Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
4, N
o
. 2
,
A
p
r
il
201
4, p
p
.
25
7
~
26
4
I
S
SN
: 208
8-8
7
0
8
2
57
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
Beamforming Techniques for Smar
t Anten
n
a using Rect
angular
Array St
ructu
r
e
S.K.
Bodhe
1
, B.G. Hogade
2
, Sha
ilesh D.
Na
ndga
onka
r
3
1
Bosh Technologies, India
1,2
Narsee Monjee Institute of
Management Stud
ies, India
1,2
Mukesh Patel
School of
Techn
o
log
y
Mana
g
e
ment
& Eng
i
neering (MPSTME),
India
3
Departem
ent
of
El
ectron
i
cs
Eng
i
neer
ing,
TEC
,
M
u
m
b
ai Univers
i
t
y
,
India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Ja
n 15, 2014
Rev
i
sed
Feb
26
, 20
14
Accepted
Mar 12, 2014
In this paper,
arra
y theor
y
in ge
ner
a
l has
been discussed. A basic
fundamental of smart antenna an
d beam
forming t
echniqu
es using
rectangular
array
theor
y
is
discussed. Two
tech
n
i
ques,
Matrix inv
e
rsio
n and IDFT
method, for th
eir pros and cons we
re descr
i
bed which were used for
beamforming.Both the techniqu
es found
to be useful as their areas of
application differs on hardware bac
kground.Th
e design of a fully
spatial
signal processor
using rectangular array
conf
igu
r
ation is presented in this
paper. It has wideband pr
op
ert
i
e
s
and,
hen
c
e
e
l
im
inates
the
req
u
irem
ent of
differen
t
an
tenn
a spacing
. Furth
e
rmore,
frequ
en
c
y
sele
ctiv
it
y
a
nd reje
cting
unwanted sign
als gives the satisf
actor
y
perform
ance f
o
r practi
c
a
l
implementation.
Keyword:
Ar
ray
ge
om
et
ry
Beam
form
ing
Sm
art antenna
Sp
atial pro
c
essin
g
Copyright ©
201
4 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
:
Shai
l
e
sh
D
.
Na
nd
ga
on
ka
r
Depa
rtem
ent of Electronics
E
ngi
neeri
n
g, TE
C, Mum
b
ai University, India
1.
INTRODUCTION
The g
r
o
w
t
h
i
n
dem
a
nd of wi
deba
n
d
wi
rel
e
s
s
servi
ces has
evo
k
e
d
t
h
e t
r
em
endo
us nee
d
t
o
i
n
crease
th
e cap
acity and
d
a
ta-rate transmissio
n
of wi
reless co
mm
unications system
s. Since, the available spect
rum
to
p
r
ov
id
e cap
aci
ty an
d
h
i
gh
d
a
ta tran
sm
issio
n
rate to
all th
e su
b
s
crib
ed
u
s
ers is li
m
i
ted
,
the n
e
ed
and
atten
tio
n
o
f
latest
research
h
a
s m
o
v
e
d
to find
a tech
n
i
q
u
e
wh
ich will b
e
ab
le
to
fu
lfill
th
ese requ
irem
en
ts. Sm
art
an
tenn
a system
s, fo
un
d to be th
e
b
e
st so
lu
t
i
o
n
,
du
e to
t
h
e
u
s
e
o
f
sp
atial filterin
g
[1
],
which
m
a
k
e
s th
e
sig
n
a
ls
sen
s
itiv
e to
comin
g
fro
m
sp
ecific d
i
rectio
n
s
an
d
prov
id
es
atten
u
a
tion
to
o
t
h
e
r d
i
rections. In
th
is way, th
e
syste
m
capacity and power
efficiency
can be increa
sed
and t
h
ere
f
ore,
reduce ove
r
all cost. Beam
f
o
rm
ing
techniques
Bea
m
fo
rm
in
g
[1
] is th
e
p
r
o
c
ess of p
e
rform
i
n
g
sp
atia
l filterin
g
,
th
e m
a
in
ob
j
ective of sp
atial filterin
g
is to
m
a
k
e
a b
e
a
m
sen
s
itiv
e to
ward
s th
e si
gn
al of in
tere
st (SOI) and
n
u
ll
o
r
attenu
ation
t
o
ward
s d
i
rectio
n
s
of
i
n
t
e
rfe
ri
n
g
si
g
n
al
s or si
gnal
s
of n
o
t
i
n
t
e
r
e
st
(SN
O
I
)
.T
h
e
re are va
ri
o
u
s
m
e
t
hods o
f
im
pl
em
ent
a
tion
of
beam
form
i
ng techni
que
s, t
i
m
e
and fre
q
u
e
n
c
y
dom
ai
n whi
c
h de
pen
d
s o
n
t
h
e spee
d of
pr
ocessi
n
g
an
d t
h
e t
y
pe
of signals to be
proces
sed.
