Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 5
,
O
c
tob
e
r
201
6, p
p
. 2
300
~230
9
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
5.1
071
9
2
300
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Single Perceptron Model for
Smart Beam Forming in
Array Antennas
K. S
.
Se
nthilk
umar
1
, K
.
P
i
ra
pa
ha
ran
2
,
P.
R
.
P.
H
o
o
l
e
3
, H. R. H. Hool
e
4
1
Department of
Mathamatics an
d
Computer Science, Papua New
Guin
ea Univ
ersity
of
Technolog
y
,
PNG
2
Department of Electrical
and
C
o
mmuni
cations
Engineering, Papua New Guin
ea
University
of Technolog
y
,
PNG
3
Departm
e
nt
of
Ele
c
tri
cal
and
E
l
ectron
i
c Engin
e
ering,
Faculty
of
Engineering,
Un
iversiti
Mal
a
y
s
ia
Sarawak
,
Mal
a
ysia
4
Departm
e
nt
of
Ele
c
tri
cal
and
C
o
m
puter Engin
e
ering,
M
i
ch
igan
S
t
ate
Univers
i
t
y
,
US
A
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Apr 4, 2016
Rev
i
sed
Au
g 7, 201
6
Accepted Aug 28, 2016
In this paper
,
a single neuron
neural
n
e
twork
beamformer is proposed. A
percep
tron model is designed to optim
ize th
e
complex weights of a dipole
arra
y
antenn
a t
o
s
t
eer th
e be
a
m
to des
i
red di
rect
ions
. Th
e o
b
jec
tive
is
to
reduce the comp
lexity
b
y
using
a single n
e
uron n
e
ural
network
and utilize it
for adaptive b
e
amforming in array
antennas.
The selection o
f
nonlinear
activation function play
s th
e piv
o
tal ro
le in optimization dep
e
nd
s on whether
the weights are
real or complex. We
have appropriately
propos
ed two ty
p
e
s
of act
ivat
ion fun
c
tions
for r
e
s
p
ec
tive r
eal
and
co
m
p
lex weight v
a
lues
.
The
optimized r
a
diation patterns obtained
from the single neuron n
e
u
r
al network
are com
p
ared
with the res
p
e
c
tive opt
im
ized
radia
tion pa
tter
n
s
from
the
traditional Least
M
ean Square (LMS)
method. Matl
ab is used to optimize th
e
weights in neural network and LMS
me
thod as
well as display
the radiation
patterns.
Keyword:
Ad
ap
tiv
e array
Ada
p
tive beam
form
ing
Artificial n
e
u
r
al n
e
two
r
k
Sm
art antenna
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
K. S. Sent
hilkum
ar,
Depa
rt
m
e
nt
of
M
a
t
h
am
at
i
c
s and
C
o
m
put
er
S
c
i
e
nce,
Papu
a
New Guin
ea Un
iv
ersity of Tech
no
log
y
,
Lae 411,
PNG.
Em
a
il: k
ssk
u
m
ar16
@g
m
a
il.c
o
m
1.
INTRODUCTION
D
u
e to its br
o
a
d
r
a
ng
e
of
ap
plicatio
n
s
, ad
ap
tiv
e arr
a
y an
tenn
a is m
o
st popu
lar
i
n
t
h
e
p
r
esen
t
w
o
r
l
d.
Prese
n
t
wo
rl
d
appl
i
cat
i
o
ns re
qui
re m
u
ch faster beam
stee
ring that can
not be achie
ved using a
m
echanical
sy
st
em
s. Henc
e i
t
i
s
re
qui
re
d t
o
u
s
e m
o
re
co
nsi
s
t
e
nt
a
n
d m
u
ch
fast
er
el
ect
roni
c
bea
m
st
eeri
ng t
echni
que
s
su
ch
as ad
ap
ti
v
e
arrays. Howev
e
r, th
e
b
e
am
fo
r
m
in
g
with
al
m
o
st id
en
tic
al ele
m
en
ts res
u
lt lack
o
f
flexib
ility.
On t
h
e ot
her
h
a
nd
, ada
p
t
i
v
e
b
e
am
form
i
ng m
e
t
h
o
d
s
by
m
e
ans o
f
wei
g
ht
o
p
t
i
m
i
zat
i
on are capabl
e
of m
a
nagi
ng
th
e co
m
p
lex
ities of d
i
stin
ct ele
m
en
ts. Th
e ad
ap
tiv
e arra
y can
d
e
tect, track
an
d
all
o
cate
n
a
rrow
b
eam
s in
th
e
di
rect
i
o
n of
t
h
e desi
re
d us
ers whi
l
e
nul
l
i
ng u
n
wa
nt
ed
so
urces
o
f
i
n
t
e
rfe
re
nces. There
are wel
l
kn
o
w
n
trad
itio
n
a
l techn
i
qu
es
for ad
ap
tiv
e
b
eam
fo
rmin
g
in
array
an
tenn
a.
Soft
com
put
i
n
g t
e
c
hni
ques
nam
e
ly
Art
i
f
i
c
i
a
l
Ne
ural
Networks
(ANN), fuzzy l
o
gics, Ge
netic
Al
g
o
ri
t
h
m
s
(G
As)
,
pr
o
v
i
d
e l
o
w cost
sol
u
t
i
o
n
s
and r
o
bust
n
e
ss t
o
di
ffe
re
nt
com
p
l
e
x real
wo
rl
d p
r
obl
em
s. AN
N
is a p
o
werfu
l
in
fo
rm
atio
n
processin
g
p
a
rad
i
g
m
th
at tries t
o
sim
u
late th
e stru
cture an
d fu
n
c
tion
a
lities o
f
t
h
e
bi
ol
o
g
i
cal
ne
r
v
o
u
s sy
st
em
s. The
AN
N i
s
u
s
ed t
o
deal
wi
t
h
m
a
ny
appl
i
cat
i
ons, a
n
d t
h
ey
have
pr
o
v
e
d
t
h
ei
r
effective
n
ess i
n
se
veral re
sea
r
ch a
r
eas s
u
c
h
as im
ag
e
reco
g
n
i
t
i
on, speec
h reco
g
n
i
t
i
on, si
gnal
a
n
al
y
s
i
s
, pr
ocess
co
n
t
ro
l, an
d
rob
o
tics. Th
e true p
o
wer of n
e
ural n
e
two
r
k
s
lies in
th
eir ab
ility to
rep
r
esen
t b
o
t
h
lin
ear and n
o
n
-
l
i
n
ear
rel
a
t
i
ons
hi
ps
.
AN
N,
l
i
k
e
hum
an l
ear
ni
n
g
, l
e
a
r
n
s
b
y
exam
pl
e. Tr
ai
ni
ng
a
ne
ura
l
net
w
or
k i
s
, i
n
m
o
st
cases, a
n
e
x
e
r
ci
se i
n
n
u
m
e
rical
o
p
t
i
m
i
zati
on
of
a
us
ual
l
y
no
nl
i
n
ea
r
fu
nc
t
i
on.
B
a
si
c b
u
i
l
di
ng
bl
oc
k
of
eve
r
y
artificial n
e
ural n
e
twork is an
ar
tificial n
e
uron
o
r
p
e
rcep
t
r
on th
at is a sim
p
le m
a
th
em
a
tical
m
o
d
e
l.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
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0
8
Si
n
g
l
e
Perce
p
t
r
on
M
odel
f
o
r
Sm
art
Be
a
m
F
o
rmi
n
g
i
n
Arr
a
y Ant
e
nn
as (
K
.
S.
Se
nt
hi
l
k
um
ar)
2
301
M
a
ny
resea
r
ch
ers ha
ve
bee
n
usi
n
g
Neu
r
al
Net
w
or
k m
e
tho
d
s i
n
ant
e
n
n
a ar
ray
si
g
n
a
l
pr
ocessi
n
g
.
