TELKOM
NIKA
, Vol. 13, No. 4, Dece
mb
er 201
5, pp. 1225
~1
232
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v13i4.1846
1225
Re
cei
v
ed Ap
ril 10, 2015; Revi
sed O
c
tob
e
r
13, 201
5; Acce
pted No
vem
ber 1, 20
15
Enhancement the Performance of OFDM based on
Multiwavelets U
s
ing Turbo Codes
Sameer A Da
w
o
od
1
, F. Malek
2
, MS Anuar
1
, HA R
a
h
i
m
1
1
School of Co
mputer an
d Co
mmunicati
on E
ngi
neer
in
g, Un
i
v
ersit
y
Ma
la
ysi
a
Perlis (U
niM
AP), Pauh Putra,
026
00, Arau, P
e
rlis, Mala
ys
ia
2
School of Elec
trical S
y
stems
Engi
neer
in
g, Universit
y
Mal
a
ysia Perlis (U
ni
MAP), Pauh Putra, 0260
0, Arau,
Pe
rl
i
s
, Ma
lay
s
ia
e-mail: sam
eer
.ad80
@
y
ah
oo.
com
A
b
st
r
a
ct
In wireless comm
unication s
ystem
s,
the
ma
in cha
lle
ng
e is to provid
e a hi
gh data r
a
te an
d reli
abl
e
transmissio
n
o
v
er a frequ
en
cy selective f
adi
ng ch
ann
el.
Orthogon
al F
r
equ
ency Div
i
s
ion Mu
ltipl
e
xi
ng
(OF
D
M) is a very attractive techn
i
qu
e for hi
gh d
a
ta
rate trans
missi
on w
i
th better b
andw
idth effici
ency. I
n
this pap
er, the effectiveness
of turbo codes
is ut
ili
z
e
d to d
e
vel
op a new
appr
oach for a
n
OFDM system
base
d
on a Dis
crete Multiw
avelet Cr
itica
l
-Sa
m
p
lin
g T
r
ansfo
rm (OF
D
M-DMW
CST
)
.
T
he use of turbo cod
i
n
g
in an OFDM-DMWCST syste
m
is us
eful
in providing the desired perfor
m
ance at higher
data rates. Two
types of
turbo
codes
w
e
re
us
ed
in
this w
o
rk,
i.e.,
Par
a
ll
el C
oncate
nate
d
C
onvo
l
utio
na
l
C
odes
(
PCCCs
)
and
Serial C
onc
ate
nated C
onv
olu
t
iona
l Cod
e
s
(
SCCCs
)
. In both types, the decod
ing is
perfor
m
e
d
by th
e
iterative
dec
od
ing
al
gorit
hm
base
d
o
n
th
e
log-MAP
(Maxi
mu
m A P
o
ster
iori)
al
gorith
m
.
T
he s
i
mul
a
tio
n
results showed that, the turbo-c
oded OFDM-DMWCST system
achieves
la
rge coding gain
with lower Bit-
Error-Rate
(BE
R
), therefor
e, o
ffering
a
hig
her
data
rate
u
n
d
e
r d
i
fferent c
h
a
nne
l co
nd
itions
. In a
dditi
on, th
e
PCCCs offer b
e
tter perfor
m
a
n
ce than SC
C
C
s.
Ke
y
w
ords
: OFDM, m
u
ltiwavelet transform
, turbo co
des, wireless channe
ls, bit error rate
Copy
right
©
2015 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
The p
r
e
s
ent
mobile
comm
unication
systems mu
st p
r
ovide hig
h
-q
u
a
lity commu
n
i
cation
and a
high d
a
ta rate fo
r
multimedia
a
pplication
s
.
One of the
promisin
g multi
c
arrie
r
mo
dul
ation
scheme
s
to f
u
lfill the high
data rate
re
q
u
irem
ent
is
O
r
thogo
nal F
r
e
quen
cy Divi
si
on Multiplexi
ng
(OFDM) [1]. OFDM is an effic
i
ent, high dat
a
rat
e
, having
a
d
vantage
s of
high
sp
ect
r
um
efficien
cy, simple and eff
i
cient implem
entation
by usin
g the Fa
st Fouri
e
r Transfo
rm (FF
T
),
mitigation of Inter-Symb
o
l Interferen
ce (I
SI) by in
serti
ng a Cycli
c
Prefix (CP) a
n
d
robu
stne
ss to
freque
ncy sel
e
ctive fading
cha
nnel
s tran
smissio
n
techniqu
e for wi
rele
ss
comm
unication [2, 3].