Va
ri
o
u
s Ti
m
e
an
d f
r
eq
ue
ncy
d
o
m
a
i
n
t
echni
que
s w
h
i
c
h i
s
bei
n
g
use
d
i
n
t
h
e
desi
g
n
a
n
d
i
m
p
l
e
m
en
tatio
n
o
f
a d
i
g
ital b
eam
fo
rm
er will b
e
d
i
scu
s
sed
in th
is
p
a
p
e
r. Perfo
r
m
a
n
ce
p
a
ram
e
ters lik
e
effi
ci
ency
, co
m
p
l
e
xi
ty
and t
h
e res
u
l
t
i
ng ad
vant
a
g
es an
d d
i
sadva
nt
ages c
a
n t
h
en
be deri
ved
.
B
eam
form
i
ng i
s
u
s
ed
in
Acoustic (SONAR) an
d
Rad
a
r (electro
m
a
g
n
e
tic ap
p
licatio
n
s
), seis
m
i
c, u
ltr
ason
ic i
m
ag
in
g
and
vari
ous
ot
her
a
ppl
i
cat
i
o
ns
[2]
.
Bea
m
fo
rm
in
g
o
r
Sp
atial filte
ring
[3
] is to
mak
e
respo
n
se o
f
th
e v
ect
o
r
sen
s
itiv
e to
SOI an
d
prov
i
d
e
nul
l
t
o
SN
OI
.
D
epe
n
di
n
g
u
p
on t
h
e ar
ray
g
e
om
et
ry
, beam
fo
rm
i
ng can f
o
rm
t
w
o o
r
t
h
r
ee di
m
e
nsi
onal
im
age
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
4, No
. 2, A
p
ri
l
20
14
:
25
7 – 2
6
4
25
8
from
an array
of sensors. The
r
e ar
e
t
w
o m
a
in t
y
pes
o
f
bea
m
for
m
ers. T
h
e
s
e are
tim
e
domain
beam
formers and
fre
que
ncy
dom
ai
n
beam
form
ers.
A gra
duate
d at
tenuation
window is
som
e
times applie
d ac
ross the
face of t
h
e array to improve side
-
l
obe s
u
pp
ressi
on
per
f
o
rm
ance, i
n
ad
di
t
i
on t
o
t
h
e
phas
e
shi
f
t
.
Ti
m
e
do
m
a
in beam
form
er wo
rk
s by
i
n
t
r
o
duci
n
g
tim
e
delays. The
basic
ope
ra
tion is called "
d
elay and
s
u
m". It
delays the
incom
i
ng si
gnal from
each
array
el
em
ent
by
a c
e
rt
ai
n am
ount
of
t
i
m
e
, and
t
h
en a
d
d
s
t
h
em
t
oget
h
er
.
The
r
e are t
w
o di
f
f
ere
n
t
t
y
p
e
s of
fre
que
nc
y
dom
ai
n beam
for
m
ers --T
h
e
fi
rst
t
y
pe separat
e
s t
h
e
diffe
re
nt fre
quency com
pone
nt
s that are present in the re
ceived sign
al into m
u
ltiple freque
ncy bi
ns (usi
ng
eith
er DFT or a
filterb
an
k). Wh
en
d
i
fferent d
e
lay and
sum
b
e
a
m
fo
rm
er
s are app
lied
t
o
each
freq
u
e
ncy b
i
n
,
the result is that the
m
a
in lo
be sim
u
ltaneously poi
nts in
m
u
ltiple different directions
at each of the
diffe
re
nt
fre
que
nci
e
s.
T
h
i
s
ca
n
be a
n
a
dva
nt
age
f
o
r
c
o
m
m
uni
cat
i
on
l
i
nks,
an
d i
s
us
ed
wi
t
h
t
h
e
ra
d
a
r.
The ot
her t
y
p
e
of fre
q
u
ency
dom
ai
n beam
fo
rm
er
m
a
kes use o
f
Spat
i
a
l
Freq
uency
[
4
]
.
Di
scret
e
sam
p
les are
ta
ken from
each
of the indi
vidual array el
e
m
ents. The samples are proce
ssed usi
ng a Discret
e
Fou
r
ier Tran
sfo
r
m
(DFT).
The DFT in
tro
duces m
u
ltip
le d
i
fferen
t
d
i
screte
ph
ase
sh
ifts du
ri
n
g
pro
cessin
g
.
Th
e
out
put
s
o
f
t
h
e DFT
are
i
ndi
vi
d
u
al
cha
nnel
s
t
h
at
c
o
rres
p
ond
with eve
n
ly spac
ed
beam
s form
ed
sim
u
l
t
a
neousl
y
. A 1 di
m
e
nsi
onal
D
F
T p
r
o
duce
s
a fan
o
f
di
ffe
rent
bea
m
s. A 2 di
m
e
nsi
o
nal
DFT
p
r
o
d
u
ces
beam
s with a
pineap
p
l
e co
nfig
uration
.
