elettromag-netismo(XXI RiNEm), Parma, pp. 164-167,12-14 Settembre 2016.

[C19℄ G. Gottardi, L. Poli, M. A. Hannan, and P. Ro a, "Wideband

phased arrays optimal design through onvex programming," 2016

IEEE AP-S International Symposium and USNC-URSI Radio

S i-en e Meeting, Fajardo, Puerto Ri o, pp. 767-768, June 26 - July 1,

2016.

[C20℄ A.Gelmini,G.Gottardi,andT. Moriyama, "A ompressive

sensing-based omputational method for the inversion of wide-band ground

penetrating radar data," 7th International Workshop on New

Com-putational Methods for Inverse Problems (NCMIP 2017), Ca han,

Fran e,May 12,2017.

[C21℄ G. Gottardi and T. Moriyama, "Indoor dete tion of passive targets

re ast as an inverse s attering problem," 7th International W

ork-shoponNew ComputationalMethodsfor InverseProblems(NCMIP

2017),Ca han, Fran e, May 12,2017.

[C22℄ G.Gottardi,L.Turrina,N.Anselmi,G.Oliveri,andP.Ro a,Sparse

onformalarraydesignformultiplepatternsgenerationthrough

multi-task bayesian ompressive sensing, 2017 IEEE AP-S International

SymposiumandUSNC-URSIRadioS ien eMeeting,SanDiego,

Cal-ifornia,USA,pp. 429-430,July 9-15,2017.

[C23℄ L.T. P.Bui, N.Anselmi,G. Gottardi,L.Poli,andP.Ro a,

Wide-band phasedarrays synthesis with maximum bandwidth through

it-erative onvexoptimization, 2017IEEEAP-SInternational

Sympo-siumandUSNC-URSIRadioS ien e Meeting,SanDiego,California,

national Symposium and USNC-URSI Radio S ien e Meeting, San

Diego,California,USA, pp. 2625-2626, July 9-15, 2017.

[C25℄ M. A. Hannan, M. Salu i, G. Gottardi, L. Poli, and P. Ro a,

Advan ed time-modulated array synthesis for dire tional

modula-tion optimization, 2017 IEEE AP-S International Symposium and

USNC-URSIRadioS ien eMeeting,SanDiego,California,USA,pp.

2027-2028,July 9-15, 2017.

[C26℄ M.Salu i, G.Gottardi,D. Pin hera, and M.D. Migliore, Antenna

measurements by design: a novel paradigm for antenna testing,

6th Asia-Pa i Conferen e onAntennas and Propagation(APCAP

2017),Xi'an, China, pp. 1-3, O tober16-19, 2017.

[C27℄ P. Ro a, G. Gottardi, M. Bertolli,F. Robol, T. Moriyama, and T.

Takenaka,"Pro essingGPRdatawith2DBayesian ompressive

sens-ing inverse s attering approa hes," 8th International Conferen e on

New Computational Methods for Inverse Problems (NCMIP 2018),

Ca han, Fran e, May 25,2018.

[C28℄ G. Gottardi and L. Poli, " Human hest imaging by real-time

pro- essing of ele tri al impedan e data tomography," 8th International

Conferen e on New Computational Methods for Inverse Problems

(NCMIP 2018), Ca han, Fran e,May 25,2018.

[C29℄ G.Gottardi,M.A.Hannan,and A.Polo,"Amulti-fo using ontrast

sour e Bayesian ompressive method for solving inverse s attering

problems,"9thInternationalWorkshoponNewComputational

Meth-ods for Inverse Problems (NCMIP 2019), Ca han, Fran e, May 24,

2019.

[C30℄ G. Gottardi, M. A. Hannan, and A. Polo, "NDT/NDE by means

of a probabilisti dierential ompressive sensing method," 9th

In-ternational Workshop on New Computational Methods for Inverse

Problems (NCMIP 2019), Ca han, Fran e, May 24, 2019.

[C31℄ G.Gottardi,M.A.Hannan,B.Li,A.Polo,M.Salu i,and F.Viani,

"PCA-Based inversion of WiFi signal for robust devi e-free indoor

targetdete tion,"9thInternationalWorkshoponNewComputational

Methods for Inverse Problems (NCMIP 2019),Ca han, Fran e,May

24,2019.

[C32℄ G.Gottardi,M.A.Hannan,andA.Polo,"Compressivesensing

Interna-lems (NCMIP 2019), Ca han, Fran e, May 24,2019.

[C33℄ F.Boulos,L.Dall'Asta,G.Gottardi,M.A.Hannan,A.Polo,andA.

Salas-San hez, "A onvex optimization-based inversion method for

the Synthesis of monopulse linear arrays," 9th International

Work-shop on NewComputational Methods for InverseProblems (NCMIP

2019),Ca han, Fran e, May 24,2019.

[C34℄ F. Boulos, L. Dall'Asta, G. Gottardi, M. A. Hannan, A. Polo, A.

Salas-San hez, and M. Salu i, "A omputational inversion method

for interferen e suppression in re ongurable thinned ring arrays,"

9th International Workshop on New Computational Methods for

In-verse Problems (NCMIP 2019),Ca han, Fran e, May 24, 2019.

[C35℄ G. Gottardi, M. A. Hannan, A. Polo, M. Salu i, and F. Viani,

"Frequen y-basedinversionofasinglewirelesslinkforindoorpassive

targetdete tion,"9thInternationalWorkshoponNewComputational

Methods forInverse Problems (NCMIP 2019),Ca han, Fran e,May

1 Introdu tion 1

2 Free-Spa e-Oriented Antenna Design Problem 7

2.1 Mathemati al Formulation . . . 8

3 Codesign Synthesis Strategy 13 3.1 Codesign Methodology -Formulation . . . 14

3.1.1 Array Clustering Step (Integer-Coded SO-GA). . . 15

3.1.2 AntennaElement Synthesis Step(

ε

-MOEA) . . . 18

3.1.3 Codesign Algorithmi Implementation . . . 20

3.2 Numeri al Assessment . . . 22

3.2.1 Calibrationof the Extended Finite Array Model . . . 22

3.2.2 Element Synthesis and Array Clustering . . . 24

4 Capa ity-Driven Antenna Design Problem 43 4.1 Capa ity-Oriented MIMO System Design Meta-Paradigm - F or-mulation . . . 44

5 Capa ity-Driven Synthesis Methodology 51 5.1 Methodologi alCustomizationandImplementationProofs-of-Con ept 52 5.1.1 FP Array Ar hite tures . . . 52

5.1.2 CC Array Ar hite tures . . . 53

5.2 Numeri al Results and ComparativeAnalysis . . . 58

5.2.1 Synthesis of Fully-Populated Layouts . . . 59

5.2.2 Design of ContiguouslyClustered Arrangements . . . 73

3.1 Array lusteringphase(Re tangularlatti e,

0.492λ

0

×0.651λ

0

unit ell,

N

= 18 × 14

) - E ien y and gain performan e assuming isotropi ,stand-alone,andembeddedradiatorsinFig. 3.5(b)

and omparisonswith CST full-wave modeling. . . 35

3.2 Array lusteringphase(Re tangularlatti e,

0.492λ

0

×0.651λ

0

unit ell,

N

= 28 × 16

) - E ien y and gain performan e assuming isotropi ,stand-alone,andembeddedradiatorsinFig. 3.5(b)

and omparisonswith CST full-wave modeling. . . 42

5.1 CC Ar hite ture (

N

= 55

,

Q

= 22

,

V

= 6

) - Aperture tiling des riptors. . . 55

5.2 FP Ar hite ture Design (NLOS IMT-A UMi,

N

= 32

,

L

= 16

,

SN R

= 20

[dB℄)- Average performan e indexes. . . 65 5.3 CC Ar hite ture Design (NLOS IMT-A UMi - S enario 1,