Neu
r
al
net
w
o
r
ks are
use
d
i
n
adapt
i
ve ant
e
nna
si
g
n
al
p
r
o
cessi
ng
[
1
]
-
[
2
]
beca
use o
f
t
h
ei
r ge
neral
pu
rp
os
e
nat
u
re, fa
st
co
nve
r
g
ent
rat
e
a
nd l
a
r
g
e scal
e
i
n
t
e
grat
i
o
n i
m
pl
em
ent
a
t
i
ons. The g
o
al
o
f
n
e
ural
net
w
or
k
t
r
ai
ni
n
g
i
s
t
o
m
i
nim
i
ze t
h
e di
ffe
renc
e bet
w
een
out
put
dat
a
an
d t
h
e t
a
rget
dat
a
.
Neur
al
net
w
o
r
k t
ech
ni
q
u
es
hav
e
ad
v
a
n
t
ag
es such
as non
lin
ear
p
r
o
p
e
rty, ad
ap
tiv
e lear
n
i
n
g
cap
ab
ility, and
fast conv
erg
e
n
ce rates. Th
ese
characte
r
istic adva
ntage
s
of t
h
e
neural net
w
ork e
n
courag
e
u
s
to u
s
e in
adap
tiv
e
b
eam
fo
rmin
g
.
Id
en
tifyin
g
th
e
in
h
e
ren
t
g
a
ins o
f
n
e
u
r
al
n
e
t
w
o
r
k
s
,
a nu
m
b
er o
f
litera
tu
res are av
ailab
l
e
o
n
n
e
ural n
e
t
w
ork
b
a
sed mo
d
e
l t
o
calculate the
weights
of an ad
ap
tiv
e ar
r
a
y anten
n
a
[3
]-
[6
].
A co
m
p
lex
m
u
l
tilayered
Rad
i
al Basis Fun
c
tio
n
Neural Netwo
r
k
(RBFNN) is
p
r
op
o
s
ed
to
success
f
ully exa
m
ine the adap
tive beam
forming of nea
rfi
eld Ultra
W
i
de
band (UWB)
array [7]. T
h
e authors
claim
e
d that
RBFNN m
e
thod is de
ri
ve
d from
regular theory, ha
s the
optim
a
l ap
proxim
ation ability
to
com
p
l
i
cat
ed fu
nct
i
o
n
s
an
d
ha
s a fast
er l
ear
n
i
ng s
p
ee
d com
p
are
d
t
o
gl
o
b
a
l
m
e
t
hods, s
u
c
h
as t
h
e M
L
P
wi
t
h
B
P
rul
e
.
Whe
r
e
t
h
ey
uses a ne
ural
net
w
o
r
k
w
i
t
h
num
ber o
f
no
des i
n
i
n
p
u
t
l
a
y
e
r, hi
d
d
en l
a
y
e
r and
out
pu
t
l
a
y
e
r
and
use
gen
e
t
i
c
al
go
ri
t
h
m
(GA)t
o
det
e
rm
i
n
e t
h
e n
u
m
b
er of
hi
d
d
en
ne
ur
o
n
s
.
M
oham
a
d [
8
]
has al
so ca
rri
e
d
o
u
t
a com
p
arative perform
a
nce analysis on stocha
stic
and GA al
g
o
ri
t
h
m
s
on sm
art
ant
e
nna
s fo
r dy
na
m
i
cal
ly
chan
gi
n
g
e
n
vi
r
onm
ent
.
A ne
ural
-f
uzz
y
based com
p
osi
t
e
t
echni
q
u
e
i
s
advo
cat
ed
t
o
desi
g
n
t
h
e
adapt
i
v
e
bea
m
for
m
er [9]
.
Whe
r
e t
h
e a
u
t
h
o
r
s
use
fee
d
fo
rwa
r
d
neu
r
al
net
w
o
r
k
f
o
r
t
r
ai
ni
n
g
t
h
e
we
i
ght
vect
o
r
s
fo
r di
ffe
rent
a
n
g
l
e o
f
in
cid
e
n
c
e o
f
t
h
e sign
al to
arriv
e
at th
e initial es
ti
m
a
te
o
f
th
e
weigh
t
s an
d
fi
n
e
tun
e
s th
e weigh
t
s till
th
e
max
i
m
u
m
sig
n
al o
u
t
p
u
t
po
wer is reach
e
d
.
Th
e
weigh
t
is
calcu
l
ated
in
each
iteration
till th
e erro
r is m
i
n
i
mized
and c
o
nve
r
g
en
ce of
wei
g
ht
i
s
achi
e
ve
d. T
h
ey
have s
h
o
w
n
th
at th
e co
nv
erg
e
n
ce ti
m
e
in
th
eir algo
ri
th
m
is
faster t
h
an th
e
LMS algo
rithm
s
u
s
in
g
sim
u
latio
n
.
Ho
we
ver
,
we
pro
p
o
se a si
ngl
e ne
ur
o
n
wei
g
ht
opt
i
m
izat
i
on m
odel
(SN
W
OM
) f
o
r ada
p
t
i
v
e
b
eam
fo
rm
in
g
in
sm
art an
ten
n
as b
y
carefu
lly selectin
g
th
e ap
pro
p
riate activ
atio
n
fu
n
c
tions to
m
a
tch
wit
h
th
e
desi
re
d
radi
at
i
o
n
pat
t
e
r
n
a
n
d
t
h
e di
pol
e l
o
ca
t
i
on.
2.
SINGLE
NE
URON WEIGHT OPTIMIZ
A
TION
MODE
L (SNWOM)
Here we
b
r
iefl
y d
e
scrib
e
th
e sin
g
l
e n
e
uro
n
m
o
d
a
l to
o
p
timize
th
e weigh
t
s wh
ich
will b
e
u
s
ed
i
n
adaptive
beamform
ing. In the
perce
p
tr
o
n
m
odel
as sho
w
n i
n
Fi
g
u
re 1
,
a si
ngl
e ne
u
r
o
n
wi
t
h
a l
i
n
ear wei
ght
e
d
net
f
unct
i
o
n a
n
d a t
h
resh
ol
d a
c
t
i
v
at
i
on f
u
nct
i
on al
s
o
kn
o
w
n
as t
r
ans
f
er
f
u
n
c
t
i
on i
s
em
pl
oy
ed. T
h
e m
odel
has
t
h
ree
part
s a
n
d
at
t
h
e fi
rst
pa
r
t
i
nput
s
(
x
1
, x
2
….,
x
n
) are m
u
ltip
lied
with
ind
i
v
i
du
al wei
g
hts (
w
1
, w
2
…w
n
). I
n
th
e seco
nd
p
a
rt
of sim
p
le p
e
rcep
tro
n
is th
e
n
e
t fun
c
tion
th
at
su
m
s
all weig
hted
inp
u
t
s and
b
i
as as:
n
k
k
k
x
w
b
z
1
(1
)
In
th
e
fin
a
l p
a
rt o
f
sim
p
le p
e
rcep
tron
th
e
su
m
o
f
p
r
ev
iou
s
ly weigh
t
ed
in
pu
ts and
b
i
as is p
a
ssi
ng
th
ro
ugh
a transfer
fun
c
tion
to
g
e
t th
e
ou
tpu
t
. In
case
of l
i
n
ear activ
ation
fu
n
c
ti
o
n
artificial n
e
u
r
on
is d
o
i
ng
sim
p
l
e
l
i
n
ear trans
f
orm
a
t
i
on ove
r t
h
e s
u
m
o
f
wei
g
ht
ed i
n
p
u
t
s
an
d bi
as
b
.