2.
A
RRA
Y THEORY
Th
e
n
u
m
b
e
r of ele
m
en
ts in
th
e array shou
ld b
e
relativ
ely lo
w
(th
e
m
i
n
i
mu
m
req
u
i
red
)
,
in
ord
e
r to
avoi
d u
nnece
ss
ari
l
y
hi
gh com
p
l
e
xi
t
y
i
n
t
h
e si
gnal
p
r
oces
sing
un
it. A
r
r
a
y an
tenn
as [5
] can
b
e
on
e-, tw
o-
, and
t
h
ree-
di
m
e
nsi
onal
,
depe
n
d
i
n
g
on
t
h
e
di
m
e
nsi
on
of
space
o
n
e w
a
nt
s t
o
ac
cess. Fi
g
u
r
e
1
sho
w
s
di
f
f
ere
n
t
array
g
e
o
m
etries th
at can
b
e
app
lied in
ad
ap
tive an
ten
n
a
s im
p
l
e
m
e
n
tatio
n
s
.
Fi
gu
re 1.
Di
ffe
rent
u
n
ifo
r
m
array
ge
om
etries f
o
r sm
art ante
nna
s
The first str
u
cture is use
d
p
r
im
arily
for bea
m
for
m
ing in the horiz
ontal plane (azim
u
th) only. T
h
is
will n
o
r
m
a
lly
b
e
sufficien
t fo
r ou
tdoo
r en
viron
m
en
ts, at
l
east in
larg
e cells. Th
e first ex
am
p
l
e (a) sh
o
w
s
a
o
n
e
-d
im
en
sio
n
a
l lin
ear array with
u
n
i
form
e
l
e
m
en
t sp
acing
o
f
x
. Suc
h
a
structure ca
n
pe
rform
beam
form
ing in one
plane
within a
n
angu
lar sector. Th
is is th
e m
o
st co
mm
o
n
stru
cture du
e to
its lo
w
co
m
p
lex
ity.
The sec
o
nd
e
x
am
pl
e (b
) s
h
o
w
s a
ci
rcul
a
r
a
rray
[8]
.
It
has
uni
fo
rm
angul
ar s
p
aci
n
g
bet
w
een
ad
jace
nt
ele
m
ents of
N
/
2
, w
h
ere
N
represents
the
num
ber of elemen
ts.
This
structure ca
n
pe
rform
b
eam
fo
rm
in
g
in
an
y d
i
rectio
n, du
e
of its symmetry,
is
m
o
re
appropriate for azim
u
thal bea
m
for
m
ing.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
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8-8
7
0
8
Bea
m
f
o
r
m
i
n
g
Tech
ni
q
u
es f
o
r
S
m
art
Ant
e
nn
a
usi
n
g Rect
an
gul
ar A
rray
St
ruct
ure
(Sh
a
ilesh
D
.
N
a
n
dga
on
kar)
25
9
The last t
w
o s
t
ructures a
r
e
used
t
o
per
f
o
rm
t
w
o
-
di
m
e
nsi
onal
beam
form
ing
,
i
.
e
.
i
n
bot
h azi
m
u
t
h
al
and el
e
v
at
i
on
angl
es
. Suc
h
s
p
eci
fi
cat
i
o
n
s
are us
ual
l
y
requ
i
r
ed f
o
r i
n
d
o
o
r
or de
nse
ur
ba
n en
vi
r
onm
ent
s
. The
fr
ont
vi
e
w
of
a
t
w
o
-
di
m
e
nsi
onal
rect
a
n
g
u
l
a
r
arr
a
y
[
6
]
[
7
]
wi
t
h
ho
ri
zo
nt
al
el
em
ent
spaci
ng
o
f
x
a
n
d ve
rtical
ele
m
ent spacing
of
y
is sho
w
n in
(c).
Bea
m
fo
rm
in
g
in
th
e en
tire sp
ace, with
in
all an
g
l
es, requ
ires
so
m
e
so
rt o
f
cu
b
i
c or sph
e
rical stru
ctu
r
e
(th
r
ee-d
im
en
si
o
n
a
l co
nfigu
r
at
io
n). Th
e fourth exam
ple (d)
shows a c
ubic
structure with
ele
m
ent separa
tions
of
x
,
y
, a
n
d
z
,
respectively,
in each direction in
s
p
ace.
2.
