Ci a ion: Lahiani, M.A.; Raida, Z.;
Veselý, J.; Oli o á, J. P e-Design o
Mul i-Band Plana An ennas by
A i icial Neu al Ne wo ks.
Elec onics 2023,12, 1345. h ps://
doi.o g/10.3390/elec onics12061345
Academic Edi o : An onio Dou ado
Recei ed: 13 Feb ua y 2023
Re ised: 3 Ma ch 2023
Accep ed: 10 Ma ch 2023
Published: 12 Ma ch 2023
Copy igh : © 2023 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
elec onics
Communica ion
P e-Design o Mul i-Band Plana An ennas by A i icial
Neu al Ne wo ks
Mohamed Aziz Lahiani 1, Zbynˇek Raida 2,3 , Jiˇ íVeselý3and Jana Oli o á3,*
1Na ional Ins i u e o Applied Sciences and Technology, Tunis 625 00, Tunisia
2Facul y o Elec ical Enginee ing and Communica ion, B no Uni e si y o Technology, B no-K álo o Pole,
616 00 B no, Czech Republic
3Facul y o Mili a y Technology, Uni e si y o De ence, B no-S ˇ ed, 662 10 B no, Czech Republic
*Co espondence: [email p o ec ed]
Abs ac :
In his communica ion, a i icial neu al ne wo ks a e used o es ima e he ini ial s uc u e
o a mul iband plana an enna. The neu al ne wo ks a e ained on a se o selec ed no malized
mul iband an ennas cha ac e ized by ime-e icien modal analysis wi h limi ed accu acy. Using he
Deep Lea ning Toolbox in Ma lab, se e al ypes o neu al ne wo ks ha e been c ea ed and ained
on he sample plana mul iband an ennas. In he neu al ne wo k lea ning p ocess, sui able ne wo k
ypes we e selec ed o he design o hese an ennas. The ained ne wo ks, depending on he desi ed
ope a ing bands, will selec he app op ia e an enna geome y. This is u he op imized using
New on’s me hod in HFSS. The use o he neu al p e-design concep speeds up and simpli ies he
design o mul iband plana an ennas. The indings p esen ed in his pape will be used o e ine and
accele a e he design o plana mul iband an ennas.
Keywo ds:
mul i-band an ennas; eed- o wa d neu al ne wo k; cascade- o wa d neu al ne wo k;
p obabilis ic neu al ne wo k; ull-wa e analysis
1. In oduc ion
When designing a con en ional mul i-band plana an enna, a p ope pa ch geome y
has o be selec ed o ob ain esonan equencies in he eques ed ope a ional bands [
1
]. In
he nex s ep, a ull-wa e nume ical model o he an enna is de eloped in an elec omag-
ne ic simula o , and he model is op imized o mee he equi ed pa ame e s o he an enna
as accu a ely as possible.
A p ope an enna geome y is selec ed by a designe expe ienced wi h i . In his
communica ion, we ain a i icial neu al ne wo ks (ANN) o ep esen he designe ’s
expe ience. ANNs a e ained on a se o no malized mul i-band an ennas cha ac e ized
by modal analysis, which e icien ly p oduces app oxima e aining pa e ns. The modal
analysis i sel and he way o c ea ing aining se s a e desc ibed in Sec ion 2.1.
When designing a plana an enna on a p esc ibed subs a e o eques ed ope a ion
bands, no maliza ion ela ed o he wa eleng h in he subs a e is pe o med, and no mal-
ized esonan equencies a e mapped by ANN o he op imum an enna geome y. Fo
mapping, h ee ypes o ANN a e used:
•Feed- o wa d back-p opaga ion ANN [2].
•Cascade- o wa d back-p opaga ion ANN [3].
•P obabilis ic ANN [4].
In Sec ion 2.2, ANN a e b ie ly in oduced, and he p ocess o hei aining is desc ibed.
In Sec ion 3, we p esen a design example o illus a e he unc ionali y o he neu al
p e-design. Sec ion 4concludes he pape .
In he open li e a u e, se e al pape s on an ANN-enhanced an enna design ha e been
published. The pape s co e he ollowing opics:
Elec onics 2023,12, 1345. h ps://doi.o g/10.3390/elec onics12061345 h ps://www.mdpi.com/jou nal/elec onics
Elec onics 2023,12, 1345 2 o 11
•
On-line neu al syn hesis o adia ion pa e ns. In an a icle abou he design o a
cogni i e an enna a ay [
5
], he adia ion pa e n o a con o mal pa ch a ay has been
adap ed o a complex en i onmen by a p ope phasing o elemen s. A used deep
ein o cemen lea ning was based on an on-line ne wo k, which upda ed pa ame e s
o aining, and a a ge ne wo k, which calcula ed he loss unc ion exploi ing da a
om an expe ience pool. In a pape in es iga ing he syn hesis o con o mal phased
a ay an enna (PAA) pa e ns using deep syn hesis [
6
], he on-line ANN and he a ge
ANN c ea ed a andem ne wo k s uc u e ha minimized he di e ence be ween he
eques ed pa e n and he cu en one.