L

=

1.1 Layout of (a)  onventional array ar hite ture and (b) thinned,

( ) lustered, and (d) sparse un onventional arrayar hite tures. 2

2.1 Elementaryradiator top-view(b) and side-view ( ). . . 8

3.1 Flow hart of the proposed odesign strategy (yellow boxes

high-lightad-ho ustomized operators). . . 15

3.2 Sket hoftheinteger- odedSO-GA de oding te hnique for luster

pla ement. . . 17

3.3 Extended nite model. . . 19

3.4 Extended nite model alibration (Re tangularlatti e,

0.492λ

0

×

0.651λ

0

unit ell) - Behaviour of

|S

k1

(f )|

versus frequen y when varying thenumberof rings

H

surroundingthe referen eantenna when (a)

k

= 2

and (b)

k

= 5

. . . 23 3.5 Antenna element synthesis phase (Re tangular latti e,

0.492λ

0

×

0.651λ

0

unit ell) - Plots of the representative points of a set of

ε

-MOEA solutions in the



e

Φ

1

, e

Φ

2



plane and asso iated Pareto

fronts (a), and geometries of sele ted Pareto-optimal tradeo

so-lutions (b)( ) asmodeled inCST Mi rowave Studio. . . 24

3.6 Antenna element synthesis phase (Re tangular latti e,

0.492λ

0

×

0.651λ

0

unit ell) - Behaviour of

E

(θ, ϕ; f )

for (a)( ) tradeo solution in Fig. 3.5(b) and (a)( ) tradeo solution in Fig. 3.5( )

when (a)(b)

f

= f

min

and ( )(d)

f

= f

max

. . . 25

3.7 Antenna element synthesis phase (Re tangular latti e,

0.492λ

0

×

0.651λ

0

unit ell)-Behaviourofthefull-wavenumeri alsimulated (a)

|S

11

(f )|

,(b)

ε

(f )

,( )realizedgain,(d)

W

AZ

(f )

and

W

EL

(f )

, and (e)

|S

k1

(f )|

(

k

= 2, ..., 9

)forthe tradeo ongurationinFig. 3.5(b). . . 26

3.8 Antenna element synthesis phase (Re tangular latti e,

0.492λ

0

×

0.651λ

0

unit ell)-Behaviourofthefull-wavenumeri alsimulated (a)

|S

11

(f )|

,(b)

ε

(f )

,( )realizedgain,(d)

W

AZ

(f )

and

W

EL

(f )

, and (e)

|S

k1

(f )|

(

k

= 2, ..., 9

)forthe tradeo ongurationinFig. 3.5( ). . . 27

3.9 Array lusteringphase(Re tangularlatti e,

0.492λ

0

×0.651λ

0

unit ell,

N

= 18 × 14

, Fig. 3.5(b) embedded radiator) - Plots of the representative pointsofaset ofSO-GA solutionsinthe

(Φ

SO

, Q)

-plane and asso iated Pareto fronts (a), and layouts of sele ted

Pareto-optimal tradeo lustered arrangements (ea h olor

iden-tifyingadierent luster)with(b)

Q

= 196

,( )

Q

= 144

, and(d)

Q

= 76

. . . 28 3.10 Array lusteringphase(Re tangularlatti e,

0.492λ

0

×0.651λ

0

unit

ell,

N

= 18 × 14

,

Q

= 196

),

(θ

0

, ϕ

0

) = (90, 60)

[deg℄ - Plots of

P (θ, ϕ; θ

0

, ϕ

0

; f )

assumingthe embedded element inFig. 3.5(b) at(a)

f

= f

min

and (d)

f

= f

max

and(g)asso iated uts versus

ϕ

and omparisons with isotropi  and stand-alone radiators. 30

3.11 Array lusteringphase(Re tangularlatti e,

0.492λ

0

×0.651λ

0

unit ell,

N

= 18 × 14

,

Q

= 196

),

(θ

0

, ϕ

0

) = (112.5, 0)

[deg℄ - Plots of

P (θ, ϕ; θ

0

, ϕ

0

; f )

assumingthe embedded element inFig. 3.5(b) at(a)

f

= f

min

and (d)

f

= f

max

and(g)asso iated uts versus

ϕ

and omparisons with isotropi  and stand-alone radiators. 31 3.12 Array lusteringphase(Re tangularlatti e,

0.492λ

0

×0.651λ

0

unit

ell,

N

= 18 × 14

,

Q

= 196

),

(θ

0

, ϕ

0

) = (112.5, 60)

[deg℄- Plots of

P (θ, ϕ; θ

0

, ϕ

0

; f )

assumingthe embedded element inFig. 3.5(b) at(a)

f

= f

min

and (d)

f

= f

max

and(g)asso iated uts versus

ϕ

and omparisons with isotropi  and stand-alone radiators. 32

3.13 Array lusteringphase(Re tangularlatti e,

0.492λ

0

×0.651λ

0

unit ell,

N

= 18 × 14

) - Pattern uts of

P (θ, ϕ; θ

0

, ϕ

0

; f )

assuming the embedded element in Fig. 3.5(b) and omparisons with

isotropi  and stand-alone radiators when (a)(b)

(θ

0

, ϕ

0

) =

(90, 60)

[deg℄,( )(d)

(θ

0

, ϕ

0

) = (112.5, 0)

[deg℄,and(e)(f)

(θ

0

, ϕ

0

) =

(112.5, 60)

[deg℄for (a)( )(e)

Q

= 144

,and (b)(d)(f)

Q

= 76

. . . 33

3.14 Array lusteringphase(Re tangularlatti e,

0.492λ

0

×0.651λ

0

unit ell,

N

= 18 × 14

,

Q

= 196

,

(θ

0

, ϕ

0

) = (112.5, 0)

[deg℄) - Plots simulated

P (θ, ϕ; θ

0

, ϕ

0

; f )

and omparisons with CST full-wave modeling. . . 34

3.15 Array lusteringphase(Re tangularlatti e,

0.492λ

0

×0.651λ

0

unit ell,

N

= 28 × 16

, Fig. 3.5(b) embedded radiator) - Plots of the representative pointsofaset ofSO-GA solutionsinthe

(Φ

SO

, Q)

-plane and asso iated Pareto fronts (a), and layouts of sele ted

Pareto-optimal tradeo lustered arrangements (ea h olor

iden-tifyingadierent luster)with(b)

Q

= 348

,( )

Q

= 252

, and(d)