1 B
e
ne
fi
ts
o
f
Arr
ayi
n
g
Ar
ray
i
ng
has m
a
ny
benefi
t
s
[5]
such as:
bet
t
e
r per
f
o
rm
ance, i
n
c
r
ease
d
o
p
erat
i
o
nal
ro
b
u
st
ness
,
i
m
p
l
e
m
en
tatio
n
co
st sav
i
ng
,
m
o
re p
r
o
g
rammatic flex
ib
ilit
y, and
b
r
o
a
d
e
r
su
ppo
rt t
o
th
e scien
ce co
mm
u
n
ity.
a. Pe
rform
a
nce Benefits
For
l
a
r
g
er
ant
e
nna
s, t
h
e
be
am
wi
dt
h
nat
u
r
a
l
l
y
i
s
narr
o
w
er.
As a
re
sul
t
, ant
e
nna
-p
oi
nt
i
n
g
er
ro
r
becom
e
s m
o
re critical. To sta
y
within
t
h
e m
a
i
n
beam
and
i
n
cu
r m
i
nim
a
l
loss,
ant
e
nna
p
o
i
nt
i
ng
has t
o
be
m
o
re
p
r
ecise. Yet t
h
i
s
is d
i
fficu
lt t
o
achieve
for la
rger structure
s
.
W
i
t
h
an
array configurati
o
n of
sm
aller an
tenn
as, an
tenn
a-po
in
ting
error is no
t an issu
e. The
d
i
fficu
lty is tra
n
sferred
fro
m
t
h
e m
ech
an
ical
to
th
e
electroni
c dom
ain. The wide
r
beam
width ass
o
ciated with
the sm
aller aperture
of eac
h a
r
ray elem
ent
make
s t
h
e ar
ray
m
o
re tolerant t
o
poi
nting
er
ro
r.
b
.
Op
erab
ility
Ben
e
fits
Arrayin
g
can
i
n
crease system op
erab
ility. First,
h
i
gh
er resou
r
ce u
tilizatio
n
can
b
e
ach
i
eved
.
In
th
e
case of a
n
arra
y, howeve
r, the set can be partitioned
int
o
many
subsets each
tailo
red a
ccording to the link
requ
irem
en
ts.
In
so
d
o
i
ng
, reso
urce u
tilizatio
n
can
b
e
en
h
a
nced
.
Secon
d
l
y, arrayin
g
o
f
fers h
i
gh
syste
m
av
ail
a
b
ility
an
d
m
a
i
n
ten
a
n
ce flex
i
b
ility. Su
p
p
o
s
e th
e array is
b
u
ilt w
ith
10
p
e
rcen
t sp
are ele
m
en
ts. Th
e regu
lar prev
entiv
e
m
a
in
ten
a
nce can
b
e
done o
n
a ro
tatin
g b
a
sis
wh
ile allowing th
e system
to
b
e
fu
lly fu
n
c
ti
o
n
a
l at all tim
e
s
.
Thi
r
dl
y
,
t
h
e
co
st
of
s
p
are
com
p
o
n
e
n
t
s
wo
ul
d
be sm
a
ller. In
stead
o
f
h
a
v
i
ng
to
su
pp
ly th
e syste
m
with
10
0
perce
n
t
s
p
ares i
n
o
r
de
r t
o
m
a
ke i
t
ful
l
y
fu
nct
i
onal
,
t
h
e ar
ray
o
f
f
e
rs
an
opt
i
o
n
o
f
f
u
r
n
i
s
hi
ng
spa
r
es at
a
fraction
a
l lev
e
l
.
Eq
ual
l
y
im
port
a
nt
i
s
t
h
e opera
t
i
onal
ro
b
u
st
ne
ss agai
ns
t failures.
W
ith
a sing
le resource, failu
re ten
d
s
t
o
b
r
i
n
g t
h
e
sy
st
em
dow
n.
Wi
t
h
an a
rray
,
fa
i
l
u
re i
n
a
n
a
rra
y
el
em
ent
degr
ades sy
st
em
perf
orm
a
nce b
u
t
doe
s
n
o
t
resu
lt in
a
co
m
p
lete serv
i
ce shu
t
down.
c. C
o
st Bene
fits
A c
o
st savi
ng
is realized from
the fact that
sm
a
ller
antennas, beca
use of
th
eir wei
ght
and size, a
r
e
easier to
bu
ild
. Th
e fab
r
ication
pro
ces
s can
be aut
o
m
a
ted to re
duce t
h
e
cost. Many com
m
ercial vendors can
p
a
rticip
ate in
th
e an
tenn
a co
n
s
t
r
u
c
tion
busin
ess, and
the
m
a
rk
et co
mp
etitio
n
will b
r
ing
th
e co
st down
furth
e
r.It is
o
f
t
e
n
approx
im
at
ed
th
at th
e an
t
e
n
n
a
con
s
tru
c
tio
n
co
st is pro
p
o
r
tion
a
l to
th
e
an
tenn
a vo
lu
m
e
. Th
e
reception ca
pa
bility, howe
v
e
r
, is propor
tional to the antenna surfa
ce area
.