In he desc ibed app oaches, an enna geome ies a e ixed, and inpu signals a e
op imized o each eques ed adia ion pa e ns. In his communica ion, he neu al ne wo k
selec s he op imum shape o he pa ch o o m he op imum cu en dis ibu ion ela ed o
mul iple esonances in he eques ed ope a ional bands.
•
Black-box modeling o an enna s uc u es. Compu e p ocessing uni (CPU)- ime
mode a e ANNs a e ained o app oxima e he esul s o CPU- ime expansi e ull-
wa e analysis o e a limi ed de ini ion space. This app oach can be applied bo h o
canonical s uc u es [
7
] and ad anced ones. A pa ch an enna wi h a g ound plane
de ec ed by spli - ing esona o s was modeled by a mul i-laye pe cep on and op i-
mized by a pa icle swa m algo i hm in [
8
]. A high-gain quasi-Yagi an enna wi h a
pa abolic e lec o was modeled by a py amidal deep eg ession ne wo k in [9].
Fo mul i-physics modeling o mic owa e il e s, he au ho s used a deep hyb id
neu al ne wo k [
10
]. The ne wo k was concei ed as a cascade o ANNs wi h di e en
pa ame e s. Fo esonan s uc u es like il e s, his modeling app oach was shown o
be bene icial.
Neu al black-box models usually ace he p oblem o su icien gene ali y and accep -
able accu acy being eached wi h easonable e o s [
11
]. A su icien ly gene al model
should co e a su icien ly la ge de ini ion space o an op imum dimension, which is
gi en by he numbe o s a e a iables. A su icien ly accu a e model usually equi es
ime-expansi e simula ions o aining pa e ns.
In o de o o e come hese di icul ies, we p opose an app oxima e classi ie ha
maps no malized ope a ion equencies o he op imum layou o an an enna elemen .
The de ini ion space is educed by wo king wi h no malized equencies and dimensions,
and he CPU ime needed o c ea e aining se s is minimized by using a ime-mode a e
modal analysis. I he p e-designed s uc u e is su icien ly accu a e, hen con en ional
local op imiza ion can be quick and inexpensi e.
•
An enna design by ANN and op imize . I he e icien and accu a e black-box model
is comple ed by an op imiza ion algo i hm, a simple design ool can be de eloped.
In [
12
], a pa ch is di ided in o pixels. The shape o he pa ch is syn hesized by
combining a con olu ional ANN in he ole o a o wa d model (geome y a he inpu
and pe o mance a he ou pu ) and a gene ic algo i hm in he ole o he op imize .
The desc ibed app oach can be used e en o a mul i-objec i e design o an ennas.
In [
13
], a deep neu al model was combined wi h Thomson sampling o e icien mul i-
objec i e op imiza ion o e eal he Pa e o on o op imal solu ions.
In [
14
], plana ul a-wideband an ennas we e designed by combining deep s uc u es
( he cascade o an ex eme lea ning machine, a deep belie ne wo k, and a es ic ed
Bol zmann machine) and a pa icle swa m op imiza ion as a global op imize .
Since p ope ly ained ANNs can p o ide he esponse e y quickly (only a ew
a i hme ic ope a ions a e needed o be execu ed in pa allel), neu al models a e ad an-
ageous when combined wi h e olu iona y algo i hms [
15
,
16
], swa m-in elligence ap-
p oaches [
17
,
18
], and o he CPU- ime expensi e global op imize s. Bu he ques ion o he
de elopmen o a su icien ly gene al and su icien ly accu a e neu al model emains.
The app oach p esen ed in his communica ion is based on neu al classi ie s. A pu e
classi ica ion o plana mic owa e il e s was p esen ed in [
19
]. A he inpu o a deep
Elec onics 2023,12, 1345 3 o 11
ne wo k, a bi map wi h a pho o o he il e was in oduced. ANN classi ied he il e as a
low-pass o band-pass one and de e mined he o de o he il e .
In [
20
], he classi ie conside ed he eques ed gain, impedance bandwid h, and ope a-
ion equency and selec ed among a pa ch an enna, a spi al an enna, o a ho n an enna.