3.16 Array lustering phase (Re tangular latti e,

0.492λ

0

× 0.651λ

0

unit ell,

N

= 28 × 16

),

Q

= 348

- Plots

P (θ, ϕ; θ

0

, ϕ

0

; f )

as-suming the embedded element in Fig. 3.5(b) and omparisons

with isotropi  and stand-alone radiators when (a)

(θ

0

, ϕ

0

) =

(90, 60)

[deg℄, (b)

(θ

0

, ϕ

0

) = (112.5, 0)

[deg℄, and ( )

(θ

0

, ϕ

0

) =

(112.5, 60)

[deg℄. . . 38 3.17 Array lustering phase (Re tangular latti e,

0.492λ

0

× 0.651λ

0

unit ell,

N

= 28 × 16

),

Q

= 252

- Plots

P (θ, ϕ; θ

0

, ϕ

0

; f )

as-suming the embedded element in Fig. 3.5(b) and omparisons

with isotropi  and stand-alone radiators when (a)

(θ

0

, ϕ

0

) =

(90, 60)

[deg℄, (b)

(θ

0

, ϕ

0

) = (112.5, 0)

[deg℄, and ( )

(θ

0

, ϕ

0

) =

(112.5, 60)

[deg℄. . . 39 3.18 Array lustering phase (Re tangular latti e,

0.492λ

0

× 0.651λ

0

unit ell,

N

= 28 × 16

),

Q

= 152

- Plots

P (θ, ϕ; θ

0

, ϕ

0

; f )

as-suming the embedded element in Fig. 3.5(b) and omparisons

with isotropi  and stand-alone radiators when (a)

(θ

0

, ϕ

0

) =

(90, 60)

[deg℄, (b)

(θ

0

, ϕ

0

) = (112.5, 0)

[deg℄, and ( )

(θ

0

, ϕ

0

) =

(112.5, 60)

[deg℄. . . 40 3.19 Array lusteringphase(Re tangularlatti e,

0.492λ

0

×0.651λ

0

unit

ell,

N

= 28 × 16

,

Q

= 348

,

(θ

0

, ϕ

0

) = (112.5, 0)

[deg℄) - Plots simulated

P (θ, ϕ; θ

0

, ϕ

0

; f )

and omparisons with CST full-wave modeling. . . 41

4.1 Problem Formulation - Multi-user multi-antenna downlink

s e-nario (a). Detailsof(a)the transmittingandthere eiving

anten-nas and of (b)the logi als hemeof the linearmulti-beamfeeding

ar hite ture ( ). . . 45

5.1 CC Ar hite ture (

N

= 55

,

Q

= 22

,

V

= 6

) - Sket h of a CC aperture(Tab. II5.1). . . 54

5.2 Ben hmark S enarios - Spatiallo ations of the BS (i.e., a

trans-mittingarrayof

S

radiatingelements)andofthe

L

user-terminals in the Madrid grid urban environment (NLOS IMT-A UMi ):

(a)S enario 1, (b)S enario2, and ( )S enario 3. . . 59

5.3 FP Ar hite ture Design (NLOS IMT-A UMi - S enario 1,

N

=

32

,

L

= 16

,

SN R

= 20

[dB℄) - Plots of (a)

C

χ,l

, (b)

D

χ,l

, and ( )

SLL

χ,l

versus the

l

-th(

l

= 1, ..., L

) re eiverindex (

χ

∈ {V, H}

). 60 5.4 FP Ar hite ture Design (NLOS IMT-A UMi - S enario 1,

N

=

32

,

L

= 16

) - Dire tivity patterns synthesized by (a)( )(e) the 

max C

 and (b)(d)(f) the 

max D

 methods when (a)(b)

b

= 1

, ( )(d)

b

= 3

,and (e)(f)

b

= 16

. . . 61

5.5 FP Ar hite ture Design (NLOS IMT-A UMi - S enario 1,

N

=

32

,

L

= 16

) -

φ

0

ut of the dire tivity pattern when (a)

b

= 1

(

φ

0

= 16

[deg℄), (b)

b

= 3

(

φ

0

= −16

[deg℄), and ( )

b

= 16

(

φ

0

= 4

[deg℄). . . 62 5.6 FP Ar hite ture Design (NLOS IMT-A UMi,

N

= 32

,

L

= 16

,

b

= 1

) - Dire tivity patterns radiated by (a)(b) the 

max C

 and ( )(d)the 

max D

 arrays for (a)( )the S enario2 and (b)(d) the S enario 3. . . 63

5.7 FP Ar hite ture Design (NLOS IMT-A UMi,

N

= 32

,

L

= 16

,

b

= 1

)-Plots of(a)(b)magnitude,





W

ψ,n,b

(i)

(f )







,and ( )(d)phase,

∠W

ψ,n,b

(i)

(f )

,ex itations (

n

= 1, ..., N

;

ψ

∈ {V, H}

) for(a)( ) the

S enario 2 and (b)(d) the S enario 3. . . 64

5.8 FP Ar hite ture Design (NLOS IMT-A UMi - S enario 1,

N

=

32

,

L

= 16

)-Plotsof(a)( )(e)





W

ψ,n,b

(i)

(f )







and(b)(d)(f)

∠W

(i)

ψ,n,b

(f )

versus the

n

-th (

n

= 1, ..., N

) antenna array index (

ψ

∈ {V, H}

) (a)(b)

b

= 1

, ( )(d)

b

= 3

,and (e)(f)

b

= 16

. . . 66 5.9 FP Ar hite ture Design (NLOS IMT-A UMi,

N

= 32

,

L

= 16

,

SN R

= 20

[dB℄) - Plots of (a)(b)

C

χ,l

, ( )(d)

D

χ,l

, and (e)(f)

SLL

χ,l

versus the

l

-th (

l

= 1, ..., L

) re eiver index (

χ

∈ {V, H}

) for(a)( )(e) the S enario2 and (b)(d)(f) the S enario 3. . . 67

5.10 FP Ar hite ture Design (NLOS IMT-A UMi - S enario 1,

L

=

16

,

SN R

= 20

[dB℄) - Behaviour of (a)

C

ave

, (b)

D

ave

, and ( )

SLL

ave

versus

N

. . . 68 5.11 FP Ar hite ture Design (NLOS IMT-A UMi - S enario 1,

N

=

72

,

SN R

= 20

[dB℄) - Behaviour of (a)

C

ave

, (b)

D

ave

, and ( )

SLL

ave

versus

L

. . . 70 5.12 FP Ar hite ture Design (

N

= 32

,

L

= 16

) - Plot of

C

ave

versus

SN R

fordierentpropagations enarios (urbans enario-NLOS IMT-A UMi; rural s enario - LOS 3GPP RMa and NLOS

3GPP RMa). . . 71

5.13 FP Ar hite ture Design (

N

= 32

,

L

= 16

,

b

= 1

) - Dire tivity patternsgenerated by (a)( )the 

max C

 and(b)(d)the 

max D

 arrays in orresponden e with (b)( ) the LOS 3GPP RMa and

(d)(e)theNLOS3GPPRMa propagationenvironmentsandthe

orresponding

φ

0

- uts (

φ

0

= 16

[deg℄). . . 72 5.14 CC Ar hite ture Design (NLOS IMT-A UMi -S enario1,

N

=

64

,

L

= 16

,

Q

= 32

,

V

= 2

,

SN R

= 20

[dB℄) - CC layouts synthesized with (a) the 

max C

 and (b) the 

max D

 methods. . 73 5.15 CC Ar hite ture Design (NLOS IMT-A UMi -S enario1,

N

=

64

,

L

= 16

,

Q

= 32

,

SN R

= 20

[dB℄) - Plots of (a)