For exam
ple, halving the a
n
tenna
apert
u
re
re
duc
es t
h
e c
o
n
s
t
r
uc
t
i
on c
o
st
o
f
a
s
i
ngl
e a
n
t
e
n
n
a
by
a fact
or
o
f
8;
h
o
w
eve
r
,
f
o
ur a
n
t
e
nnas
w
oul
d
be
neede
d
t
o
ac
hi
eve a
n
e
qui
val
e
nt
ape
r
t
u
re.
T
h
e
net
ad
va
nt
a
g
e i
s
a
n
a
p
pr
ox
im
at
e 50 p
e
rce
n
t
co
st
savi
ng
.
d
.
Flex
ib
ility
Ben
e
fits
Arraying
offers a
programm
a
tic flexibility because
a
d
ditional elem
ents can
be i
n
crem
entally adde
d
to
in
crease th
e to
tal ap
ertu
re at th
e ti
me o
f
n
eed. Th
is optio
n
allo
w
s
f
o
r a sp
r
e
ad
in
r
e
q
u
i
r
e
d
f
und
ing and
minimizes the
need to ha
ve
all the c
o
st in
curred at
o
n
e
ti
m
e
. Th
e add
iti
on
of ne
w elem
ents can be
done
wit
h
litt
le i
m
p
act to
th
e ex
isting
facilit
ies th
at suppo
rt
on
go
ing
operatio
n
s
.
3.
SMA
R
T
AN
TEN
NA
Practically sp
eak
ing
,
an
tenn
as b
y
th
em
selv
es
are n
o
t
sm
art. It
i
s
t
h
e di
gi
t
a
l
si
gnal
p
r
oce
ssi
ng
(D
SP)
cap
ab
ility, alon
g with th
e arrays o
f
an
ten
n
a
s, wh
ich m
a
k
e
th
e system
s
m
art. Di
g
ital
sign
al pr
ocessing
(
D
SP)
u
n
it,
wh
ich
com
p
u
t
es weigh
tin
g
factors t
h
at m
u
lt
ip
ly th
e s
i
gnal at eac
h e
l
e
m
ent of t
h
e a
ssociated a
rray
.
T
h
is
wei
g
ht
i
n
g
cal
c
u
l
a
t
i
on c
a
n
be
real
i
zed
usi
n
g
di
ffe
re
nt
beam
fo
rm
i
ng t
ech
ni
que
s.
Three
m
a
in concepts
of sm
ar
t antennas
are
a
s
follow:
a. s
p
ace-tim
e s
i
gnal
processi
ng,
b. s
p
ace
-freque
n
cy sign
al
pr
oc
essi
ng
an
d
c.
fu
lly
sp
atial sig
n
a
l p
r
o
cessi
n
g
The space
-time and s
p
ace-fre
que
ncy si
gnal processi
ng tec
hni
que
s are ba
sed on large ba
nks
of
delay
n
e
two
r
k
s
o
r
freq
u
e
n
c
y filters, wh
ich
resu
lt in
h
i
g
h
co
st an
d h
i
g
h
h
a
rdware co
m
p
lex
ity. On
th
e o
t
h
e
r h
a
n
d
,
fu
lly sp
atial sig
n
a
l
p
r
o
cessing
n
e
g
l
ect th
e use o
f
filters
and
d
e
lay n
e
twork
s
,
h
e
reb
y
h
a
s
b
een
i
d
en
tified as th
e
m
o
st
advant
a
g
eou
s
of t
h
ese t
h
ree
t
ech
nol
og
i
e
s an
d t
h
e
r
ef
o
r
e i
t
i
s
at
t
r
act
i
v
e f
o
r
wi
de
ba
nd
com
m
uni
cat
i
on.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
4, No
. 2, A
p
ri
l
20
14
:
25
7 – 2
6
4
26
0
Th
ere are two b
eam
fo
rm
in
g
alg
o
rith
m
s
d
i
scu
ssed
to
ob
tain
th
e op
timu
m
weig
h
tin
g co
efficien
t
s
usi
n
g
ful
l
y
s
p
a
t
i
a
l
si
gnal
p
r
oc
essi
ng
co
n
f
i
g
ur
at
i
on,
base
d
o
n
rect
an
g
u
l
a
r a
r
r
a
y
geom
et
ry
.
4.