Then, he selec ed an enna was designed by an in e se neu al model ha mapped e-
ques ed an enna pa ame e s o an enna dimensions. An enna geome ies we e gi en, and
dimensions we e compu ed.
In he p esen ed app oach, he ope a ional equencies o a plana mul iband an enna
a e mapped by he ained neu al ne wo k o he op imum no malized geome y o he
pa ch. Consecu i ely, he selec ed geome y is modeled in he High F equency S uc u e
Simula o (HFSS) and op imized by he New on algo i hm. Thanks o he success ul p e-
design, he local op imiza ion is su icien , and a low numbe o i e a ion s eps
is equi ed
.
This p o ides u he accele a ion o he an enna s uc u e design. Acco ding o ou
knowledge, he desc ibed exploi a ion o ANN o he an enna p e-design has no been
p esen ed in he open li e a u e ye .
2. Me hods
We in end o c ea e an e icien ool o he design o plana mul i-band an ennas.
In o de o ensu e a su icien design e iciency, we use a classi ie o he selec ion o an
op imal no malized an enna geome y, which is he i s s ep. Second, he geome y is
deno malized, aking in o accoun he wa eleng h o he used subs a e, and a ull-wa e
HFSS model is de eloped. Finally, he model is op imized by he local New on op imize
in a ew s eps.
In he ollowing pa ag aphs, he indi idual design s eps a e desc ibed in de ail.
2.1. T aining Se s by Modal Analysis
The no malized an enna geome ies conside an ai subs a e wi h he dielec ic
cons an
ε
= 1, negligible loss an
δ
= 0, and a hickness o h= 1 mm. Since he co esponding
wa eleng h is
λ0
= 300 mm, we c ea e a se o slo ed pa ches wi h he undamen al
dimension 150 mm ×150 mm.
Geome ies o aining pa e ns a e depic ed in Figu e 1, wi h pixel dimensions o
5 mm
×
5 mm. The g een pixels ep esen me alliza ion (a pe ec elec ic conduc o in
an app oxima ion, a s anda d coppe oil in an implemen a ion), and he whi e pixels
ep esen an unco e ed subs a e.
The size o he pa ch is ixed a 30
×
30 pixels excep o he ex ended pa ch an enna
(Figu e 1b). The wid h o slo s is ixed a 1 pixel, excep o he squa e slo (Figu e 1i).
T aining geome ies a e going o co e he mos impo an mechanisms o exci ing
mul i-band beha io :
•
The con en ional pa ch (Figu e 1a) plays he ole o e e ence. The mul i-band beha io
co esponds o he highe modes o he pa ch. The ex ended pa ch an enna (Figu e 1b)
can be unde s ood as a con en ional pa ch wi h a capaci i e p olonga ion [21].
•
The L-slo an enna (Figu e 1c) ep esen s pa ches wi h a wo-segmen slo ha b eaks
he pa ch edge in o wo pa s. The cu en s in bo h sub-a eas o he pa ch a e gal ani-
cally connec ed [21].
•
The U-slo an enna (Figu e 1d) ep esen s pa ches wi h a h ee-segmen slo ha
b eaks he pa ch edge in o wo pa s. The cu en s in bo h sub-a eas o he pa ch a e
sepa a ed [21].
•
The T-slo an enna (Figu e 1e) can be unde s ood as a olded slo dipole ed by a
coplana wa eguide (CPW) [
22
]. A magne ic cu en lowing in he slo loop is he
sou ce o he adia ion.
Elec onics 2023,12, 1345 4 o 11
Elec onics 2023, 12, x FOR PEER REVIEW 4 o 12
• The T-slo an enna (Figu e 1e) can be unde s ood as a olded slo dipole ed by a
coplana wa eguide (CPW) [22]. A magne ic cu en lowing in he slo loop is he
sou ce o he adia ion.
The double-U an enna, he G an enna, and he H an enna a e pa ches wi h slo s in-
side he an enna elemen . These slo s di ec ly in luence he cu en dis ibu ion on he
pa ch and he mul iband beha io o he pa ch. The double-U an enna (Figu e 1 ) consis s
o a la ge adia o ( he whole pa ch) and a small one ( he a ea inside slo s), which de ine
wo ope a ional bands [21]. The G an enna (Figu e 1g) di ides he pa ch in o an in e nal
a ea and wo ex e nal ones, po en ially o e ing a iple-band ope a ion [23]. In he case o
a non-symme ically loca ed non-symme ical H slo (Figu e 1h), mo e han h ee bands
can be c ea ed [24]. Finally, a squa e slo (Figu e 1i) c ea es he equi alen o a loop an-
enna [25].