Although the
con
c
e
p
t of CP traditionally
has be
en
a
s
so
ciated with
OFDM
syste
m
s, however,
the
CP introd
uce
s
a loss in tra
n
smi
ssi
on po
wer a
nd ba
nd
width [4].
Due to
the di
sadva
n
tage
o
f
OFDM
syst
em
cau
s
ed b
y
using CP, an
alte
rnative
method
is to use of t
he Di
screte
Wavelet Tran
sform
(DWT
) instea
d of FFT has b
een p
r
opo
se
d re
ce
ntly
[5-8]. By usin
g the DWT, t
he spe
c
tral
containme
n
t o
f
the cha
nnel
s is
better
si
nce th
ey are
not
usin
g CP.
Multiwavelet
s are a
ne
w
developm
ent
of th
e
wave
let theo
ry. It has two
scaling a
nd
wavelet fun
c
t
i
ons in
ea
ch l
e
vel, rathe
r
than on
e scali
ng fun
c
tion a
nd one
wavel
e
t function th
at
wavelet tran
sform h
a
s. M
u
ltiwavelets
are de
si
gn
ed t
o
po
sse
ss
sy
mmetry, orth
ogon
ality and
a
highe
r order
of approxim
ation simulta
n
e
ously, whi
c
h
are imp
o
ssibl
e
for a scala
r
wavelet [9, 10].
Da
woo
d
et al
. [11], prop
osed a
n
OF
DM
system
ba
se
d on
Di
screte
Multiwavel
et
Critical-
Sampling Tra
n
sform
(DM
W
CST
)
.
Th
e DM
WCST wa
s
p
r
op
osed a
n
alternative
method i
n
ste
ad o
f
DWT and
FF
T. In the prop
ose
d
sy
stem, there i
s
no n
eed for
usi
n
g
CP be
cau
s
e
of the excelle
nt
orthog
onality
that is offered by DM
WCST, and
su
bse
que
ntly, redu
ce the
system comple
xity,
increa
se the
transmissio
n rate, an
d increa
se
sp
e
c
tral effici
en
cy. They were found that
the
prop
osed
system a
c
hi
eved mu
ch l
o
wer Bit-Error-Rate
(BER) and b
e
tter
perfo
rman
ce
than
OFDM b
a
se
d on DWT and OF
DM
based on F
FT unde
r Additive White
Gaussia
n
Noise
(AWG
N), flat fading,
and
freque
ncy
-
sel
e
ctive fadi
ng
ch
ann
els. Al
so, they
we
re foun
d that,
at
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Enhan
cem
e
n
t
the Perform
ance of OFDM base
d
on
Multiwa
v
elet
s Usin
g …
(S
a
m
eer A. Dawood)
1226
high data
rat
e
tran
smissio
n
and in a fre
quen
cy
-sele
c
tive fading ch
annel, the B
E
R perfo
rma
n
ce
of OFDM
-DM
W
CST
be
co
mes
con
s
tant
after a cert
ai
n Signal
-to-Noise
Ratio
(S
NR). Thi
s
is
due
to the resid
u
a
l
of ISI which
is ca
used, be
ca
u
s
e
CP is not use
d
in the prop
osed system.
One m
e
thod
sug
g
e
s
ted to
improve the
perfo
rm
a
n
ce
of a
com
m
u
n
icatio
n
syst
em is to
use
the ch
an
nel codi
ng (al
s
o call
ed erro
r corre
c
ting
code
s). E
rro
r
correctin
g
cod
e
s
are a
meth
od
of addi
ng
red
unda
ncy to
i
n
formatio
n in
a
controlled
mann
er in
o
r
de
r to
give t
he a
b
ility of the
receiver to de
tect and co
rre
c
t the erro
rs that oc
curred i
n
transmissio
n [12]. As a p
o
we
rful co
din
g
techni
que, turbo co
de
s are
a prime
ca
ndi
date for
wirel
e
ss appli
c
atio
ns an
d bei
ng
con
s
id
ere
d
fo
r
future mobil
e
radio
comm
u
n
icatio
ns [13,
14].
In this paper,
two approach of turbo
codes
will be
used to im
prove the performance of
OFDM
-DMWCST sy
stem,
the first on
e i
s
Paralle
l
Co
ncate
nated Convolutional Cod
e
s (PCCCs)
and the
se
con
d
on
e i
s
Seri
al Co
ncate
nat
ed Convol
utional
Cod
e
s (S
CCCs).