FU
LLY
SPATIA
L SIGNA
L
PR
OC
ESSING BEAM
F
ORM
I
NG U
S
ING REC
T
AN
GU
LA
R
A
RRA
YS
Rectangular li
near arrays,
when s
u
bjected
to a
n
alm
o
st fixed eleva
t
i
o
n
angl
e,
m
a
y
be
use
d
t
o
f
u
l
l
y
spat
i
a
l
si
gnal
pr
ocessi
ng o
f
wi
de
ban
d
si
g
n
a
l
s
.In t
h
i
s
p
r
o
cessi
ng t
ech
ni
que
, t
h
e shar
p
n
ess o
f
t
h
e be
am
s i
s
main
tain
ed
n
o
t
on
ly
in
t
h
e b
r
o
a
dsid
e bu
t
at th
e
en
dfire d
i
rectio
n
s
of
th
e array
as
well. Th
e b
eam
wid
t
h
[1
] of
th
e d
i
recti
o
n
a
l
p
a
ttern
can
b
e
co
n
t
ro
lled
at al
l an
g
l
es.F
requen
c
y do
m
a
in
filterin
g
[7
] is easily ach
iev
e
d
in
th
e
desi
g
n
pr
oced
ure
.
t
h
i
s
p
r
ope
r
t
y
i
s
cal
l
e
d as fre
q
u
en
cy s
e
lective wide
ba
m
d
beam
forming (FSW
B
)
.It can
com
p
ensat
e
f
o
r
t
h
e
fre
que
ncy
depe
ndence
of
the elem
ents.
Th
e configu
r
at
io
n of th
e wi
d
e
b
a
nd
b
eam
fo
rm
er, con
s
titu
ted b
y
a rect
an
gu
lar array
o
f
N
1
N
2
an
tenn
a elem
e
n
ts along
with
a
m
p
lifiers or atten
u
a
tors
a
n
d
a sum
m
i
ng net
w
o
r
k
,
i
s
sh
o
w
n i
n
Fi
g.
2.
Inc
o
m
i
ng
signal
arriving
at rectangular
array
with azi
m
u
th angle
and
e
l
ev
a
tion
angle
.
Each element is
connected t
o
a real m
u
ltip
lie
r as sho
w
n
i
n
t
h
e
figu
re
2
.
Figure
2. Rectangular array of
N
an
tenn
a elemen
ts with
am
p
lifiers and
summer
Each a
n
t
e
n
n
a e
l
em
ent
has a
fr
eque
ncy
-
de
pen
d
ent
gai
n
an
d
i
s
de
n
o
t
e
d
by
(
n
1
,
n
2
),
Whe
r
e,
0
≤
n
1
≤
N
1
−
1
a
n
d 0
≤
n
2
≤
N
2
– 1.
The i
n
ter-element dista
n
ces a
r
e
d
1
and
d
2
i
n
th
e d
i
rectio
n of
n
1
and
n
2
, res
p
ectively.
The di
rect
i
o
n
of t
h
e ar
ri
vi
n
g
si
gnal
i
s
det
e
r
m
i
n
ed by
t
h
e azim
u
t
h
angl
e
ϕ
, and the eleva
tion angle
θ
.
As in m
o
st practical cases, it
is assum
e
d that the eleva
tio
n an
g
l
es of th
e in
cid
e
n
t
sign
al
s to
th
e b
a
se statio
n
an
tenn
a array
are alm
o
st co
nstan
t
, and w
itho
u
t
lo
ss of g
e
n
e
rality, we
con
s
id
er
θ
≈
90
°
.
As
s
u
mi
n
g
th
a
t
th
e
pha
se re
fere
nc
e point is l
o
cated at
(
n
1
0,
n
2
0) , t
h
e
phase
of the
signal at t
h
e elem
ent (
n
1
,
n
2
) is:
∅
,
2
⁄
sin
cos
(1
)
Whe
r
e
f
i
s
t
h
e
fre
que
ncy
a
nd
c
is the vel
o
city of a
n
electromagnetic
wa
ve
in free s
p
ace.
There
f
ore, the
array
freq
u
e
n
c
y-ang
l
e resp
on
se can
b
e
written
as:
,
,
(2
)
There a
r
e t
w
o
m
a
i
n
beam
form
i
ng al
go
ri
t
h
m
s
di
scusse
d t
o
de
vel
o
p f
u
l
l
y
spat
i
a
l
si
gnal
pr
ocessi
ng
[1]
[7] [8] based
on a rectangula
r
array an
tenn
a. Th
e first on
e i
s
a
m
a
trix
in
v
e
rsion
techn
i
qu
e wh
ich
is sim
p
l
e
an
d
pr
o
duces
wi
der
beam
and
has
l
o
w
beam
wi
dt
h.
The sec
o
n
d
t
echni
que i
s
i
n
v
e
rse di
sc
ret
e
f
o
u
r
i
e
r t
r
a
n
sf
o
r
m
(IDFT
) [
1
]
[7]
,
w
h
i
c
h p
r
o
duce
s
sha
r
pe
r
beam
s and m
o
re controlled
perform
a
nce. The m
a
in an
d the m
o
st im
p
o
rta
n
t advanta
g
e of the a
bove two
technique is t
h
at both yields real wei
ghi
ng coeffi
cients
whic
h are
easily im
ple
m
ented by attenuators and
a
m
p
lifiers.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Bea
m
f
o
r
m
i
n
g
Tech
ni
q
u
es f
o
r
S
m
art
Ant
e
nn
a
usi
n
g Rect
an
gul
ar A
rray
St
ruct
ure
(Sh
a
ilesh
D
.