(a) (b) (c)
(d) (e) ( )
(g) (h) (i)
Figu e 1. T aining geome ies o no malized mul i-band pa ches: (a) con en ional pa ch, (b) ex-
ended pa ch, (c) L-slo pa ch, (d) U-slo pa ch, (e) T-slo pa ch, ( ) double U-slo pa ch, (g) G-slo
pa ch, (h) H-slo pa ch, and (i) squa e-slo pa ch. Pixel dimensions: 5 mm × 5 mm. G een: conduc i e
su ace; whi e: unco e ed subs a e.
Wi h a ying posi ions and dimensions o slo s, 60 aining layou s we e c ea ed.
Each layou was modeled in he pa ial di e en ial equa ion (PDE) ool o MATLAB [26]:
• Me allic pa s o he layou we e enclosed by Neumann bounda y condi ions.
• The sol e was se o e alua e eigenmodes.
Figu e 1.
T aining geome ies o no malized mul i-band pa ches: (
a
) con en ional pa ch, (
b
) ex ended
pa ch, (
c
) L-slo pa ch, (
d
) U-slo pa ch, (
e
) T-slo pa ch, (
) double U-slo pa ch, (
g
) G-slo pa ch,
(
h) H-slo
pa ch, and (
i
) squa e-slo pa ch. Pixel dimensions: 5 mm
×
5 mm. G een: conduc i e
su ace; whi e: unco e ed subs a e.
The double-U an enna, he G an enna, and he H an enna a e pa ches wi h slo s inside
he an enna elemen . These slo s di ec ly in luence he cu en dis ibu ion on he pa ch
and he mul iband beha io o he pa ch. The double-U an enna (Figu e 1 ) consis s o a
la ge adia o ( he whole pa ch) and a small one ( he a ea inside slo s), which de ine wo
ope a ional bands [
21
]. The G an enna (Figu e 1g) di ides he pa ch in o an in e nal a ea
and wo ex e nal ones, po en ially o e ing a iple-band ope a ion [
23
]. In he case o a
non-symme ically loca ed non-symme ical H slo (Figu e 1h), mo e han h ee bands can
be c ea ed [
24
]. Finally, a squa e slo (Figu e 1i) c ea es he equi alen o a loop an enna [
25
].
Wi h a ying posi ions and dimensions o slo s, 60 aining layou s we e c ea ed. Each
layou was modeled in he pa ial di e en ial equa ion (PDE) ool o MATLAB [26]:
•Me allic pa s o he layou we e enclosed by Neumann bounda y condi ions.
•The sol e was se o e alua e eigenmodes.
•Eigen alues we e conside ed wi hin he in e al <0; 5 ×104>.
Elec onics 2023,12, 1345 5 o 11
Since eigen alues a e equal o he squa ed wa e numbe , he ope a ional equencies
o an ennas can be e alua ed acco ding o [27]:
n=
c
2π√an(1)
whe e
n
is he n- h esonan equency o he an enna, co esponding o he n- h eigen alue
ancompu ed by he PDE ool, and cis he eloci y o ligh in acuum.
The nume ical model o he G-slo pa ch is depic ed in Figu e 2. Bounda ies (black
lines) a e associa ed wi h he Neumann bounda y condi ion. The dimensions o he pa ch
a e ixed. Posi ion and dimensions o he slo a e a ied by changing he coo dina es o
polygon e ices A h ough L.
Elec onics 2023, 12, x FOR PEER REVIEW 5 o 12
• Eigen alues we e conside ed wi hin he in e al <0; 5 × 10
4
>.
Since eigen alues a e equal o he squa ed wa e numbe , he ope a ional equencies
o an ennas can be e alua ed acco ding o [27]:
2
nn
c
a
π
=, (1)
whe e
n
is he n- h esonan equency o he an enna, co esponding o he n- h eigen-
alue a
n
compu ed by he PDE ool, and c is he eloci y o ligh in acuum.
The nume ical model o he G-slo pa ch is depic ed in Figu e 2. Bounda ies (black
lines) a e associa ed wi h he Neumann bounda y condi ion. The dimensions o he pa ch
a e ixed. Posi ion and dimensions o he slo a e a ied by changing he coo dina es o
polygon e ices A h ough L.
Figu e 2. Modal analysis o he G-slo pa ch an enna by he ini e-elemen me hod in he PDE ool
o MATLAB.