C

χ,l

, (b)

D

χ,l

, and ( )

SLL

χ,l

versus the

l

-th (

l

= 1, ..., L

) re eiver index (

χ

∈ {V, H}

). . . 74

5.16 CC Ar hite ture Design (NLOS IMT-A UMi - S enario1,

N

=

64

,

L

= 16

,

Q

= 32

,

SN R

= 20

[dB℄) - Dire tivity patterns radiated by (a)(b) the 

max C

 and ( )(d) the 

max D

 arrays when (a)( )

b

= 1

and (b)(d)

b

= 16

. . . 75 5.17 CC Ar hite ture Design (NLOS IMT-A UMi - S enario1,

N

=

64

,

L

= 16

,

Q

= 32

,

SN R

= 20

[dB℄) - Plots of (a)(b) mag-nitude,





W

ψ,n,b

(i)

(f )







, and ( )(d) phase,

∠W

(i)

ψ,n,b

(f )

, ex itations

(

n

= 1, ..., N

;

ψ

∈ {V, H}

) when (a)( )

b

= 1

and (b)(d)

b

= 16

. . 76 5.18 CC Ar hite ture Design (NLOS IMT-A UMi - S enario1,

N

=

64

,

L

= 16

,

Q

= 32

,

SN R

= 20

[dB℄) -

φ

0

ut of the dire tivity pattern when (a)

b

= 1

(

φ

0

= 16

[deg℄) and (b)

b

= 16

(

φ

0

= 4

[deg℄). . . 77

5.19 CC Ar hite ture Design (NLOS IMT-A UMi - S enario 1,

L

=

16

,

Q

N

= 0.5

,

SN R

= 20

[dB℄) - Behaviour of (a)

C

ave

, (b)

D

ave

, and ( )

SLL

ave

versus

N

. . . 78 5.20 CC Ar hite ture Design (NLOS IMT-A UMi - S enario 1,

L

=

16

,

Q

N

= 0.5

,

SN R

= 20

[dB℄,

b

= 1

) - CC layouts (a)(b)(e)(f) and asso iated dire tivity patterns ( )(d)(g)(h) synthesized with

(a)( )(e)(g) the 

max C

 and (b)(d)(f)(h) the 

max D

 methods for BS arrays of (a)-(d)

N

= 128

and (e)-(h)

N

= 144

elements. 79 5.21 CC Ar hite ture Design (NLOS IMT-A UMi GF - S enario 1,

L

= 16

,

Q

N

= 0.5

,

b

= 1

)-

θ

0

- ut (

θ

0

= 92

[deg℄) of the dire tivity pattern when (a)

N

= 64

,(b)

N

= 128

, and (b)

N

= 144

. . . 80 5.22 CC Ar hite ture Design (

N

= 64

,

L

= 16

,

Q

= 32

) - Plot of

C

ave

versus

SN R

for dierent propagation s enarios (urban s enario - NLOS IMT-A UMi; rural s enario - LOS 3GPP RMa and

Introdu tion

The next generation of mobile wireless te hnologies, ommonly labeled as

5G ,isexpe tedtodelivermulti-gigabit-per-se onddatarateswhileminimizing

osts, onne tion laten y, and power onsumption[1℄[2℄[3℄. To t these

require-ments,signi antadvan eswithrespe ttoprevious-generationsystems[2℄[4℄are

expe tedandrequiredfromthe te hnologi al, themethodologi al,and the

ar hi-te tural viewpoints. This onsideration holds true even more for the radiating

segment of 5G base stations (BSs) [2℄[3℄[4℄[5℄ as these systems are expe ted to

rely more and more on omplex multi-input multi-output (MIMO) antenna

ar-rayar hite tures toguarantee unpre edented levelofexibilityand performan e

[6℄[7℄[8℄ (i.e., supporting real-time adaptive beam re onguration/user tra king

features and MIMO pro essing) to address the needs of next-generationmobile

wirelesssystemsintermsofdataratesandnetwork apa ity[2℄. Moreover, these

latterobje tiveswillhavetobe obtained withinexpensivear hite tures and

an-tennaelementstominimizethefabri ationandthemaintenan e osts[2℄[3℄[4℄[5℄.

Towards this aim, a tive ele troni ally s anned arrays (AESAs) [9℄[10℄ are a

promisingte hnologytoaddress5G BS antennadesign[3℄[11℄[12℄[13℄[14℄[15℄that

are required to have a wide steering angle, a wide bandwidth, MIMO

apabili-ties [9℄[10℄,and real-time beam ontrol. Indeed, a broad lass ofstate-of-the-art

synthesismethodshavebeen formulated,andsu essfullyapplied,forthedesign

of AESA  onventional ar hite tures to optimize the free-spa e performan e

of the radiated pattern [9℄[10℄[16℄[18℄[19℄[20℄[21℄[22℄[23℄[32℄. The exploitation of

free-spa e gures-of-merit,su hasthedire tivity(D),thehalf-powerbeamwidth

(HPBW) or the sidelobe level (SLL) [9℄[10℄[16℄[17℄[19℄[20℄[21℄[22℄[23℄[32℄ omes

fromtheideathat, a ordingtotheFriis'equation,theBS radiatedpowermust

be fo used along the terminal dire tion to maximize the link quality and the

information transfer. Thus, the signal-to-noise ratio (SNR) at the re eiver an

be improved, forinstan e, by in reasing the antennagain and redu ing the SLL

(b)

( )

(d)

Figure1.1: Layout of (a)  onventional array ar hite ture and (b) thinned, ( )

Generally speaking,  onventional,or fully-populated,AESA ar hite tures

[Fig. 1.1(a)℄are hara terizedfromaregularpla ementofradiatingelementson

a regular latti e, or grid, and an independent ontrol of amplitude and phase,

of eitherthe transmitted orthe re eived signals, onea hradiatingelement (i.e.,

a transmit/re eive module, TRM, for ea h radiating element is provided) [9℄.

Despite the fa t that fully-populated ar hite tures provide optimal/full pattern

ontrol,these solutionsgenerally turnout to beexpensive ar hite tures [10℄[24℄,

due to the high number of TRMs in the feeding network, and therefore not

suitable for the onsidered appli ation. To redu e the ost of AESA

ar hite -tures still yielding satisfa tory free-spa e performan es, un onventional

ar hi-te tures, su h as thinned [Fig. 1.1(b)℄, lustered [Fig. 1.1( )℄, or sparse [Fig.