There i
s
n
o
si
ngl
e
best
m
e
t
hod
fo
r
no
nl
i
n
ea
r
opt
i
m
i
zat
i
on an
d i
s
base
d
o
n
t
h
e
c
h
ar
acteristics
of th
e prob
lem
t
o
b
e
so
lv
ed
.
Fi
gu
re
1.
Perce
p
t
r
on
m
odel
fo
r w
e
i
g
ht
o
p
t
i
m
i
zat
i
on
We si
m
p
lify th
e calcu
latio
n
co
m
p
lex
ity
to
red
u
ce th
e pro
c
essin
g
d
e
lay. Hen
ce
we h
a
ve u
s
ed
sing
le
n
e
uran
for th
is
p
r
ob
lem
an
d
a
n
o
n
lin
ear activatio
n
fun
c
tion
σ
to
find
o
u
t
the ou
tpu
t
y
as
when the
wei
ght
s are
real val
u
e.
y
σ
(z
)
Z
=
b
+
∑
Perceptron
x
1
x
2
x
3
.
.
x
n
1
W
1
W
2
W
3
.
.
W
n
b
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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08
I
J
ECE
Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
r
20
16
:
230
0
–
23
09
2
302
z
e
z
y
1
1
)
(
(2
)
Many ne
ural network arc
h
itectures
ge
nerall
y operat
e on real data. But there are m
a
ny applications
whe
r
e c
onsi
d
er
at
i
on o
f
c
o
m
p
lex i
n
put
s i
s
qu
i
t
e
desi
rabl
e. T
r
ai
ni
n
g
t
h
e
ne
ur
al
net
w
o
r
ks u
s
i
ng c
o
m
p
l
e
x i
n
put
s
was d
o
n
e usi
n
g t
ech
ni
q
u
es l
i
k
e t
h
e bac
k
-p
r
opa
gat
i
o
n,
Ho
pfi
e
l
d
m
odel
and
perce
p
t
r
o
n
l
earni
n
g
r
u
l
e
s.
Thei
r
per
f
o
r
m
a
nces were t
e
st
ed
u
s
i
ng t
h
e
pat
t
e
rn cl
assi
fi
cat
i
on
[1
0]
, si
g
n
a
l
proce
ssi
n
g
[
11]
an
d t
i
m
e seri
es
ex
p
e
rim
e
n
t
s and
its
g
e
n
e
ralizatio
n
cap
a
b
ility was
foun
d to
be satisfacto
r
y.
In com
p
l
e
x-
va
l
u
ed ne
u
r
al
ne
t
w
o
r
k
,
i
n
p
u
t
s
,
out
put
, t
h
res
h
o
l
d, an
d wei
g
ht
s are com
p
l
e
x val
u
es a
nd
selectin
g
activatio
n
fun
c
tio
n
is a ch
allen
g
i
ng
p
a
re. Becau
s
e o
f
th
e
n
e
u
r
al
n
e
two
r
k
’
s
ou
tstan
d
i
n
g
cap
a
bilit
y o
f
fittin
g
on
no
n-lin
ear m
o
d
e
ls
man
y
researches h
a
v
e
b
een
d
o
n
e
in
th
e recen
t
p
a
st
[12
]-[13
]. Ham
i
d
et al [14
]
h
a
v
e
stud
ied
new typ
e
s
o
f
co
m
p
lex
-
v
a
l
u
ed sig
m
o
i
d
activ
atio
n
fun
c
tio
n for m
u
lti-laye
red
n
e
u
r
al
n
e
twork.
Th
eir sim
u
lati
o
n
resu
lts proved
th
at th
ei
r pro
p
o
s
ed
n
e
tw
ork re
duced 54%
of testing time com
p
ared t
o
neural
net
w
or
k
uses
n
o
rm
al
si
g
m
oi
d
act
i
v
at
i
on
fu
nc
t
i
on as
gi
ven
b
e
l
o
w.
z
i
z
r
e
C
z
z
j
e
C
z
z
z
y
Im
Re
Im
1
Im
tanh
Re
1
Re
tanh
(3
)
The c
o
efficient
s
C
r
and
C
i
can be a
d
justa
b
le t
o
ac
hieve t
h
e
fast
o
p
tim
izat
io
n
with
h
i
gh ac
curacy. In
or
der t
o
t
r
ai
n t
h
e wei
g
ht
s t
o
m
eet
t
h
e desi
red o
u
t
p
ut
of
0
y
, t
h
e de
vi
at
i
on
Δ
i
s
obt
ai
ned a
n
d t
h
e wei
ght
s
are
iterated
un
til it reach
t
h
e trai
n
e
d m
ean
s erro
r
TMR
i
s
bel
o
w
t
h
e
pre
d
ef
i
n
ed
val
u
e.
W
h
ere
t
h
e
de
vi
at
i
on,
a
n
d
trained m
eans error as
below.
y
y
0
(4
)
100
*
0
y
TMR
(5
)
Also
t
h
e
weigh
t
s are adju
sted
in ev
ery iteratio
n
u
s
i
n
g t
h
e
de
vi
at
i
on a
n
d
t
h
e sel
ect
ed
l
earni
ng
rat
e
also known
as coefficient
0
k
as gi
ve
n bel
o
w:
i
i
i
x
k
w
w
0
(
6
)
The iteration is allowed eithe
r
it reaches the
TMR
b
e
lo
w
th
e
p
r
ed
ef
in
ed
v
a
lu
e
TMR
m
o
r
t
h
e defi
ne
d
m
a
xim
u
m
num
ber
N
o
f
i
t
e
rat
i
ons
.
The
S
N
WOM
wei
ght
opt
i
m
i
zati
on fl
owc
h
a
r
t
i
s
gi
ve
n i
n
Fi
g
u
r
e
2.
3.
AD
APTI
VE AR
R
A
Y
M
O
DEL
In ada
p
tive
array design, the
pl
acem
ent of
dipoles ca
n
be
any m
a
nner since the
curre
nt am
plitude
and
t
h
e
pha
se
coul
d
be ad
j
u
s
t
abl
e
t
o
get
t
h
e desi
re
d
radi
a
t
i
on
pat
t
e
rns
.
Ho
we
ver
,
anal
y
t
i
cal
ly
we can s
h
o
w
t
h
at
fo
r any
a
r
bi
t
r
a
r
y
set
of
di
p
o
l
e
s arra
n
g
ed i
n
a st
rai
ght
l
i
n
e
wo
ul
d
pr
od
uce a
ra
di
at
i
on
pat
t
e
rn
t
h
at
i
s
symm
e
t
rical on both side
of t
h
e pla
n
e
whe
r
e
the di
poles
a
r
e
placed. As
a result, the
place
ment of
dipole
m
u
s
t
be c
h
o
s
en
ba
se
d
on
t
h
e
desi
re
d
radi
at
i
o
n
pat
t
e
rns
.
If t
h
e set
of
desi
red
ra
di
at
i
on
pat
t
e
rn
s
are sy
m
m
et
ri
cal
on
a
co
mm
o
n
ax
is t
h
en th
e d
i
p
o
l
es can b
e
p
l
aced
in th
at
co
mm
o
n
ax
is
wh
ere all th
e cu
rren
t co
m
p
on
en
ts will in
pha
se wi
t
h
di
f
f
ere
n
t
set
o
f
a
m
pli
t
ude
s wit
h
resp
ectiv
e rad
i
atio
n
p
a
ttern
s.