N
a
n
dga
on
kar)
26
1
4.1. Be
am
for
mer Using
Matrix I
n
ver
s
ion
Fo
r th
is m
e
th
od
,
we
n
e
ed
to defin
e
t
w
o v
ect
o
r
s as
fo
llow:
,
,….
(3
)
,
,
,
,
,
,
…
,
,
(4
)
Ass
u
m
e
that
H
(
s
1
,
s
2
) is expressed
b
y
th
e
m
u
l
tip
licatio
n
o
f
two
b
a
sic polyn
o
m
ia
ls as follo
w:
,
.
(5
)
The rel
a
t
i
ons
hi
p bet
w
ee
n
b
l
an
d
w
n
1
,
n
2
can
b
e
o
b
tained
rea
r
ran
g
in
g
(5
) as:
,
.
(6
)
There
f
ore, afte
r calculation
of
b
, we
ca
n find
w
n
1,
n
2
fr
om
abo
v
e e
q
uat
i
o
n.
4.2. Be
am
for
mer Using
IDFT
Thi
s
m
e
t
hod i
s
m
o
st
l
y
used i
n
sm
al
l
array
s
, whe
r
e i
t
i
s
ass
u
m
e
d t
h
at
t
h
e
ori
g
i
n
poi
nt
(
0
,
0
) i
s
l
o
cat
ed
at th
e cen
ter
o
f
th
e an
tenn
a array. Using
th
is n
e
w lo
cation
,
th
e array’s sy
mme
try can
b
e
exp
l
o
ited
.
W
i
t
h
th
is
assu
m
p
tio
n
th
e frequ
en
cy
-angle respon
se can b
e
written
as:
,
,
(7
)
A careful exa
m
ination of a
b
ove equa
tion rev
eals th
at i
t
rese
m
b
les a
d
i
screte Fo
urier tran
sfo
r
m
(DFT).
There
f
ore,
by
t
a
ki
n
g
t
h
e
I
D
F
T
o
f
t
h
e
val
u
es
o
f
H
(
s
1
,
s
2
)
/
G
a
(
s
1
,
s
2
)
in
th
e
s
1
−
s
2
plane e
n
ables
to
calculate weig
hing c
o
efficients as follow:
,
1
.
,
,
.
.
.
.
(8
)
5.
R
E
SU
LTS AN
D ANA
LY
SIS
5.
1 Ma
trix
In
versio
n Meth
o
d
Resu
lts
are ob
tain
ed
fo
r
N
1
= 6
&
N
2
= 4
(Re
c
tang
ular a
rray
size)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
4, No
. 2, A
p
ri
l
20
14
:
25
7 – 2
6
4
26
2
Fi
gu
re 3.
Beam
formation
at
A.
O.
A
Fi
gu
re
4.
Di
rec
t
i
onal
pat
t
e
r
n
In M
a
t
r
i
x
i
nve
rsi
o
n m
e
t
hod,
we get
wi
der
beam
at
A.O.
A o
f
4
5
*
(
f
i
g
u
r
e 3
)
an
d i
n
t
h
e di
rect
i
o
nal
p
a
t
t
e
rn
(fi
g
u
r
e 4) al
s
o
we can
obse
r
v
e
t
h
e sam
e
at
gi
ve
n A.
O.
A.
T
h
i
s
m
e
t
hod i
s
easy
t
o
im
pem
e
nt
com
p
are t
o
IDFT
m
e
t
hod.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Bea
m
f
o
r
m
i
n
g
Tech
ni
q
u
es f
o
r
S
m
art
Ant
e
nn
a
usi
n
g Rect
an
gul
ar A
rray
St
ruct
ure
(Sh
a
ilesh
D
.
N
a
n
dga
on
kar)
26
3
5.
2 I
.
D
.
F.T
M
e
th
od
Fi
gu
re 5.
Beam
formation
at
A.
O.
A
Fi
gu
re 6.
di
rect
i
onal
pat
t
e
rn
Aft
e
r
com
p
ari
n
g
resul
t
s
,
we
c
a
n say
t
h
at
usi
n
g
I
D
FT
m
e
t
h
od
,
we
get
s
h
ar
per
beam
pat
t
e
rn
t
h
at
ca
n
be s
een i
n
the fi
gu
re
5 a
n
d sam
e
is refle
c
ted in
fig
u
r
e
6
.
Co
m
p
arin
g
bo
th
th
e techn
i
qu
es as fo
llow:
Martix inversion
I.D.F
.
T
.Meth
o
d
Si
m
p
le
Pr
oduces wider
beam
and
Has low fractional
bandwidth.