The h ee lowes modes compu ed by he PDE ool (Figu e 3) we e used o compose
a aining pa e n. O he aining pa e ns we e p epa ed in a simila way.
(a) (b)
(c)
Figu e 3. The lowes 3 modes o he G-slo an enna we e compu ed by he ini e-elemen me hod in
he PDE ool in MATLAB.
Figu e 2.
Modal analysis o he G-slo pa ch an enna by he ini e-elemen me hod in he PDE ool
o MATLAB.
The h ee lowes modes compu ed by he PDE ool (Figu e 3) we e used o compose a
aining pa e n. O he aining pa e ns we e p epa ed in a simila way.
Elec onics 2023, 12, x FOR PEER REVIEW 5 o 12
• Eigen alues we e conside ed wi hin he in e al <0; 5 × 10
4
>.
Since eigen alues a e equal o he squa ed wa e numbe , he ope a ional equencies
o an ennas can be e alua ed acco ding o [27]:
2
nn
c
a
π
=, (1)
whe e
n
is he n- h esonan equency o he an enna, co esponding o he n- h eigen-
alue a
n
compu ed by he PDE ool, and c is he eloci y o ligh in acuum.
The nume ical model o he G-slo pa ch is depic ed in Figu e 2. Bounda ies (black
lines) a e associa ed wi h he Neumann bounda y condi ion. The dimensions o he pa ch
a e ixed. Posi ion and dimensions o he slo a e a ied by changing he coo dina es o
polygon e ices A h ough L.
Figu e 2. Modal analysis o he G-slo pa ch an enna by he ini e-elemen me hod in he PDE ool
o MATLAB.
The h ee lowes modes compu ed by he PDE ool (Figu e 3) we e used o compose
a aining pa e n. O he aining pa e ns we e p epa ed in a simila way.
(a) (b)
(c)
Figu e 3. The lowes 3 modes o he G-slo an enna we e compu ed by he ini e-elemen me hod in
he PDE ool in MATLAB.
Figu e 3.
The lowes 3 modes o he G-slo an enna we e compu ed by he ini e-elemen me hod in
he PDE ool in MATLAB.

Elec onics 2023,12, 1345 6 o 11
As a esul , we ha e 60 iple s o esonan equencies o 60 pa ch layou s. Neu al ne -
wo ks a e ained o map iples o equencies on he inpu o he index o a co esponding
pa ch layou on he ou pu . De ails a e gi en in he nex pa ag aph.
2.2. ANN and T aining P ocess
We use neu al ne wo ks o map iple s o esonan equencies compu ed by he
modal analysis o he index o a co esponding pa ch layou . Hence, he ne wo ks ha e
h ee neu ons in he inpu laye and a single neu on in he ou pu laye . The inpu neu ons
simply dis ibu e signals o neu ons in he hidden laye . The ou pu neu on collec s signals
om neu ons in he hidden laye and p ocesses he signal using he ac i a ion unc ion [
1
].
In o de o selec op imal pa ch layou s, we used 3 ANNs om he Deep Lea ning
Toolbox o MATLAB [28]:
•Feed- o wa d back-p opaga ion ne wo k. Inpu pa e ns a e sequen ially in oduced
o inpu neu ons, he ANN esponse is compu ed, and he di e ence (an e o ) be ween
he ou pu and he esponse om he aining se is e alua ed. The e o p opaga es
back o he inpu and changes he se ings o neu ons o minimize he e o .
When implemen ing he ne wo k, we used TRAINLM as a aining unc ion, LEARNGND
as a lea ning unc ion, MSE as a pe o mance unc ion, and TANSIG as an ac i a ion
unc ion. T aining de ails a e gi en in Figu e 4a.
Elec onics 2023, 12, x FOR PEER REVIEW 7 o 12
(a) (b)
Figu e 4. T aining neu al classi ie s in he Deep Lea ning Toolbox o MATLAB: (a) eed- o wa d
back-p opaga ion ANN; (b) cascaded- o wa d back-p opaga ion ANN.
In o de o es he quali y o aining, ou an ennas di e ing om aining pa e ns
(Figu e 5) we e c ea ed and analyzed. Co esponding iple s o esonan equencies
we e in oduced o he inpu s, and ANN was asked o classi y he op imum layou :
• Feed- o wa d ANN succeeded wi h 61.2%/59.3%/41.2%/61.4%;
• Cascaded- o wa d ANN succeeded wi h 63.2%/52.3%/40.0%/46.0%;
• The p obabilis ic ANN ailed.
Since he eed- o wa d back-p opaga ion ne wo k showed he bes pe o mance, we
used his classi ie in u he es s.