Altern
ativ
ely, wh
en
th
e
set o
f
d
e
sired
rad
i
atio
n
p
a
ttern
s are u
n
symmetrica
l
o
n
a co
mm
o
n
ax
is, th
e
p
l
ace
m
en
t o
f
d
i
p
l
o
e
s
will n
o
t
be in
a
com
m
on axis while the c
u
rre
n
t com
pone
nts
will be in di
fferent
phase
s a
nd am
plitudes. Conse
q
uently, the in
p
h
a
se an
d th
e d
i
fferen
t
ph
ase curren
t
co
mp
on
en
ts
w
ill resu
lt real and
co
m
p
lex
op
timized
weigh
t
v
a
lu
es,
respect
i
v
el
y
.
T
h
ere
f
o
r
e,
we h
a
ve p
r
o
p
o
se
d t
w
o t
y
pes
o
f
ac
t
i
v
at
i
on f
u
nct
i
ons
f
o
r
opt
i
m
izi
ng r
eal
an
d com
p
l
e
x
wei
g
ht
s. Acc
o
r
d
i
n
gl
y
,
we m
o
del
a gene
ral
set
up as sh
o
w
n
i
n
Fi
gu
re 3
wh
ere
n
num
b
ers of
dipoles are plac
e
d
arb
itrarily.
For the
arbitrary placem
ent of di
poles, the
c
u
rre
nts
w
ill be
differe
nt in
phase am
plitude and it ca
n
be
represe
n
ted by
com
p
lex curre
nt phas
o
rs. The respective
com
p
lex current
pha
sors of the dipoles are taken as
I
1
,
I
2
, a
n
d
I
n
. Hence the
electric field
(fa
r-
fi
el
d)
at
t
h
e o
b
ser
v
at
i
o
n
p
o
i
n
t
P coul
d be gi
ve
n as:
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Si
n
g
l
e
Perce
p
t
r
on
M
odel
f
o
r
Sm
art
Be
a
m
F
o
rmi
n
g
i
n
Arr
a
y
Ant
e
nn
as (
K
.
S.
Se
nt
hi
l
k
um
ar)
2
303
n
r
j
n
r
j
r
j
e
I
A
e
I
A
e
I
A
E
0
2
0
1
0
...
2
1
(7)
wh
ere
A
0
and
ar
e a cons
tan
t
and th
e
ph
as
e con
s
tan
t
,
r
e
s
p
e
c
t
ive
l
y.
S
u
bst
i
t
ut
i
n
g f
o
r
r
1
,
r
2
, a
n
d
r
n
i
n
t
e
rm
s o
f
t
h
e di
st
a
n
ce
f
r
o
m
ori
g
i
n
,
e
q
ua
t
i
o
n
(
7
) ca
n
b
e
si
m
p
l
i
f
i
e
d
to
:
si
n
cos
sin
cos
2
sin
cos
1
...
2
2
1
1
n
n
y
x
j
n
y
x
j
y
x
j
e
w
e
w
e
w
E
(8)
wh
ere
w
1
,
w
2
, a
n
d
w
n
ar
e the co
m
p
lex
w
e
i
g
h
t
s and
i
n
propor
ti
on
al t
o
the co
m
p
lex
curr
en
t
ph
aso
r
s
I
1
,
I
2
, and
I
n,
resp
ecti
v
e
ly
. To
ach
i
eve th
e
obj
ecti
v
e
of form
ing
a resultan
t
si
ng
le
b
e
am
, th
e
v
a
l
u
e
of the co
mp
l
e
x
wei
g
ht
s
w
1
,
w
2
, a
n
d
w
n
needs
to
be
op
tim
ized
su
ch
t
h
at t
h
e resu
ltan
t
fi
el
d m
u
st m
a
tch
e
d to
a
d
e
sired
si
ng
l
e
be
am
f
u
nct
i
o
n
f
. Thus
equ
a
ti
on (8) can
be
wr
i
tten as,
f
e
w
e
w
e
w
n
n
y
x
j
n
y
x
j
y
x
j
sin
cos
sin
cos
2
sin
cos
1
...
2
2
1
1
(9
)
Fi
gu
re 2.
T
h
e SN
WOM
wei
g
ht
o
p
t
i
m
i
zat
i
on
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
r
20
16
:
230
0
–
23
09
2
304
Fi
gu
re
3.
Sc
he
m
a
t
i
c
Di
agram
o
f
Di
p
o
l
e
Pl
ac
em
ent
4.
RESULTS
A
N
D
DI
SC
US
S
I
ON
4.
1.
Rea
l
Va
lue
Weig
hts
The
dipoles are placed
on a
straight lin
e by
fixing
the de
sired beam
function
f
as
2
cos
and
t
a
ki
ng t
h
e di
st
ance bet
w
ee
n
t
w
o el
em
ent
s
as hal
f
wavel
e
ngt
h,
we ha
ve
opt
i
m
i
zed t
h
e wei
g
ht
s f
o
r
fi
ve an
d
sev
e
n
elem
en
t
s
to
find
th
e
actu
a
l o
u
t
p
u
t
u
s
ing
th
e ab
ov
e SNWOM
m
o
d
e
l with
in
itial weig
h
t
s,
b
i
as and
learning rate also known as
coefficient. For training, we
have used di
ff
erent
an
gl
es
in the range of 0
0
to
36
0
0
.
D
u
ri
ng
t
h
e t
e
st
i
n
g
pr
oc
ess we
ha
ve
us
ed
di
ffe
re
nt
an
gl
es
in
th
e
rang
e
o
f
0
0
to
3
6
0
0
.Ha
v
i
n
g obt
ai
ne
d
t
h
e o
p
t
i
m
i
zed wei
g
ht
s aft
e
r c
o
n
v
e
r
ge
nce,
w
e
ha
ve
dra
w
n t
h
e r
a
di
at
i
o
n
pa
t
t
e
rns
usi
n
g
o
p
t
im
i
zed wei
ght
s an
d
co
m
p
ared
with th
e rad
i
atio
n
p
a
ttern
s of th
e d
e
sired
b
eam
fo
r fi
ve elem
ents ar
ray
as
s
h
ow
n i
n
t
h
e Fi
g
u
re
4.
The Perce
p
tron ge
nerate
d antenna beam
is
seen to closel
y
m
a
tch
with
th
e d
e
sired
b
eam with
wh
ich
it
is to
b
e
o
p
tim
ized
. The b
eam
is seen
to
g
i
v
e
th
e
max
i
m
u
m
rad
i
atio
n
in th
e
desired
d
i
rection
an
d
nu
ll po
in
ts th
at
m
a
t
c
h t
h
e des
i
red beam
s nu
l
l
poi
nt
s. T
h
e
beam
wi
dt
h i
s
wi
der
,
t
h
u
s
l
eadi
n
g t
o
som
e
i
n
t
e
rfere
nce
whe
n
receiving, as
well as a m
e
a
s
ure
of
power wastage
whe
n
tra
n
sm
itting. It
is see
n
tha
t
there is m
a
xim
u
m
radiation over
a wider a
r
ea than what is
requ
ired
b
y
th
e d
e
sired
b
eam
. Ho
wev
e
r, as sh
own
in
Figu
re
5, th
is is
rectified by increasing the
num
b
er of
elements from
five to seve
n, thus
getting
greate
r
accuracy at a cost. It
sh
ou
l
d
b
e
rem
e
m
b
ered
th
at wh
ereas m
o
st
mu
ltilayer n
e
u
r
al n
e
two
r
k
b
eam
form
ers as well as th
e o
p
tim
i
zatio
n
pr
oce
d
u
r
es t
h
a
t
use al
go
ri
t
h
m
s
such as t
h
e
l
east
m
ean sq
uare
m
e
t
hods
(
L
M
S
)
req
u
i
r
es
hea
v
y
com
put
at
i
onal
ti
m
e
an
d
m
e
mo
ry t
o
store m
u
ltilayer weights, fo
r in
stance, th
e
Percep
tron
requ
ires littl
e m
e
m
o
ry an
d g
i
v
e
s
fast
co
nve
r
g
en
ce whe
n
t
r
ai
ni
ng a
n
d ra
pi
d
g
e
nerat
i
o
n
of t
h
e beam
when i
n
o
p
e
r
at
i
on
o
n
l
i
n
e. The
bea
m
s of
Fi
gu
re
4 t
o
7 a
r
e
beam
s requi
red
t
o
c
o
m
m
uni
cat
e fr
om
t
h
e ju
nct
i
o
n
of
u
n
d
er
gr
o
u
n
d
t
u
n
n
el
s i
n
m
i
nes, as wel
l
as along the st
reets with
ve
hicles from
a base
st
at
i
on
beam
at
a j
unct
i
on
.