Used in s
m
all
size
arra
y.
L
e
ss cover
a
ge.
More prone to inte
rf
erence.
Less power is
tran
s
m
itted in desire
directon.
Co
m
p
lex
Pr
oduces shar
per
beam
s and
Has higher
fr
actio
nal bandwidth
M
o
r
e
contr
o
lled per
f
orm
a
nce,
hence can be used in lar
g
e
size ar
rays
.
M
o
r
e
cover
a
ge ar
ea.
Less interference
.
M
ore power
is trans
m
itted in desire
dir
ection
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
4, No
. 2, A
p
ri
l
20
14
:
25
7 – 2
6
4
26
4
6.
CO
NCL
USI
O
N
In t
h
i
s
pa
pe
r,
ful
l
y
spat
i
a
l
signal
p
r
ocessi
n
g
[
1
]
i
s
di
scus
sed usi
ng
rect
ang
u
l
a
r ar
ray
geom
et
ry
.It
eli
m
inates TDL’s and filters whic
h we
re use
d
in
space
ti
m
e
and spac
e fre
que
ncy processing techniques.
Hence
,
it re
duces ha
rdwa
re
com
p
lexity, and the
r
efore,
t
h
e overall c
o
st
of the system
.The m
a
in proble
m
in
th
is p
r
o
cessing tech
n
i
qu
es is to
find
ou
t th
e o
p
tim
u
m
we
ig
h
tin
g
co
efficien
ts. To
so
lv
e th
is p
r
ob
lem
,
th
ere are
t
w
o b
eam
form
i
ng al
g
o
ri
t
h
m
s
pr
op
ose
d
,
bas
e
d o
n
rect
a
n
g
u
l
ar array
ge
om
et
ry
[7]
.
The a
l
go
ri
t
h
m
s
based o
n
rectangula
r
array yields real num
b
er wei
ghts
he
nce,
pr
actically it can
b
e
easily i
m
p
l
e
m
en
ted
u
s
i
n
g
attenu
ators
or am
pl
i
f
i
e
rs. The I
D
FT [
1
]
m
e
t
hod i
s
m
o
re com
p
l
e
x but
pr
o
v
i
d
es sh
ar
p
e
r beam
s, and t
h
e M
a
t
r
i
x
In
v
e
rsi
o
n
m
e
t
hod
[
1
]
,
i
s
sim
p
l
e
r b
u
t
h
a
s
wi
de
r
beam
and l
o
we
r f
r
act
i
o
nal
ba
n
d
wi
dt
h.
M
a
ny
di
f
f
ere
n
t
app
r
oa
ches
have
bee
n
pr
o
pos
ed
f
o
r i
m
pl
em
ent
i
ng o
p
t
i
m
u
m
beam
form
er. Fut
u
r
e
work
will lik
ely ad
d
r
ess si
gn
al can
cellation
prob
lem
s
, furth
e
r
redu
ct ion
s
in
co
m
p
u
t
atio
n
a
l lo
ad
for larg
e
arrays and
imp
r
ov
ised
stru
ct
u
r
es
for im
p
l
e
m
en
tatio
n
.
Beam
fo
r
m
in
g
tru
l
y rep
r
esen
ts a
v
e
rsatile app
r
oach
to
sp
atial filterin
g
.
REFERE
NC
ES
[1]
M Ghavami. “Wideband
Smart Antenna Theor
y
U
s
ing Rectangular
Array
Structures”.
IEEE Transa
c
tions on
Signa
l
Proc
e
ssing
. 200
2; 50(9): 2143-2
151.
[2]
JC Libert and TS Rappaport.
“Smart Antennas for Wireless Communica
tions: IS-95 and Third
Generation CDM
A
Applica
tions”
.
Englewood Cliffs, NJ,
Prentice Hall. 1999.
[3]
C Loadman,
Z Chen and
D Jorgensen.
“An overview
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te
nna technolo
g
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”.
CNSR 2003,
Moncton, N
e
w
Brunswick, Can
a
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[4]
M Uthansakul and ME Bialkowski.
"
I
n
vestiga
t
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I
E
EE Antenn
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r
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)
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[5]
M Uthansakul and
ME Bialkowski.
"
A
n
investigation in
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enna configuratio
n for wideband
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in pro
c
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International Co
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M
i
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a
da
r and
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Warsaw, Poland. May
2004
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[6]
B Allen
and
M
Ghavam
i.
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ptative Array
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M Uthansakul and ME Bialko
wski. "F
ully
sp
atial wideb
a
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lar array
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IEEE Transaction
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06; 54: 527-533.
[8]
P Ioannides and
CA Balan
i
s.
“
W
ideband b
e
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c
ular arrays”.
in IEEE Antenn
as and Propagation
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Intern
ational
S
y
m
posium. 2004; 3: 2627 –
2630.
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