1.1(d)℄ arrays ar hite tures have been introdu ed [9℄ [25℄. Clustered

ar hite -tures [Fig. 1.1( )℄ inparti ular, have been widely used in the literature asthey

allows to a hieve AESA ar hite tures with good trade-os between omplexity

andperforman e [9℄-[39℄. Indeed, lusteredphasedarraysare hara terizedfrom

anar hite turewheremultipleelementsaregroupedinto lusters(orsub-arrays)

and ea h luster is fed from a single TRM [Fig. 1.1( )℄, leading to an

ar hite -ture whose number of ontrol points (i.e., the number of TRMs) is lower than

the number of radiating elements. Along with the redu ed omplexity of the

feeding network, the osts of lustered ar hite tures an be further redu ed if

adopted sub-arrays have similar and simple shapes (e.g., the same number of

grouped elements or identi al shapes) that are suitable for modular assembling

[26℄. Unfortunately, lusteredar hite turesmaybeae tedbysevere limitations

in the operationalbandwidth and in the re onguration exibility. Indeed, the

redu ed number of ontrol points, and the unavoidable quantization of

ampli-tude and phase at the element-level, leads to a limited ontrol on the radiated

patternanderrorsinthe apertureillumination[27℄. Su hadrawba k is

parti u-larlyevidentwhentheapertureissimplypartitionedintore tangularsub-arrays

of equal shapes and orientations (i.e., a regularly lustered layout is adopted)

as the periodi errors in the aperture illumination generate undesired grating

lobes in the radiation pattern when steered [9℄[27℄. To avoid these drawba ks,

a-periodi arrangements of sub-arrays (i.e., irregular lustered ar hite tures )

havebeen shown toa hieveasigni antlymoderationofthe quantizationphase

lobesinthe radiationpatternasthey allowtobreakthe quantizationperiodi ity

[9℄[28℄.

The advantages of irregular lustered ar hite tures have been rstly shown

in [29℄[30℄[31℄, where su h ar hite tures have been introdu ed to in rease the

operational bandwidth of the array ar hite tures, showing that the a-periodi

arrangement of sub-arrays allows to mitigate the level of the undesired

side-lobes. Su essively, several e ient lo al-sear h te hniques have been proposed

to ompute the optimal pla ement of sub-arrays subje t to onstraints on the

radiation pattern, for instan e a Geneti Algorithm (GA)-based approa h [32℄,

to be sele ted from an a-priori dened alphabet) have been also introdu ed to

enhan e the modularity of the designed ar hite ture. [37℄[38℄[39℄. Although

ef- ient methods for the design of jointly lustered ex itations magnitudes and

phasesare available,the design of the system nowat handis stillvery

halleng-ingtasksin e, tothebest of theauthor's knowledge,state-of-the-art-approa hes

are employed only for very limited s an angles/bands [10℄[38℄, while more

om-plexarrangements omprisingmanymorephaseshiftersthanmagnitude ontrols

are adopted if wider elds-of-view (su h as those of interest in5G) are required

[9℄[39℄.

In this thesis the design of un onventional lustered array ar hite tures

has been addressed by introdu ing new methodologiesand new methodologi al

paradigms inthe design pro ess. Firstly,the simultaneoussynthesis of irregular

lustered ar hite tures and antenna elements, for 5G BSs, is dis ussed and an

innovative odesign pro ess in whi h the antenna element, embedded in the

-nite layout, andthearrayar hite ture (i.e.,theradiatorsdispla ementandtheir

feedings)aresimultaneouslysynthesized by takingintoa ountreal-systems

im-pa tisformulated. Indeed,the proposed odesign strategyisaimedatee tively

handlingtheinterrelationshipsarisinginthe5G s enariobetweenthesingle

radi-atorandthearrayar hite turesin e(i)thearraygeometrydire tlymodiesthe

mutual ouplingee ts among the antenna elements that ae t the 5G

gures-of-merit of the single array element (e.g., the impedan e, the isolation, and the

radiationpattern) and, in turn, (ii) the antenna response (e.g., the beamwidth

and the patternslope) impa ts the sidelobe ontroland the steering features of

the resulting array layout. In the se ond part, an innovative meta-paradigm is

introdu ed to design un onventional apa ity-driven antenna ar hite tures, for

MIMO appli ations, to maximize the ommuni ation quality depending on the

a tual Green's fun tion of the whole propagation s enario, in luding the

an-tennasystems, insteadof onsideringstandard free-spa e onditions andrelated

performan e indexes. With respe t to the free-spa e-oriented odesign

strat-egy, the expression of the link quality measure is expli itly derived from the

time-domainmodelofthe ele tromagneti environmentand the problemof

syn-thesizing MIMO arrays is formulated as the maximization of the quality of the

ommuni ation system. A ordingly,the proposed apa ity-driven design

meta-paradigmis then ustomized to two relevant and representative ex itation-only

synthesis problems, on erned with fully-populated and ontiguously- lustered

Thesis outline

The thesis is organized as follows, Firstly, the 5G base station design problem

is mathemati ally formulated as the optimization of free-spa e parameters in

Chapter 2. Then the odesign synthesis pro ess is formulated and detailed in

Chapter 3toee tively addressthe arisingMMO design problem. InChapter 4

the apa ity-drivendesignparadigmisformulatedandtheimplemented

apa ity-driven synthesis methodology is applied to the design of fully-populated and

ontiguously- lusteredarrangementsinChapter 5. Finallysome on lusions are

Free-Spa e-Oriented Antenna

Design Problem

In this Chapter, the mathemati al formulation for the design of un onventional

arrayar hite tures,featuringirregularly lusteredex itations,isaddressed. More

in details, the 5G base station design problem,aimed at tting multiple

obje -tives/requirementsonthe free-spa e performan e ofthearrayar hite ture and

of the the array element radiation, is formulated as a massive-multi-obje tive

[MMO℄problem. Consequently, the MMO ost fun tionand thetermsen oding

the synthesisobje tivesof theMMO designproblemare dened and

2.1 Mathemati al Formulation

Letus onsideraplanararrangementof

N

elementsdispla edinthe

yz

-planeand lusteredin

Q

sub-arraysof ontiguouselements[Fig. 1.1( )℄asindi atedbythe membershipve tor

c

, {c

n

∈ [0, Q − 1] ; n = 1, ..., N}

, whose

n

-thentry

c

n

= q

indi atesthemembershipof the

n

-tharrayelementtothe

q

-th luster. Sin e all the elements of the

q

-th luster are fed with the same ex itationmagnitude,

a

q

, and phase,

ψ

q

(θ

0

, ϕ

0

; f )

, whi h depends on the steering angle

(θ

0

, ϕ

0

)

and the working frequen y

f

, the far-eld power pattern radiated by the array is given by [9℄[10℄

P (θ, ϕ; θ

0

, ϕ

0

; f ) =







P

Q−1

q=0

{a

q

exp [jψ

q

(θ

0

, ϕ

0

; f )]

P

N−1

n=0

δ

qc

n

E

n

(θ, ϕ; f ) exp j

2π

λ

r

n

· ˆr

o



2

(2.1)

where

λ

is the wavelength at

f

,

δ

qc

n

is the Krone ker delta fun tion (

δ

qc

n

= 1

if

c

n

= q

and

δ

qc

n

= 0

otherwise), and

ˆr = sin (θ) sin (ϕ) ˆ

y

+ cos (θ) ˆz.

(2.2) Moreover,

r

n

= y

n

y

ˆ

+ z

n

ˆz

is the position of the the

n

-th (

n

= 1, ..., N

) array element, while

E

n

(θ, ϕ; f )

is the orresponding radiation pattern, whi h is a fun tion of the

M

-size ve tor of its geometri al des riptors

g

, {g

m

, m

= 1, ..., M} .