Fi
gu
re
4.
C
o
m
p
ari
s
on
o
f
R
a
d
i
at
i
on pat
t
e
r
n
b
e
t
w
een
opt
i
m
i
zed bea
m
and desi
re
d
beam
obt
ai
ne
d
by
S
N
W
O
M
wh
en
th
e nu
mb
e
r
of
ad
a
p
tiv
e a
r
r
a
y
ele
m
ents is five
Fi
gu
re
5.
C
o
m
p
ari
s
on
o
f
R
a
d
i
at
i
on pat
t
e
r
n
b
e
t
w
een
opt
i
m
i
zed bea
m
and de
si
red
beam
obt
ai
ne
d
by
S
N
W
O
M
wh
en
th
e nu
mb
e
r
of
ad
a
p
tiv
e a
r
r
a
y
ele
m
ents is seven
0.
2
0.
4
0.
6
0.
8
1
30
210
60
240
90
270
120
300
150
330
180
0
0
.
2
0
.
4
0
.
6
0
.
8
1
30
21
0
60
240
90
27
0
120
30
0
15
0
330
180
0
r
1
r
2
r
n
φ
P
x
y
x
1
x
2
x
n
y
1
y
2
y
n
Desire
d Beam
****
***
Optim
i
z
e
d Beam
Desire
d Beam
****
**
Op
tim
ize
d
Beam
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
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:
208
8-8
7
0
8
Si
n
g
l
e
Perce
p
t
r
on
M
odel
f
o
r
Sm
art
Be
a
m
F
o
rmi
n
g
i
n
Arr
a
y Ant
e
nn
as (
K
.
S.
Se
nt
hi
l
k
um
ar)
2
305
Si
m
ilarly, we
h
a
v
e
o
p
tim
ize
d
th
e weigh
t
s u
s
ing
stated
SNWOM. Th
e o
p
tim
ized
resu
lts are sh
o
w
n
for seve
n elements as in Figure 5.
As we
have exp
ected, with increa
sed num
ber
of elements, the ada
p
tive
array
beam
forming is very
m
u
ch close to
the
de
si
red
be
am
. Ho
we
ver t
h
e am
pl
i
t
udes
i
n
t
h
e
0
o
an
d
1
8
0
o
are
better in
five
ele
m
ents array
than seve
n el
e
m
ents arra
y t
h
at due t
o
the
chara
c
terstic
of t
h
e
desire
d bea
m
selected.
Fi
gu
re
6.
C
o
m
p
ari
s
on
o
f
R
a
d
i
at
i
on pat
t
e
r
n
b
e
t
w
een
opt
i
m
i
zed bea
m
and desi
re
d
beam
when
t
h
e
n
u
m
b
er
of ada
p
tive a
r
ray ele
m
ents is five
Fi
gu
re
7.
C
o
m
p
ari
s
on
o
f
R
a
d
i
at
i
on pat
t
e
r
n
b
e
t
w
een
opt
i
m
i
zed bea
m
and desi
re
d
beam
when
t
h
e
n
u
m
b
er
of ada
p
tive a
r
ray ele
m
ents is seve
n
In
order t
o
ha
ve the com
p
arison
betwee
n
accur
acy of weights optim
iz
ed from
SNWOM m
e
thod
with
th
e wei
g
hts o
p
timized
fro
m
trad
itio
n
a
l LMS m
e
th
o
d
, the weights are calculated for five elem
ents and
seve
n el
em
ent
s
array
ant
e
n
n
a
usi
n
g LM
S opt
i
m
i
zati
on.
The ra
di
at
i
on
pat
t
e
rns
fo
r fi
ve an
d seve
n
el
em
ent
s
opt
i
m
i
zed fr
o
m
LM
S
m
e
t
h
o
d
s a
r
e s
h
ow
n i
n
Fi
gu
re
6 a
n
d
Fi
gu
re
7,
res
p
e
c
t
i
v
el
y
.
C
o
m
p
ari
s
on
of
Fi
gu
re 4 an
d
Fi
gu
re 6
di
spl
a
y
s
t
h
at
t
h
e resul
t
s
obt
ai
ned
fr
om
SNWO
M
has bet
t
e
r
m
a
t
c
h t
h
an
L
M
S m
e
t
hod t
h
ou
g
h
si
gni
fi
ca
nt
di
ffe
rence
c
a
nn
ot
be
ob
ser
v
ed
bet
w
een
Fi
gu
re
5 a
n
d Fi
g
u
re
7
.
In o
r
der t
o
f
u
r
t
her t
e
st
t
h
e pr
eci
si
on o
f
t
h
e SN
WOM
m
e
tho
d
wi
t
h
va
ri
e
t
y
of desi
red f
unct
i
o
n,
we
sel
ect
a desi
re
d
f
unct
i
o
n as
[
1
5]
:
cos
2
cos
2
cos
cos
4
3
9
1
f
(1
0)
We o
p
t
i
m
i
ze
wei
g
ht
s by
t
a
k
i
ng t
h
e di
st
a
n
c
e
bet
w
een t
w
o
el
em
ent
s
as hal
f
wavel
e
ngt
h
for
fi
ve an
d
seve
n el
em
ents usi
n
g
SN
W
O
M
.
T
h
e
opt
i
m
i
zed radi
at
i
o
n patterns a
r
e
com
p
ared
w
ith th
e d
e
sired rad
i
atio
n
p
a
tter
n
s in Figu
r
e
8 and Figu
r
e
9 fo
r f
i
v
e
an
d sev
e
n elemen
ts, r
e
sp
ect
iv
ely.
W
e
ob
ser
v
e th
e clo
s
e m
a
tch
bet
w
ee
n de
si
re
d an
d
opt
i
m
i
z
ed ra
di
at
i
on
pat
t
erns.
It
i
s
evi
d
ent
fr
om
t
h
e resul
t
s
t
h
at
t
h
e
d
e
si
red
nar
r
o
w
beam
co
u
l
d
no
t b
e
ach
iev
e
d
u
s
i
n
g
5
ele
m
en
ts
m
o
d
e
l wh
ile it is f
easib
le with
7
ele
m
en
t
m
o
d
e
l. Th
erefo
r
e, it can
b
e
reco
g
n
i
zed t
h
a
t
t
h
e na
rr
o
w
d
e
si
red
beam
requi
re m
o
re n
u
m
ber of
di
p
o
l
e
el
em
ent
s
. T
h
e si
de
l
o
bes
of t
h
i
s
broa
dside ante
nna are relatively s
m
all, as
seen in Figure
8.
Whe
r
e this linear array an
tenna need to be us
ed as
a single beam
antenna, a
re
flector m
a
y be use
d
t
o
flip over t
h
e
unwanted
of
th
e two m
a
in
b
eam
s. Th
e
Per
c
ep
tr
on
b
e
a
m
f
o
r
m
in
g
m
e
th
od
pr
opo
sed
m
a
y w
o
r
k
with
an
y ch
ip-
b
ased
MI
M
O
tech
n
i
q
u
e
s, in
clu
d
i
ng
transm
it bea
m
form
ing, spatial
m
u
ltiplexing,
space-
tim
e block c
odi
ng and
cyclic delay diversity.