Figu e 4.
T aining neu al classi ie s in he Deep Lea ning Toolbox o MATLAB: (
a
) eed- o wa d
back-p opaga ion ANN; (b) cascaded- o wa d back-p opaga ion ANN.
•
A cascade- o wa d back-p opaga ion ne wo k is simila o a eed- o wa d ne wo k,
bu includes connec ions om he inpu and e e y p e ious laye o he ollowing
laye s. The ne wo k accommoda es he nonlinea ela ionship be ween he inpu and
he ou pu bu does no elimina e he linea ela ionship in be ween.
Elec onics 2023,12, 1345 7 o 11
When implemen ing he ne wo k, we used TRAINSCG as a aining unc ion, LEARNGND
as a lea ning unc ion, MSE as a pe o mance unc ion, and LOGSIG as an ac i a ion
unc ion. T aining de ails a e gi en in Figu e 4b.
•
A p obabilis ic ne wo k con ains adial neu ons wi h a Gaussian ac i a ion unc ion in
he hidden laye . The ou pu laye sums con ibu ions o each class o inpu pa e ns,
p oducing a ec o o p obabili ies as he ou pu . The ans e unc ion o he ou pu
laye picks he maximum o hese p obabili ies and p oduces 1 o he co esponding
class. Fo o he classes, 0 is p oduced.
When implemen ing he ne wo k, we used NEWPNN o c ea e and ain he ANN.
In o de o es he quali y o aining, ou an ennas di e ing om aining pa e ns
(Figu e 5) we e c ea ed and analyzed. Co esponding iple s o esonan equencies we e
in oduced o he inpu s, and ANN was asked o classi y he op imum layou :
•Feed- o wa d ANN succeeded wi h 61.2%/59.3%/41.2%/61.4%;
•Cascaded- o wa d ANN succeeded wi h 63.2%/52.3%/40.0%/46.0%;
•The p obabilis ic ANN ailed.
Elec onics 2023, 12, x FOR PEER REVIEW 8 o 12
(a) (b)
(c) (d)
Figu e 5. Tes ing he geome ies o no malized mul i-band pa ches: (a) iangle-slo pa ch, (b) ci cu-
la slo pa ch, (c) single no ch pa ch, and (d) double no ch pa ch. Pixel dimensions: 5 mm × 5 mm.
G een: conduc i e su ace; whi e: unco e ed subs a e.
3. Design Example
In o de o demons a e he unc ionali y o he de eloped me hodology, we de-
signed a h ee-band an enna co e ing wi eless local a ea ne wo k (WLAN) channels:
• 802.11b/g/n/ax:
1
= 2.4 GHz;
• 802.11y:
2
= 3.6 GHz;
• 802.11j:
3
= 4.9 GHz.
The an enna should be designed o he subs a e ARLON 25N wi h ε
= 3.38, an δ =
0.0025, and a heigh h = 1.524 mm. Since he whole pa ch is assumed o be in he hal -
wa eleng h esonance a
1
= 2.40 GHz, we can e alua e he wa eleng h in he dielec ics
acco ding o [27]:
d
c
λ
ε
=
, (2)
whe e
= 2.4 GHz, c is he eloci y o ligh , and he dielec ic cons an equals o ε
= 3.38.
Nume ically, λ
d
= 68 mm, and he scaling ac o ela ed o he neu al model equals o n =
λ
d
/λ
0
= 68/300 = 0.227.
In oducing he iple o no malized equencies [2.4/2.4; 3.6/2.4; and 4.9/2.4] o he
inpu o he neu al classi ie , a G-slo an enna (Figu e 2) is ecommended as an op imum
s uc u e. The size o he pa ch W × L was 150 mm × 150 mm in he neu al model and 34.1
mm × 34.1 mm in he ecompu ed model.
The coo dina es o he e ices A h ough L o he polygonal slo (Figu e 2) p oduced
by he neu al classi ie a e gi en in Table 1. The dimensions we e ecompu ed using he
scale n = 0.227 (Table 1), and a nume ical model in HFSS was de eloped (Figu e 6).
Table 1. Coo dina es o e ices in he polygonal G slo in he pa ch depic ed in Figu e 2. Compa i-
son o he neu al model, he ecompu ed one, and he op imized one.
Neu al Ne wo k Recompu ed Op imized
Figu e 5.
Tes ing he geome ies o no malized mul i-band pa ches: (
a
) iangle-slo pa ch, (
b
) ci cula
slo pa ch, (
c
) single no ch pa ch, and (
d
) double no ch pa ch. Pixel dimensions: 5 mm
×
5 mm.