(2.3) Alongwith the far-eld powerpattern

P (θ, ϕ; θ

0

, ϕ

0

; f )

, the dire tivity pattern

D

(θ, ϕ; θ

0

, ϕ

0

; f ) =

4πP (θ, ϕ; θ

0

, ϕ

0

; f )

R

π

0

R

2π

0

[P (θ, ϕ; θ

0

, ϕ

0

; f ) sin (θ)] dθdϕ

(2.4)

and inparti ular,the dire tivityvalue alongthe steeringangle,

D

(θ

0

, ϕ

0

; f )

, has been onsidered in the synthesis pro ess as a fundamental metri of the

free-spa e performan e of the ar hite ture.

(a) (b)

PROBLEM

To design a 5G base station antenna, manifold free-spa e-based

obje -tives/requirements pertainingthe array pattern(i.e., sidelobe mask omplian y

for allthe steeringangles and withinthe whole frequen y band of interest) and

the array element radiation features (i.e., impedan e mat hing, isolation from

surrounding elements, polarization ellipti ity, gain, and beamwidth) must be

tted [3℄[40℄[14℄.

A ording toabove onsiderations, the synthesis athand turns out to

inher-entlybeaMMO problemwhenformulatedasthat ofofthe optimalsetupof the

unknown ve tors

n

c, a

_{, {a}

q

, q

= 1, ..., Q} , Ψ, g

o

su h that

{c, a, Ψ, g}

opt

= arg

min

{c, a, Ψ, g}

[Φ (c, a, Ψ, g)]

(2.5) where

Ψ

,



ψ

q

(θ

0

, ϕ

0

; f ) ; q = 1, ..., Q; θ

0

∈



θ

₀

min

, θ

max

₀



,

ϕ

0

∈



ϕ

min

0

, ϕ

max

0



, f

∈



f

min

_{, f}

max



(2.6) is the set of ex itation phases of the

Q

lusters in the ranges

f

∈



f

min

, f

max



,

θ

0

∈



θ

min

0

, θ

0

max



, and

ϕ

0

∈



ϕ

min

₀

, ϕ

max

₀



of the 5G requirements. Moreover,

Φ

(c, a, Ψ, g)

, {Φ

l

(c, a, Ψ, g) , l = 1, ..., L}

(2.7) is the MMO ost fun tion set omprising

L

terms en oding the synthesis obje -tives as follows

1

:

•

Array Sidelobe Mask Complian y Term (

l

= 1

):

Φ

1

(c, a, Ψ, g)

,

_(f

max

_−f

min

_)(ϕ

max

1

_−ϕ

min

_)(θ

max

_−θ

min

₎

×

×

R

_f

f

min

max

R

θ

max

₀

θ

min

₀

R

ϕ

max

₀

ϕ

min

₀

max

θ,ϕ

{R [P (θ, ϕ; θ

0

, ϕ

0

; f ) −

P

T

_{(θ, ϕ; θ}

0

, ϕ

0

; f )



dθ

0

dϕ

0

df

(2.8) where

P

T

_{(θ, ϕ; θ}

0

, ϕ

0

)

is the target sidelobe when the array is steered to-wards

(θ

0

, ϕ

0

)

and

R [·]

istheramp fun tion(

R [·]

, [·]×H [·]

,

H [·]

being the Heaviside fun tion);

•

Element Impedan eMat hing Term (

l

= 2

):

Φ

2

(c, a, Ψ, g) =

= Φ

2

(c, g)

,

R

f max

f min

R

[

|S

11

(f )|−

|

S

T

11

|]

df

(f

max

_−f

min

₎

(2.9) where

S

11

(f )

and

S

T

11

arethesynthesizedand thetargetantennaree tion oe ient atthe input port atthe frequen y

f

,respe tively;

1

Forthesakeofnotation ompa tness,thedependen yof alltheradiationquantities(i.e.,

pattern,gain,sidelobe,ree tion oe ient,et .) ontheDoFsve tor

(c, a, Ψ, g)

isomitted hereinafter.

•

Element Polarization Term (

l

= 3

):

Φ

3

(c, a, Ψ, g) = Φ

3

(c, g)

,

R

f

max

f

min



ε

(f ) − ε

T



2

_df

(f

max

_{− f}

min

₎

where

ε

(f )

and

ε

T

arethe synthesized andthe targetantennapolarization

ellipti ity angle atthe frequen y

f

, respe tively;

•

Element Beamwidth Terms (

l

= 4, 5

):



























Φ

4

(c, a, Ψ, g) =

= Φ

4

(c, g)

,

R

f max

f min

R

[

W

AZ

(f )−W

T

AZ

]

df

(f

max

_−f

min

₎

Φ

5

(c, a, Ψ, g) =

= Φ

5

(c, g)

,

R

f max

f min

R

[

W

EL

(f )−W

T

EL

]

df

(f

max

_−f

min

₎

(2.10) where

W

AZ

(f ) =





arg min

ϕ∈[0,ϕ

M

]







E(θ

M

,ϕ;f )

E(θ

M

,ϕ

M

;f )

− 0.5





 −

arg min

_ϕ∈

_[

₋

π

2

,ϕ

M

]







E(θ

M

,ϕ;f )

E(θ

M

,ϕ

M

;f )

− 0.5













(2.11) and

W

EL

(f ) =





arg min

θ∈[θ

M

,π]







E(θ,ϕ

M

;f )

E(θ

M

,ϕ

M

;f )

− 0.5





 −

arg min

θ∈[0,θ

M

]







E(θ,ϕ

M

;f )

E(θ

M

,ϕ

M

;f )

− 0.5













(2.12)

are the antenna half-power beamwidths in azimuth and elevation, while

W

T

AZ

and

W

T

EL

the orrespondingtargetvalues, being

θ

M

=

π

2

, ϕ

M

= 0

the element

broadsidedire tion,and

E

(θ, ϕ; f ) =

1

N

P

N

−1

n=0

E

n

(θ, ϕ; f )

istheaverageelement fa tor;

•

Element Realized Gain Term (

l

= 6

):

Φ

6

(c, a, Ψ, g)

,

=

R

f max

f min

R



G

T

₋

4πκ1(f)κ2(f)E

(

θM,ϕM;f

)

R 2π

0

R π

0 [E(θ,ϕ;f ) sin(θ)]dθdϕ



df

(f

max

_−f

min

₎

(2.13) where

G

T

is the target realized gain value, while

κ

1

(f )

and

κ

2

(f )

are the average elemente ien y and the average mismat hfa tor, respe tively;

•

Element Isolation terms (

l

= 7, ..., L

):

Φ

l

(c, a, Ψ, g)

,

=

R

f max

f min

R

[

|S

k1

(f )|−

|

S

T

k1

|]

df

(f

max

_−f

min

₎

k

= l − 6; l = 7, ..., L

(2.14) where

S

k1

(f )

and

S

T

k1

are the synthesized and the target isolation oe- ients between the referen e antenna and its

k

-thneighborelement at the frequen y

f

,respe tively.