0
.
2
0
.
4
0
.
6
0
.
8
1
30
210
60
24
0
90
270
12
0
300
150
330
180
0
0.
2
0.
4
0
.
6
0
.
8
1
30
210
60
24
0
90
27
0
12
0
30
0
150
33
0
18
0
0
Desire
d Beam
****
***
Optim
i
z
e
d Beam
Desire
d Beam
****
***
Optim
i
z
e
d Beam
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
r
20
16
:
230
0
–
23
09
2
306
Fi
gu
re
8.
C
o
m
p
ari
s
on
o
f
R
a
d
i
at
i
on pat
t
e
r
n
b
e
t
w
een
opt
i
m
i
zed bea
m
and desi
re
d
beam
obt
ai
ne
d
by
S
N
W
O
M
wh
en
th
e nu
mb
e
r
of
ad
a
p
tiv
e a
r
r
a
y
ele
m
ents is five
Fi
gu
re
9.
C
o
m
p
ari
s
on
o
f
R
a
d
i
at
i
on pat
t
e
r
n
b
e
t
w
een
opt
i
m
i
zed bea
m
and desi
re
d
beam
obt
ai
ne
d
by
S
N
W
O
M
wh
en
th
e nu
mb
e
r
of
ad
a
p
tiv
e a
r
r
a
y
ele
m
ents is seven
Si
nce o
n
l
y
a singl
e Perce
p
t
r
o
n
i
s
used f
o
r b
e
am
form
i
ng, t
h
e t
echni
que i
s
fast
, and co
ul
d pr
o
v
i
d
e t
h
e
best
set
of ant
e
nna
pat
t
e
rns w
i
t
h
i
n
m
i
ll
i
s
econds
. Eve
n
t
h
o
u
g
h
,
t
h
e preci
si
on
of t
h
e SN
W
O
M
i
s
depen
d
i
ng
on
the dipole plac
e
m
ent and the
character
istics o
f
th
e
d
e
sired b
eam
selec
t
ed
, it is a fast, e
fficien
t and
si
m
p
l
e
m
e
t
hod f
o
r
t
h
e
wei
g
ht
o
p
t
i
m
i
zat
i
on
com
p
are
d
t
o
t
h
e
p
r
evi
ousl
y
pr
o
p
o
se
d neu
r
al
ne
t
w
o
r
k
base
d
a
d
apt
i
v
e
beam
form
i
ng m
e
t
hods
.
4.
2.
Co
mplex Va
lue Weig
hts
Whe
n
t
h
e
de
si
re
d
ra
di
ati
o
n
patte
rns
are
uns
y
mm
etrical on com
m
on a
x
i
s
the
n
t
h
e
pla
c
e
m
ent of t
h
e
di
p
o
l
e
s ca
n
n
o
t
be i
n
c
o
m
m
on a
x
i
s
a
s
di
sc
u
sse
d e
a
r
l
i
e
r. B
o
d
h
e et
al
[
1
6]
ha
ve
p
r
o
p
o
s
e
d a r
ect
a
n
g
u
l
a
r a
r
r
a
y
struct
ur
e to
prov
i
d
e so
l
u
ti
on
for
such
cond
iti
on. Ho
wev
e
r, it is po
ssi
b
le to
const
r
u
c
t an
array
wit
h
mi
n
i
mu
m t
h
r
e
e
e
l
e
m
e
n
ts
th
a
t
c
a
n
n
o
t
b
e
i
n
co
mmo
n
ax
is
wh
ich
w
i
ll
l
e
ad
to
co
mp
l
e
x
we
ig
h
t
v
a
l
u
e
s
.
Th
er
efor
e we
h
a
ve consi
d
ered t
h
e m
i
n
i
m
u
m
th
r
e
e al
ong
w
i
t
h
four and
si
x
el
em
en
t
arr
a
y
s
t
o
co
m
p
ar
e t
h
e
accur
acy of b
eam
for
m
in
g
as
shown in
Fi
gur
e 10
. The d
e
si
r
e
d
fun
c
t
i
on
is selected
as
0
sinc
f
t
o
form
a si
ngle be
am
, whe
r
e
0
is th
e
d
e
s
i
r
e
d ang
l
e.
Fi
gur
e
10
.
Schem
a
tic Diagr
a
m
o
f
Arr
a
y
M
o
d
e
l
s
(a)
Equ
i
l
a
ter
a
l
Tr
iangu
l
a
r M
o
d
e
l
,
(b
)
Squ
a
r
e
M
o
d
e
l
and
(
c
)
Regu
l
a
r H
e
x
a
gonal M
o
d
e
l
We ha
ve
opt
i
m
i
zed t
h
e wei
ght
s
fo
r t
h
r
ee and
fo
u
r
an
d s
i
x el
em
ent
s
t
o
di
sco
v
er t
h
e act
ual
out
pu
t
u
s
ing
th
e above SNWO
M mo
d
e
l w
ith
i
n
itial w
e
ig
h
t
s,
b
i
as an
d
learn
i
ng
rate also
k
nown
as co
efficient w
ith
th
e ap
pro
p
riate activ
atio
n
fu
n
c
tion
.
Th
e
rad
i
atio
n
p
a
ttern
in
Figu
re
11
shows th
e resu
lts ob
tain fro
m
con
d
u
ct
i
n
g
S
N
WOM
o
p
t
i
m
i
zat
i
on. T
h
e
ra
di
at
i
on
pat
t
e
rn c
o
m
p
ares t
h
e si
gni
fi
cant
of m
a
t
c
hi
ng
bet
w
ee
n t
h
e
d
e
sired
p
a
ttern and
th
e op
tim
i
zed
p
a
ttern.
0
.
2
0.
4
0.
6
0
.
8
1
30
210
60
240
90
270
120
30
0
150
330
18
0
0
0
.
2
0
.
4
0
.
6
0
.
8
1
30
210
60
240
90
270
120
30
0
150
330
180
0
Desire
d Beam
****
***
Optim
i
z
e
d Beam
Desire
d Beam
****
***
Optim
i
z
e
d Beam
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Si
n
g
l
e
Perce
p
t
r
on
M
odel
f
o
r
Sm
art
Be
a
m
F
o
rmi
n
g
i
n
Arr
a
y Ant
e
nn
as (
K
.
S.
Se
nt
hi
l
k
um
ar)
2
307
3
Elem
ents
4
Elem
ents
6 Elem
ents
Fi
gu
re
1
1
. C
o
m
p
ari
s
on
of
R
a
di
at
i
on
Pat
t
e
r
n
s
of
3
,
4 a
n
d
6 El
em
ent
s
usi
n
g
S
N
WOM
It
can
be o
b
se
rve
d
f
r
o
m
Fi
gure
1
1
that as
the num
b
er of elem
en
ts increases the
optimized bea
m
p
a
ttern
s h
a
v
e
better m
a
tch
to
t
h
e
d
e
sired
b
e
am
fro
m
th
ree to
fou
r
t
o
size ele
m
en
ts. In additio
n
to
b
eam
p
a
ttern
match
i
n
g
,
th
e
b
eam
wid
t
h
is
also
redu
ced
.
A n
a
rro
w
b
e
am wo
u
l
d
h
a
v
e
a g
r
eater co
v
e
rag
e
wh
ile u
tili
zin
g
less
powe
r as c
o
mpare t
o
a
n
Om
ni-directiona
l antenna.