Fu
rt
her
perfo
rman
ce
gain
s
an
d hi
gher spe
c
tral
efficien
cy
were
mad
e
by
com
b
inin
g t
u
rbo
code
s
and
DM
WCST in t
he de
sign of
OFDM
syste
m
s.
The re
st of the pape
r is
arrang
ed as fo
llows. Se
ction 2 presents the turb
o cod
e
s
prop
osed in
this work. Section
3 p
r
e
s
ent
s t
he p
r
opo
sed
syst
em. Section
4 discu
s
se
s
the
simulatio
n
re
sults, an
d se
ction 5 pre
s
ent
s our
con
c
lu
si
ons.
2. Turbo Co
des
There are t
w
o main types of turbo
cod
e
s,
i.e.,
seri
al co
ncatenation an
d
parallel
concatenation. The concepts
of SCCCs and PCCCs used in this
work are i
n
troduced in the
fo
llo
w
i
ng
s
u
bs
ec
tio
n
s
.
2.1. Serial Conca
t
ena
t
ed
Conv
olutional Codes
(SCCCs
)
Figure 1,
sho
w
s the bl
ock
diagram of
a
n
SC
C
C
s
y
s
t
e
m
. T
h
e o
u
t
er
a
n
d
th
e in
ne
r
c
o
des
are Convoluti
onal Co
de (CC), and the i
nner
cod
e
must be Re
cu
rsive Systema
t
ic Convolutio
nal
(RS
C
) code.
In Figure 1a,
a rate of
k/
n
SCCC is
obta
i
ned u
s
ing
an
outer e
n
code
r of a rate
k/
l
, and an
inner
en
cod
e
r
of a rate
l/n
. A rand
om
interleave
r
(
π
) pe
rmute
s
t
he outp
u
t co
deword
s
of t
he
outer code
b
e
fore
pa
ssing
them to
the
i
nner
cod
e
.
Rate 1/3
is obt
ained
by u
s
in
g an
o
u
ter of
rate
1/2 and an in
ner of rate 2/
3.
Figure 1b,
sh
ows the d
e
co
ding p
r
o
c
e
s
s
of SC
CC, whi
c
h
wa
s do
ne
by iterative d
e
co
ding
usin
g a Soft-Input/Soft-Out
put (SISO) module
ba
se
d on the Log
-M
AP (Maximum A Posterio
ri)
algorith
m
. The symbol
s
λ
(.,
I
) and
λ
(.,
O
) at the input and output ports of SISO refer to L
og-
Likeli
hood
Ra
tio (LLR). The
LLR of a bin
a
ry bit z
(-1,1) is defined a
s
[15]:
(1
/
)
()
l
n
(1
/
)
zy
z
zy
(
1
)
whe
r
e
y
i
s
the noisy re
ceiv
ed co
de
word
s and
is probability.
Duri
ng the first iteration,
λ
(
UI
,
I
) is set to
zero,
since no prio
r information is ava
ilable on
the inp
u
t info
rmation
bits o
f
the inn
e
r en
cod
e
r. T
he
e
x
trinsic LL
Rs,
λ
(
UI
,
O
), a
r
e
passe
d throu
g
h
the de-inte
rle
a
ver (
1
π
) to obtain
λ
(
CO
,
I
).
The value of
λ
(
UO
,
I
) is
always
s
e
t to z
e
ro. After
interleavin
g, the
value
s
of
λ
(
CO
,
O
)
are fe
edb
ack to the
lo
wer ent
ry (correspon
ding
to
informatio
n bi
ts of th
e in
ne
r co
de
) of
the i
nner SISO
d
e
c
od
er to
start
the second
it
eration.
In fin
a
l
iteration, a
si
mple threshol
d ope
ration i
s
perfo
rmed
o
n
the
λ
(
UO
,
O
), to pro
d
u
c
e
a hard de
ci
si
on
estimation fo
r the transmitt
ed bits.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No
. 4, Decem
b
e
r
2015 : 122
5 – 1232
1227
Figur
e 1. Block di
agr
am of
SCCC: (
a
) S
C
C
C
en
co
der
, (b) SC
CC d
e
co
der
2.2. Parallel
Conc
ate
n
ate
d
Conv
olutional Code
s (P
CCCs
)
Figure 2
a
sho
w
s the
blo
c
k
diagram
of a
PCCC
en
cod
e
r. Th
ere a
r
e
two
RSC encoders
of
rate
1/2 in parallel,
separated b
y
a pseudo-random
interleaver
. A natural
rate
for su
ch
a
code
is
1/3 (on
e
sy
stematic bit a
n
d
two pa
rity bits fo
r o
ne
data bit). Th
e multiplexer conve
r
ts two o
r
more p
a
rall
el seq
uen
ce
s to
a single
seri
al seq
uen
ce.