PROBLEM

Although5G standards have notyetbeen o iallypublished,aset offrequen y

bands have already been released [41℄, and guidelines regarding the envisaged

performan eandindi atorstobeoptimizedfor3Dbeamforming,a tiveantenna,

and massive MIMO systems have already been dis ussed [3℄[40℄[14℄[42℄. Thus,

owing to its full generality, the formulated design problem and the proposed

synthesis strategy willbeseamlessly exploitable/ ustomized a ording tofuture

Codesign Synthesis Strategy

In this Chapter, the odesign synthesis strategy of un onventional array

ar hi-te tures, featuring irregularly lustered ex itations and an elementary antenna

onsisting ofa avity-ba ked planar pat h stru ture witha spline-based ontour

[43℄[44℄[Fig. 2.1(a)-(b)℄isaddressed. The ombinationofspline- ontouredpat h

antennas[43℄[44℄with avity ba kinghas been hosen asitisexpe tedtoenable

awideexibility(when omparedtostandardgeometries[43℄[44℄)toaddressthe

5G MMO problem as well as to allow a low inter-element oupling with

te h-nologi ally simple and quite inexpensive stru tures. A ordingly, the proposed

odesign methodology is introdu ed and detailed. Following the No-free-lun h

Theorem[45℄,ad-ho sear hstrategiesaresele tedtoe ientlyaddresstheabove

5G design sub-problems. Namely,

•

asingle-obje tiveGeneti Algorithm(SO-GA)[50℄[32℄[46℄ featuringan in-novative integer oding of the variables and ad-ho operators for handling

the irregular lustering [Fig. 1.1( )℄.

and

•

a

ε

-MOEAapproa h [47℄[48℄ aimedatoptimizingthe shapeof the elemen-taryradiator [Fig. 2.1(a)-(b)℄to meet the 5G ele tri alrequirements (i.e,

inputimpedan e,beamwidth,isolation,polarization,et ....) when

embed-ded in a nite array and not alone or in an innite periodi arrangement

asusually done in the state-of-the-art literature.

Sele ted numeri alexamples, drawn fromanexhaustive designpro ess,are then

presented toassessthe advantagesandthe ee tivenessoftheproposed odesign

3.1 Codesign Methodology - Formulation

Solving the MMO problem in (2.5) with a single step pro edure is not feasible

be ause of the unavailability of ee tive and e ient MO optimization

strate-gies when

L

≥ 4

, the omplex and highly non-linear nature of the obje tive fun tions/termsin (2.7), and the large number of DoFs,

{c, a, Ψ, g}

, resulting in a too huge and omputationally untra table sear h spa e. To address su h

hallenges, the MMO problem in (2.5) has been split into two (still onne ted)

simplerones on erned with (i) the array design and (ii) the element synthesis.

However, solving the two problems is still a very hallenging task as it yield to

the derivation of ompletely new designs, both for the array and for the

ele-mentary radiator, with respe t to traditionalsolutions [2℄. Indeed, to the best

of the author's knowledge, (i) no methodologies exist that allow the ontrol of

the sidelobe prole of sub-arrayed layouts over wide s anning angles and

band-widthswhenthe ex itationmagnitudes andphases are jointly lustered and (ii)

spline- ontoured pat hes have never been designed in a 5G MMO s enario by

taking into a ount their intera tions with the surrounding elements in view of

the reliable base stationprototyping [43℄[44℄ 1

To address su h hallenges, the proposed odesign pro edure exploits the

om-binationof

•

asingle-obje tive (SO)array lusteringproblemwhere theDoFs omprise the lustering s heme

s

and the ex itation ve tors

a

and

Ψ

, the SO ost fun tionbeing dened, for a xed radiatorgeometry (

g

= g

), asfollows

Φ

SO

(c, a, Ψ)

, Φ

1

(c, a, Ψ, g) ;

(3.1)

•

aMMO radiatingelementdesignproblemwheretheDoFsarethegeometry parameters

g

,whiletheMMO ostfun tion,foraxedsetoftheremaining parameters (



c, a, Ψ

), is given by

Φ

M M O

(g)

,



Φ

l

c, a, Ψ, g

; l = 2, ..., L

.

(3.2)

Itisworthremarkingthat(3.1)and (3.2)are generallytightly oupledproblems,

buteven moreinthe5Gs enario, anda ordinglyanalternatetwo-step odesign

pro ess (Se t. 3.1.3) is onsidered by rst optimizing the ost fun tion

Φ

SO

(3.1) when

g

= g

(Array Clustering Phase - Se t. 3.1.1) and then (Antenna Element Synthesis Phase - Se t. 3.1.2)

Φ

M M O

(3.2) is minimized for a xed DoFs onguration



c, a, Ψ

(Fig. 3.1). 1

Conventionalspline- ontouredantennas havebeenproposedonlyforstand-alone

3.1.1 Array Clustering Step (Integer-Coded SO-GA)

In order to properly address the SO problem (3.1) of the Array Clustering

step, let us rst noti e that, for a given membership ve tor

c

and a xed setup of

g

(

g

= g

), the optimal values of the array ex itations in both amplitude,

a

, and phase,

Ψ

, for auser-spe ied frequen y

f

(

f

∈



f

min

, f

max



)and asteering dire tion(

θ

0

,

ϕ

0

)(

θ

0

∈



θ

min

₀

, θ

₀

max



,

ϕ

0

∈



ϕ

min

₀

, ϕ

max

₀



),are unique and they an be found by solving the following onvex problem [49℄

[a (c) , ψ (θ

0

, ϕ

0

; f ; c)]

opt

,

= arg min

a(c), ψ(θ

0

,ϕ

0

; f ; c)

[D (θ

0

, ϕ

0

; f )]

−1

s.t

P (θ, ϕ; θ

0

, ϕ

0

; f ) ≤ P

T

(θ, ϕ; θ

0

, ϕ

0

; f ) .

(3.3)

Indeed,

Φ

SO

[a (c) , ψ (θ

0

, ϕ

0

; f ; c)]

opt

= 0

. A ordingly, sin e the solution of the onvexproblem(3.3)isuniqueand it an befoundwithstate-of-the-art

on-vex programmingtools [49℄, itturns out that the DoFs of the Array Clustering

phaseare onlythe membershipsofthe arrayelementslisted inthe integer

mem-bershipve tor

c

and theoptimizationproblemathand anbe lassiedasaSO dis rete one.

Figure3.1: Flow hart of the proposed odesign strategy (yellowboxes highlight

As for the determinationof the unknown integer ve tor

c

, it annot be ignored that the hoi e of

c

(i.e., the type, the size, and the nature of the array lus-ters/tiles) signi antly impa ts on the osts of the resulting arrangements [9℄,

thus it annot be totallyfree and the designer must be allowed to spe ify what

lass/es of lusters(e.g., the sizes and/orthe shapes aswellas

ontiguous/non- ontiguous types) has/have to be used as building blo k/s for the arising 5G

ar hite ture. Therefore, the 5GArray Clustering problemis formulatedas that

of nding the best ombinationof

Q

lusters taken from an alphabet of

D

user-dened sub-arrays [39℄ su h that (2.8) is minimized.