H
o
weve
r t
h
e
co
m
p
l
e
x wei
ght
s
o
p
t
i
m
i
zed fr
o
m
LM
S
m
e
t
hod
fo
r t
h
e
sam
e
cases gi
ve s
upe
ri
o
r
m
a
t
c
h w
h
e
n
t
h
e
n
u
m
b
er o
f
el
em
ent
s
i
s
i
n
c
r
ease
d
as s
h
ow
n i
n
Fi
gu
re
12
. In t
h
i
s
pap
e
r we ha
ve co
m
p
ared wi
t
h
LM
S
m
e
t
hod f
o
r t
h
e fo
rm
at
i
o
n of a de
si
red
beam
usi
ng an
t
e
nna
-
b
a
sed
b
eam
fo
rmin
g
as op
po
sed
to
ch
ip-b
ased
b
eam
fo
rm
in
g
.
In
ch
ip
b
a
sed
b
eam
fo
rm
in
g
m
u
ltip
le b
eam
s
are
created that shoul
d constructively add to
get
h
er at the recei
ver (m
obile stati
on), thus re
quiring the rece
iver t
o
send
sign
als t
o
th
e
b
a
se station
tran
sm
it
ter to steer th
e b
eam
.
Wh
ere th
e receiv
e
r m
a
y h
a
ve m
u
lt
ip
le an
ten
n
a
s,
an am
biguity a
r
ises as to the specifi
c an
tenna th
at h
a
d
sen
t
a sig
n
a
l to
th
e tran
sm
i
tter. In th
e an
ten
n
a
based
beam
form
ing, reported
here
in, the
beam
form
er m
a
y
handle
both si
gnal receiver or
a single cl
uste
r
of
receivers in
one ge
om
etrical location,
or m
u
ltiple clusters or ante
nna
s
as in Figure
5 for i
n
stance
. The
position and velocity of the receiver (MS
)
a
n
tenna m
a
y
be determ
ined a well-establishe
d m
e
thod [17] whe
r
e
autom
a
tic beam steering is needed i
n
t
h
e ca
se of m
obi
l
e
re
cei
vers.
Th
us
t
h
e tra
n
sm
itter antenna
beam
may be
o
p
tim
ized
at th
e MS’s
present lo
catio
n,
rat
h
er t
h
a
n
t
h
e M
S
’s
pre
v
i
o
us l
o
c
a
t
i
on.
Fi
gur
e 12
.
C
o
m
p
ar
ison of
R
a
d
i
ati
o
n
Pattern
s of
3
,
4
and 6
El
em
en
ts u
s
i
ng
LM
S op
timizati
on
5.
CO
NCL
USI
O
NS
A sim
p
le, acc
urate and effic
i
ent approa
ch
to th
e p
r
o
b
l
e
m
of a
d
apt
i
v
e
b
e
am
form
i
ng w
a
s pr
o
pose
d
and i
m
pl
em
ent
e
d usi
ng
si
n
g
l
e neu
r
o
n
neu
r
al
net
w
or
k. T
h
e wei
ght
s
we
re o
p
t
i
m
i
zed u
s
i
ng
SN
WOM
wi
t
h
0.
2
0.
4
0
.
6
0
.
8
1
30
210
60
240
90
270
120
300
150
330
18
0
0
0.
2
0
.
4
0
.
6
0.
8
1
30
210
60
24
0
90
270
12
0
300
150
33
0
180
0
0
.
2
0
.
4
0
.
6
0
.
8
1
30
210
60
24
0
90
27
0
12
0
30
0
150
330
18
0
0
Desire
d Beam
Optim
ized Beam
******
0.
2
0
.
4
0
.
6
0
.
8
1
30
210
60
24
0
90
270
12
0
300
150
330
18
0
0
0
.
2
0.
4
0.
6
0
.
8
1
30
21
0
60
240
90
27
0
120
30
0
15
0
330
18
0
0
0
.
2
0
.
4
0
.
6
0
.
8
1
30
210
60
240
90
27
0
120
300
150
33
0
180
0
3 Elem
ents
4 Elem
ents
6 Elem
ents
Desire
d Beam
****
***
Optim
i
z
e
d Beam
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
r
20
16
:
230
0
–
23
09
2
308
app
r
op
ri
at
e act
i
v
at
i
o
n
f
unct
i
o
ns a
n
d c
o
m
p
ared
wi
t
h
t
h
at
o
f
t
r
a
d
i
t
i
onal
L
M
S m
e
t
hod
fo
r t
h
e
com
p
ari
s
on
o
f
per
f
o
r
m
a
nce. The ra
di
at
i
o
n
pat
t
e
rns
o
b
t
a
i
n
ed f
r
om
op
timized
weigh
t
s
were cl
o
s
e m
a
tch
with
the desired
rad
i
ation
p
a
ttern
s wh
en
th
e
weig
h
t
s co
effici
en
ts were real
b
u
t
it was
m
a
rg
in
ally
m
a
tch
e
d
for co
m
p
lex
weigh
t
coefficients.
It showe
d
that t
h
e ac
tiv
ation
fu
n
c
tion
s
select
ed
fo
r t
h
e co
m
p
l
e
x wei
ght
coef
fi
ci
ent
s
ha
ve n
o
t
fu
lly supp
orted th
e
o
p
tim
izat
i
o
n.
6.
FUTU
RE W
O
RK
Whe
n
t
h
e di
poles are
place
d in st
raight line alo
n
g
with
th
e selected d
e
sire
d beam,
the weight
coefficients turne
d
t
o
be
re
al values
.
For the
pr
esen
t
setu
p, th
e selected
n
o
n
lin
ear activ
atio
n fun
c
tio
n
match
e
d
v
e
ry
well and
wei
g
h
t
co
efficien
ts
co
u
l
d
b
e
op
tim
ised
easily. Howev
e
r, it will
n
o
t
b
e
th
e case in
real
tim
e
application where the
dipole pl
acem
ent and desire
d
beam
function
m
a
y not be as taken in this
m
odel
whe
r
e the expected weight coeffici
ent
s
w
oul
d be com
p
l
e
x val
u
es.
In
orde
r t
o
o
p
t
i
m
i
s
e co
m
p
l
e
x wei
g
h
coefficients, the prese
n
tly propos
ed
no
nl
i
n
ea
r act
i
v
at
i
on
fu
n
c
t
i
on m
a
y
not
be t
h
e m
o
st
sui
t
a
bl
e. The
r
ef
or
e, t
h
e
fut
u
re
w
o
r
k
c
a
n
be f
o
c
u
se
d
o
n
sel
ect
i
n
g
app
r
op
ri
at
e n
o
n
l
i
n
ear
act
i
v
at
i
on
fu
nct
i
o
n i
n
or
der t
o
opt
im
i
s
e
com
p
lex wei
g
hts coefficients.
REFERE
NC
ES
[1]
H. L. Southall,
et al.
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finding in
phased array
s
wi
th a
neural network
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[2]
A.
H.
E.
Zooghby
,
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[3]
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A. H. E. Zooghby
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N
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Y.
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[6]
J. L. Fournier
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M. Wang,
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[8]
J. R. Mohammed, “Compara
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h
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JECE)
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[9]
M. Anitha and
N. G. Kurahatti,
“Neural fuzz
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g,”
Internationa
l
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l
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vanced
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[10]
R. H
¨
a
n
sch and
O. Hellwich
,
“
C
lassifi
c
a
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e
tri
c
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y
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m
p
lex Valued
Neural Network
s
,”
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oceed
ings
of
I
S
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k
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hop
, Hannover
,
Ger
m
an
y
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[11]
M. S. Kim and C. C. Gues
t, “Modification of B
a
ck-propagation f
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r co
mplex-valu
ed-signal pro
ces
sing in frequen
c
y
domain,”
Intern
ational
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t Co
nference on
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r
alNetworks
, (San Diego, CA), p
p
. III-27–III-31
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[12]
T. Kim
and
T.