Figur
e 2b, sh
ow
s the de
co
ding pr
oc
es
s
of P
CCC. Th
e de-m
u
ltiple
x
e
r bloc
k c
o
n
v
erts the
seri
al data th
at are re
ceiv
ed to para
llel
data. Duri
ng
the first itera
t
ion,
λ
(
U
1
,
I
) a
nd
λ
(
U
2
,
I
)
ar
e s
e
t
to z
e
ro.
λ
(
U
1
,
O
) are pa
ssed throu
gh interleave
r
(
π
) to obtain
λ
(
U
2
,
I
), while
λ
(
U
2
,
O
) i
s
de-
interleave
d
(
1
π
) to obtai
n
λ
(
U
1
,
I
) to
start t
he
se
con
d
ite
r
ati
on. At the
final iteration
,
λ
(
U
2
,
I
)
an
d
λ
(
U
2
,
O
)
will b
e
adde
d toge
ther, and a h
a
rd de
ci
sion
is made o
n
the sum
m
atio
n to obtain the
estimated inf
o
rmatio
n bits.
Figur
e 2. Block di
agr
am of
PCCC: (
a
) P
C
C
C
en
co
der
, (b) PC
CC d
e
co
der
Not used
(a)
I
n
f
o
r
m
a
tion bits
Encoder 1
r
a
te
=
1
/2
Encoder 2
r
a
te
=
1
/2
π
Multiple
x
e
r
U
1
U
2
To channel
(b)
R
ecei
ved dat
a
S
I
SO De
coder
1
S
I
SO De
coder
2
π
π
-
1
De
-
m
ultiple
x
e
r
(,
)
1
CI
(,
)
2
CI
(,
)
1
CO
(,
)
2
CO
(,
)
1
UI
(,
)
2
UI
(,
)
1
UO
(,
)
2
UO
Estima
te
d output
Not used
Not used
(a)
Outer
encoder
r
a
te
=
k
/l
π
UO
In
n
e
r
encoder
r
a
te
=
l/n
UI
CO
C
I
(b)
S
I
SO I
nne
r
SI
S
O
O
u
t
e
r
π
-
1
π
(,
)
CI
I
(,
)
CI
O
(,
)
CO
O
(,
)
UI
I
(,
)
UI
O
(,
)
UO
O
Not used
(,
)
CO
I
(,
)
UO
I
F
r
om demodulator
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Enhan
cem
e
n
t
the Perform
ance of OFDM base
d
on
Multiwa
v
elet
s Usin
g …
(S
a
m
eer A. Dawood)
1228
2.3. SISO Decoding Algo
rithm
The SISO mo
dule i
s
a fou
r
-po
r
t device that
acce
pts t
w
o in
put seq
uen
ce
s an
d g
i
ves two
output seque
nce
s
at any t
i
me. The tw
o
input vecto
r
s of SISO at time
t
are
λ
t
(
C
,
I
), which is a
prio
r informat
ion LLR of a
cod
e
word a
n
d
λ
t
(
U
,
I
), whi
c
h is a prio
r in
formation L
L
R of informati
o
n
word.
While t
he two o
u
tput
vecto
r
s at ti
me
t
ar
e
λ
t
(
C
,
O
),
whi
c
h i
s
t
he extrin
si
c in
formation
LL
R of
a cod
e
word a
nd
λ
t
(
U
,
O
), which i
s
the extrinsi
c info
rma
t
ion LLR of in
formation
word.
SISO Log-M
AP decod
er u
s
e
s
the max*( )
operation which i
s
define
d
as [15]:
ma
x
*
(
)
l
n
(
e
)
j
a
j
j
a
(
2
)
The SISO Lo
g-MAP algo
rithm req
u
ire
s
a forwa
r
d a
n
d
backward recu
rsi
on. The
forwa
r
d
recursio
ns of
state
s
at time
t
(
t
=
0
, 1,....
.
...,
2
m
-1) are
given by:
1
:(
)
11
(
)
m
a
x
*
((
)
)
(
)
(,
)
(
)
(
,
)
E
kn
Sj
j
j
j
tt
t
t
es
e
s
jj
s
se
u
e
u
I
c
e
c
I
(3)
The ba
ckwa
rd recursio
ns
of state
s
at time
t
(
t
=2
m
-1, 2
m
-2,....
....