Due to dis rete nature of the problem unknowns,

c

n

,

n

= 1, ..., N

, it would be quitenaturalto onsider asoptimization solver[50℄[51℄[52℄abinary GA [32℄[46℄

inwhi hthe membershipof the generi

n

-th array element,

q

,is en oded intoa stringof

⌈log

2

D⌉

bits [39℄. However, this hoi ewouldbenumeri allyinee tive sin e it would result in GA individuals with hromosomes of

⌈log

2

D⌉ × Q

bits (i.e.,proportionaltothe sizeof the alphabetandthe aperture)potentially

aus-ing GA onvergen e issues [50℄ be ause of their long length when implemented

for medium/large arrays as those in 5G appli ations. In order to prevent these

latter, an Integer-Coded SO-GA strategy is adopted hereinafter, the shape/size

hoi e of the

q

-th luster in the

p

-th (

p

= 1, ..., P

;

P

being the GA population size)GA individualatthe

i

-thiteration(

i

= 1, ..., I

;

I

beingthe maximum num-ber of GA iterations),

d

p,i

_,



_d

p,i

q

; q = 1, ..., Q

, being en oded in an integer

variable,

d

p,i

q

∈ [1, D]

thusredu ing theoverall lengthofthe hromosometo

Q

as wellas the dimension ofthe sear hing spa e from

2

(⌈log

2

D⌉×Q)

down to

D

Q

. The

pri e to pay for this hoi e isthe need to ustomize the standard GA operators

tosu h anInteger-Coded SO-GA.

More spe i ally (Fig. 3.1),

•

Mutation - If the

p

-th individual is sele ted for mutation (

η

being the mutationprobability),the

q

-thgeneofthe orresponding hromosome(i.e., the

q

-th tile of the

p

-th lustering solution) is randomly mutated with probability

µ

by setting

d

p,i

q

toa randomintegervalue inthe range

[1, D]

;

•

De oding (Array Tiling)-Atthe

i

-thiteration,ea hgene

d

p,i

q

(

q

= 1, ..., Q

) isrstly de oded intothe orresponding lustershape/size/orientation

a - ordingtoastrategyinspiredby[39℄and onsideringthe alphabetlook-up

table in Fig. 3.2. In short, the

p

-th lustered arrangement orresponding to the

p

-th GA individual at the

i

-th iteration,

c

p,i

, is generated by

pla -ingthe

Q

lusters within the aperturesu h that the rst tile islo ated in the top-rightedgeof the aperture,while the followingones are distributed

over the array surfa e through a ir ular ( lo kwise) pla ement by taking

into a ount the lo ation of already lustered elements and exploiting a

Figure 3.2: Sket h of the integer- oded SO-GA de oding te hnique for luster

pla ement.

•

CostFun tion Evaluation -The optimalex itations

[a (c

p,i

_{) , Ψ (c}

p,i

_)]

opt

of

the lustering s heme

c

p,i

are omputed by solving (3.3) with a standard

onvex programming tool [49℄ and the orresponding ost fun tion value

Φ

p,i

_SO

is determined by substituting

c

p,i

and

[a (c

p,i

_{) , Ψ (c}

p,i

_)]

opt

in (3.1),

Φ

p,i

SO

, Φ

SO

(c

p,i

, a

(c

p,i

) , Ψ (c

p,i

))

;

•

Convergen e Che k - The GA pro edure isiterateduntil either

i

= I

or





Φ

(I)

SO

−

P

I

i=I−b

I

Φ

(i)

SO







Φ

(I)

_SO

≤ τ

(3.4) where

Φ

(I)

SO

, min

p=1,...,P ;i=1,...,I



Φ

p,i

SO

is the ost fun tion value of the

globalbestindividualattheiteration

I

,while

I

b

and

τ

arethe onvergen e window and the onvergen e threshold, respe tively.

As for the Sele tion and Crossover operators, standard roulette-wheel

imple-mentationsand (integer- oded)single-point rossoverwith rossoverprobability

χ

are adopted [50℄.

It isworth pointing out that hoosing su han optimizationstrategy (i)enables

theusertoa-priori spe ify, bydeningthetilealphabet,the lustershapes

om-pliantwith the te hnologi al onstraints of the referen e 5G implementationas

itminimizesthe dimension of the sear h spa e,thus mitigatingthe onvergen e

issues of the optimization whenlarge apertures are of interest.

3.1.2 Antenna Element Synthesis Step (

ε

-MOEA)

As for the se ond step of the odesign pro ess, it onsists of a MMO

ontinu-ous optimization problem sin e it involves the joint minimization of

L

− 1

ost fun tion terms [i.e.,

Φ

M M O

(g)

- 3.2℄ to determine the optimal values of the ( ontinuous) geometri al parameters of the array element.

Akeyme hanismofthis pro eduralstep istheso- alledantennageometry

gen-erator (AGG),whi his responsible toen ode/de ode the shapeof the antenna

elementstartingfromthe orrespondingve torof geometri alparameters

g

[43℄. The requirements for su h an operator are that, on the one hand, a wide set

of stru tures should be modeled toallowthe explorationof dierent geometries

duringthe design phase[Fig. 2.1(a)℄and, onthe otherhand, a smallnumberof

des riptors,

M

, shouldbeenoughfor faithfullyidentifyingthe radiatorshape in order to keep low the dimensionality of the optimization problemthus avoiding

omplex and time-expensive sear hes in the sampling the sear h spa e looking

for the optimalsolution. A ording tothese inputs and following the guidelines

adoptedforthe designofstand-alonewidebandantennasystems[43℄,the hosen

AGG operator is the result of a ombination of parametri  and spline-based

des riptors used, the former, to des ribe the avity radius,

g

1

, and the avity height,

g

2

,aswellastheprobefeedpositioninthe

yz

-plane,

(g

3

, g

4

)

[Fig. 2.1(b)℄ and, the latter, toen ode omplex antenna ontours through spline urves with

M−4

2

ontrol points in the

yz

-plane,



g

m

, g

_m+

M −4

2



,

m

= 5, ..., M −

M−4

2

[Fig. 2.1(a)℄. Of ourse,su hamodellingwouldbeenough(atleastinprin iple)when

dealingwith stand-alone radiators[43℄, but itis unsatisfa tory when addressing

synthesis problems su h as that for 5G systems and, even more, when the

de-sign result is not limited to a lab- ontrolled experiment, but it must be lose

to the nal manufa turing, thus numeri ally predi ting real world impa ts and

guaranteeing a reliable working. More in detail, unlike the stand-alone design,

the solution of (3.2) must manage shape/size onstraints that vary depending

on the solution to the SO dis rete problem (3.1) iteratively arried out in the

odesign array lustering phase (Se t. 3.1.1). Moreover, the evaluation of the

mutual intera tionsamong nearby radiatorswhen arranged inanitearray

lay-out is mandatory (3.2), as well. To properly fa e with those di ulties, it is

needed to ouplethe AGG operator withanotherone [here alledSystem

Char-a terization (SC)operator℄abletomodeltheelementaryradiatorbytakinginto

a ount spa ing onstraints oming from the array lustering blo k and to

re-liably estimate the inter-element isolation/ oupling parameters by onsidering

the nite size of the nal arrangements, that is, without re urring to simplied

periodi models for the array stru ture. Towards this end, an extended nite