Adali, “Full
y
co
m
p
lex m
u
lti-layer
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cept
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on network for non-li
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Journal of
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l. 32,
pp. 29-43
, 2002
.
[13]
H. E. M
i
chel
,
et al.
, “
A
rtif
ici
a
l
Neural Network
s
using Com
p
lex
number and Phase encod
e
d w
e
ights – Electro
n
ic
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em
entat
i
ons
,”
In
ternational jo
int
confer
en
ce on N
e
ural Networks
, 2006.
[14]
A.
Hamid,
et al.
,
“
N
ew activat
ion
functions
for co
mplex-valued n
e
ural network
,
”
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n
ternational
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r
nal of Physica
l
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ces
, vol/issue: 6(7)
, pp
. 176
6-1772, 2011
.
[15]
P.
R.
P. Hoole,
“S
ma
rt
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m
unication
,
”
Biomedical and Radar Systems, W
I
T
Pre
ss,
UK
, 2001
.
[16]
S. K. Bodh
e,
et a
l
.
, “Beamf
o
rming Techn
i
q
u
es for Smart
Ante
nnas using
Rectangular A
rray
Structure,”
International Jo
urnal of
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and Computer Engin
eering
(
I
JECE)
, vol/issue:
4(2), pp
. 257-26
4, 2014
.
[17]
X. Wang,
et al.
, “An electrom
a
gneti
c-tim
e delay
m
e
thod for determ
in
ing the p
o
sitions and vel
o
citi
es of m
obil
e
stations in
a GSM network,” J
A Kong (Editor
)
,
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, vol. 2
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, pp. 165-186
,
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I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Si
n
g
l
e
Perce
p
t
r
on
M
odel
f
o
r
Sm
art
Be
a
m
F
o
rmi
n
g
i
n
Arr
a
y Ant
e
nn
as (
K
.
S.
Se
nt
hi
l
k
um
ar)
2
309
BIOGRAP
HI
ES OF
AUTH
ORS
K.
S.
Se
nthilkumar
receiv
e
d his
B.S
c
. and M
.
S
c
. Degrees
in Com
puter S
c
ienc
e from
the
University
of
Peraden
i
y
a
, Sri
Lanka in
1998
a
nd 2003, respectiv
ely
.
Th
en, h
e
received h
i
s
M.Tech
. Degree in 2006 and Ph.D. Degree in
2011, from Jawaharlal Ne
hru U
n
iversity
, New
Delhi,
India. He did research on
Multipl
e
Robot
Terr
ain
exploration and
cover
a
g
e
for his Ph.D
.
Degree
in Computer Science.
He is a Senior
le
c
t
urer in the Departm
e
nt
of
M
a
them
ati
c
s
an
d
Computer Science, Papua New
Guinea University
of Technolog
y
.
His research area cov
e
rs
Robotics,
Artifi
c
ial
Inte
llig
enc
e
a
nd Soft Com
puti
ng. He
is a
Mem
b
er of
the
IE
T.
Dr
.
K.
P
i
r
a
pahar
a
n
, B.S
c
.
Eng
.
Hons
(P
eradeni
y
a
,
S
r
i La
nk
a),
M.Eng., PhD (Kinki, Jap
a
n), is
an As
s
o
ciate P
r
ofes
s
o
r of Elect
rica
l and Comm
unications
En
gineer
ing at the
Univers
i
t
y
of
Techno
log
y
, Papua New Guinea. Prev
iously
he was
a S
e
nior
L
ectur
er a
t
T
a
ylor
’s
Univers
i
t
y
in
Mala
y
s
ia
. His doctora
l
resear
ch was in
m
i
crowave and m
illim
ete
r
waves from Ki
nki Universi
t
y
,
Japan. From 2001 to 2003, he was a postdoctoral
re
search
associate at C
e
ntre for C
o
mputational
Electromagnetics, University
of
I
llinois at Urbana Champaign,
USA. From 2004 to
2011, he was
a S
e
nior
Le
ctur
er in
the
El
ec
tri
cal
and Inform
ation Eng
i
neerin
g Department at University
o
f
Ruhuna, Sri Lanka where he
was the h
ead
of the department from 2005
to 2008
. Dr.
Pirapahar
a
n’s research in
terests
includ
e wave
pr
opagation in in
homogeneous media, adap
tiv
e
antenn
a t
echn
i
qu
es
and
com
putat
i
onal
ele
c
trom
ag
neti
cs
. He
is
a M
e
m
b
er of
the
IE
EE
and I
ET.
Pau
l
R.P. Hoo
l
e
was born in Jaffna, Sri Lanka in 1958.
After
having his basic schooling in
J
a
ffna, h
e
earn
e
d all his
deg
r
ees
, firs
t degr
ee
to
postgraduate, in
the United King
dom. He holds
an M.Sc d
e
gre
e
in
Ele
c
tri
c
a
l
E
ngineer
ing with
a Mark
of Dist
inction
from
th
e
Universit
y
of
London and an
MSc degree in
Plasma Science
fro
m University
of Oxford. His doctorate,
the
D.P
h
il. d
e
gre
e
,
i
s
from
the Univ
ers
i
t
y
of Oxford
. In his
engin
eer
ing ca
reer
he h
a
s
s
p
ent tim
e
in
Singapore, Papua New Guinea,
USA,
Sri Lanka and Malay
s
ia.
After a long
car
eer
as Professor
of Electrical
En
gineer
ing, becau
se of his interest
s in lightning
en
gineer
ing, he h
a
s just embarked
on a job as
Professor of Electri
c
a
l and Ele
c
troni
c Engine
ering at
Universiti Mala
ysia
, Sarawak,
Malay
s
ia. Prof.
Hoole has autho
r
ed several pap
e
rs and books in engineering
.
His latest book
(with K. Pirapaharan
and S.R.H. Hoole),
Electromagnetics Engineering Handbook
, w
a
s
published b
y
WI
T Press, UK, in
June 2013.
S. Ratnajeevan H. Hoole,
B.S
c
.
Eng. Hons Cey
.
, M.Sc. w
ith
Mark of Distin
ction
London,
Ph.D. Carnegie Mellon, is Professor of Electrical
and Com
puter Engine
ering at
M
i
chigan S
t
at
e
Universit
y
in t
h
e US. For his accom
p
lishm
ents in ele
c
trom
agnet
i
c produc
t
sy
n
t
hesis the
University
of Lo
ndon awarded him its higher docto
rate, the D.Sc. (
E
ng.) degr
ee, in
1993, and the
IEEE e
l
ev
ated
him
to the grad
e of Fellow in 1995 with the
cit
a
tion “
F
or contributions to
computation
a
l methods for design optimization o
f
el
ectrical devices.” Prof
. Hoole has been Vice
Chance
llor of Univers
i
t
y
of J
a
ffna in S
r
i La
nka, and as
M
e
m
b
er of the Univers
i
t
y
Grants
Commission there, was responsible with six others
for the regulation of the administration of all
15 Sri L
a
nkan u
n
iversiti
es and
t
h
eir
acad
em
ic st
andards,
adm
i
ssions and funding
. Prof. Hool
e
has been
trained in Human Rights Resear
ch a
nd Teaching
at
The Ren
é
Cassin Intern
ation
a
l
Institute of Hum
a
n Rights
,
Stras
bourg, France,
and has pioneered teaching
hum
an rights in
th
e
engineering curr
iculum.
Evaluation Warning : The document was created with Spire.PDF for Python.