G een: conduc i e su ace; whi e: unco e ed subs a e.
Since he eed- o wa d back-p opaga ion ne wo k showed he bes pe o mance, we
used his classi ie in u he es s.
3. Design Example
In o de o demons a e he unc ionali y o he de eloped me hodology, we designed
a h ee-band an enna co e ing wi eless local a ea ne wo k (WLAN) channels:
•802.11b/g/n/ax: 1= 2.4 GHz;
•802.11y: 2= 3.6 GHz;
•802.11j: 3= 4.9 GHz.
Elec onics 2023,12, 1345 8 o 11
The an enna should be designed o he subs a e ARLON 25N wi h
ε
= 3.38, an
δ= 0.0025
, and a heigh h= 1.524 mm. Since he whole pa ch is assumed o be in he hal -
wa eleng h esonance a
1
= 2.40 GHz, we can e alua e he wa eleng h in he dielec ics
acco ding o [27]:
λd=
c
√ε (2)
whe e
= 2.4 GHz, cis he eloci y o ligh , and he dielec ic cons an equals o
ε
= 3.38.
Nume ically,
λd
= 68 mm, and he scaling ac o ela ed o he neu al model equals o
n=λd/λ0= 68/300 = 0.227.
In oducing he iple o no malized equencies [2.4/2.4; 3.6/2.4; and 4.9/2.4] o he
inpu o he neu al classi ie , a G-slo an enna (Figu e 2) is ecommended as an op imum
s uc u e. The size o he pa ch W
×
L was 150 mm
×
150 mm in he neu al model and
34.1 mm ×34.1 mm in he ecompu ed model.
The coo dina es o he e ices A h ough L o he polygonal slo (Figu e 2) p oduced
by he neu al classi ie a e gi en in Table 1. The dimensions we e ecompu ed using he
scale n= 0.227 (Table 1), and a nume ical model in HFSS was de eloped (Figu e 6).
Table 1.
Coo dina es o e ices in he polygonal G slo in he pa ch depic ed in Figu e 2. Compa ison
o he neu al model, he ecompu ed one, and he op imized one.
Neu al Ne wo k Recompu ed Op imized
A−70.0 25.0 −15.9 5.7 −13.4 4.7
B−60.0 25.0 −13.6 5.7 −11.6 4.7
C−60.0 65.0 −13.6 14.8 −11.6 13.3
D 0.0 65.0 0.0 14.8 0.5 13.3
E 0.0 0.0 0.0 0.0 0.5 −0.5
F−20.0 0.0 −4.5 0.0 −4.0 −0.5
G−20.0 5.0 −4.5 1.1 −4.0 0.6
H−5.0 5.0 −1.1 1.1 −0.6 0.6
I−5.0 60.0 −1.1 13.6 −0.6 12.1
J−55.0 60.0 −12.5 13.6 −10.5 12.1
K−55.0 20.0 −12.5 4.5 −10.5 3.5
L−70.0 20.0 −15.9 4.5 −13.4 3.5
Elec onics 2023, 12, x FOR PEER REVIEW 9 o 12
A −70.0 25.0 −15.9 5.7 −13.4 4.7
B −60.0 25.0 −13.6 5.7 −11.6 4.7
C −60.0 65.0 −13.6 14.8 −11.6 13.3
D 0.0 65.0 0.0 14.8 0.5 13.3
E 0.0 0.0 0.0 0.0 0.5 −0.5
F −20.0 0.0 −4.5 0.0 −4.0 −0.5
G −20.0 5.0 −4.5 1.1 −4.0 0.6
H −5.0 5.0 −1.1 1.1 −0.6 0.6
I −5.0 60.0 −1.1 13.6 −0.6 12.1
J −55.0 60.0 −12.5 13.6 −10.5 12.1
K −55.0 20.0 −12.5 4.5 −10.5 3.5
L −70.0 20.0 −15.9 4.5 −13.4 3.5
In he nume ical model, he pa ch was comple ed by a mic os ip eede and a wa e
po (Figu e 6). The an enna was simula ed in he equency ange o 1.5 GHz–5.0 GHz.
The impedance cha ac e is ics (Figu e 7a) showed ha esonance equencies a e shi ed.
Figu e 6. Nume ical model o he G-slo an enna in HFSS. The pa ch is comple ed by a mic os ip
eede and he wa e po .
In a consequen s ep, New on op imiza ion was un o shi esonances owa ds he
eques ed bands. A e he op imiza ion, pa ch dimensions we e 30 mm × 30 mm. The
e ices o he op imized slo polygon a e gi en in Table 1. The impedance cha ac e is ics
o he op imized an enna a e depic ed in Figu e 7b. Ob iously:
•
1
= 2.4 GHz is shi ed o 2.5 GHz and is no su icien ly deep.
•
2
= 3.6 GHz co esponds o a shallow minimum, while he deep one is a 3.5 GHz.
•
3
= 4.9 GHz is uned success ully wi h |S11| < −10 dB.
Figu e 6.
Nume ical model o he G-slo an enna in HFSS. The pa ch is comple ed by a mic os ip
eede and he wa e po .
In he nume ical model, he pa ch was comple ed by a mic os ip eede and a wa e
po (Figu e 6). The an enna was simula ed in he equency ange o 1.5 GHz–5.0 GHz. The
impedance cha ac e is ics (Figu e 7a) showed ha esonance equencies a e shi ed.
Elec onics 2023,12, 1345 9 o 11
Elec onics 2023, 12, x FOR PEER REVIEW 9 o 11
K −55.0 20.0 −12.5 4.5 −10.5 3.5
L −70.0 20.0 −15.9 4.5 −13.4 3.5
In he nume ical model, he pa ch was comple ed by a mic os ip eede and a wa e
po (Figu e 6). The an enna was simula ed in he equency ange o 1.5 GHz–5.0 GHz.
The impedance cha ac e is ics (Figu e 7a) showed ha esonance equencies a e shi ed.
Figu e 6. Nume ical model o he G-slo an enna in HFSS. The pa ch is comple ed by a mic os ip
eede and he wa e po .
In a consequen s ep, New on op imiza ion was un o shi esonances owa ds he
eques ed bands. A e he op imiza ion, pa ch dimensions we e 30 mm × 30 mm. The
e ices o he op imized slo polygon a e gi en in Table 1. The impedance cha ac e is ics
o he op imized an enna a e depic ed in Figu e 7b. Ob iously:
•
1
= 2.4 GHz is shi ed o 2.5 GHz and is no su icien ly deep.
•
2
= 3.6 GHz co esponds o a shallow minimum, while he deep one is a 3.5 GHz.
•
3
= 4.9 GHz is uned success ully wi h |S11| < −10 dB.
(a)
(b)
Figu e 7. Impedance cha ac e is ics o he G-slo an enna: (a) ini ial model, (b) op imized model.
In a consequen s ep, New on op imiza ion was un o shi esonances owa ds he
eques ed bands. A e he op imiza ion, pa ch dimensions we e 30 mm
×
30 mm. The
e ices o he op imized slo polygon a e gi en in Table 1. The impedance cha ac e is ics
o he op imized an enna a e depic ed in Figu e 7b. Ob iously:
• 1= 2.4 GHz is shi ed o 2.5 GHz and is no su icien ly deep.
• 2= 3.6 GHz co esponds o a shallow minimum, while he deep one is a 3.5 GHz.
• 3= 4.9 GHz is uned success ully wi h |S11| < −10 dB.
4. Resul s
In his communica ion, we ained a i icial neu al ne wo ks on he app oxima e esul s
o modal analysis. Neu al models mapped a iple o he lowes esonan equencies
o he co esponding layou o a pa ch. In o de o de elop su icien ly gene al neu al
models, an ena s uc u es we e no malized. In o al, 60 aining pa e ns we e c ea ed
using 9 an enna layou s.
In MATLAB’s Deep Lea ning Toolbox, we c ea ed a eed- o wa d ANN, a cascaded-
o wa d ANN, and a p obabilis ic ANN. On ou an enna layou s, which we e no included
in he aining se s, he unc ionali y o neu al classi ie s was es ed. Whe eas he p oba-
bilis ic ANN ailed, he eed- o wa d ANN showed ela i ely good esul s.
Using he eed- o wa d ANN, we ied o design a iple-band an enna co e ing
WLAN bands 2.4 GHz, 3.6 GHz, and 4.9 GHz. The neu al model e u ned a G-slo an enna
as an op imum s uc u e. The no malized an enna was ecompu ed o he subs a e
ARLON 25N, and a co esponding HFSS model was de eloped. Due o he shi o
esonan equencies wi h espec o he eques ed ones, he an enna was op imized by he
New on algo i hm.
The op imized impedance cha ac e is ics a e close o he eques ed ones, bu he ma ch
is no pe ec . Ob iously, he concep o mul iband an enna p edesign by neu al classi ie s
can wo k, bu much mo e e o has o be de o ed o he composi ion o a la ge and mo e