,0) are given by:
11
1
:(
)
11
()
m
a
x
*
(
(
)
)
(
)
(
,
)
(
)
(
,
)
E
kn
Ej
j
j
j
tt
t
t
es
e
s
jj
s
se
u
e
u
I
c
e
c
I
(4)
whe
r
e:
e
de
scrib
e
s the tra
n
sition
(e
dge
) betwe
en
st
at
es of th
e trell
i
s at time i
n
st
ants
t
a
nd
t
+1
,
s
S
(
e
) is th
e starting state
of edge
(
e
),
s
E
(
e
) is th
e e
nding
state o
f
edge (
e
),
u
(
e
) i
s
the in
p
u
t
symbol
of ed
ge (
e
),
c
(
e
) i
s
the
output
symbol
of ed
ge (
e
),
k
/
n
i
s
the
code
rate, and
m
is
th
e
maximum nu
mber of sta
g
e
s
(me
m
ory si
ze) in the e
n
coder.
The forward and ba
ckward recursio
ns
will be initialized as [15]:
0
0
0
()
ss
s
ot
he
r
w
ise
(
5
)
0
1
()
2
m
s
(6)
Then, the two
outputs of the SISO deco
der at time
t
are define
d
as:
1
:(
)
1
1
1
:(
)
1
1
(,
)
m
a
x
*
(
(
)
)
(
)
(
,
)
(
(
)
)
m
a
x
*
(
(
)
)
()
(
,
)
(
()
)
j
j
n
jS
j
j
E
tt
t
t
eu
e
j
n
Sj
j
E
tt
t
eu
e
j
uO
s
e
c
e
c
I
s
e
se
c
e
c
I
s
e
(
7
)
1
:(
)
1
11
1
:(
)
1
11
(
,
)
m
a
x
*
(
()
)
(
)
(
,
)
()
(
,
)
(
()
)
m
a
x
*
(
(
))
(
)
(
,
)
(
)
(
,
)
(
(
))
j
j
kn
jS
i
i
i
i
E
tt
t
t
t
ec
e
ii
ij
kn
S
i
ii
iE
tt
t
t
ec
e
ii
ij
cO
s
e
u
e
u
I
c
e
c
I
s
e
se
u
e
u
I
c
e
c
I
s
e
(8)
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TELKOM
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Vol. 13, No
. 4, Decem
b
e
r
2015 : 122
5 – 1232
1229
3. Proposed
Sy
stem
The blo
c
k di
agra
m
in Fi
gure
3, give
s the p
r
o
p
o
s
ed
model
for OF
DM
b
a
se
d on
DM
WCST sy
stem with
tu
rbo co
de
s.
Ran
dom bi
n
a
ry data
are
gene
rate
d a
t
the tran
smi
tter.
These data
are en
co
ded
by turbo co
de (SCCC o
r
PCCC) of
rate 1/3 as
pre
s
ente
d
in
the
previou
s
secti
on. The next step is Se
rial
-to-Parall
el (S/P) conve
r
sion
, and it is con
ducte
d to form
OFDM
sym
b
ols
and
to m
ap the
bit
s
to
symb
ols.
Th
en,
the
traini
ng seq
uen
ce
(pilot su
bca
rri
ers)
is in
se
rted. T
he
N
-p
oint In
verse
DM
WCST (IDM
WCST) is
appli
e
d to the
sign
al to a
c
hieve
the
multica
rrie
r
modulatio
n tech
niqu
e. Ze
ros
are i
n
serted in seve
ra
l bins of IDM
W
CST to
red
u
ce
interferen
ce
of the adjace
n
t carriers. T
he data
conv
erted to a fra
m
e stru
ctu
r
e
and sent to th
e
receiver ove
r
the cha
nnel.
At the receiv
er sid
e
, the inverse ope
ra
tions
are pe
rforme
d to re
cover the correct data
strea
m
. The receive
d
sig
n
a
l is co
nverte
d to
a parall
e
l versio
n via S/P conversi
on. No
w,
N
-p
oint
DM
WCST a
r
e performed to achieve the
multicarri
er d
e
modul
ation tech
niqu
e, and the zero p
a
d
s
are remove
d
.
Then,
the training se
qu
ence
is
utili
zed to
estim
a
te the cha
nnel fre
que
n
cy
respon
se (
H
(
k
)) as
follows
:
()
(
)
,
1
,
2
,
.
.
...
.
()
Yk
p
Hk
k
Xk
p
(
9
)
whe
r
e
Y
p
(k
)
repre
s
e
n
ts th
e re
ceived
pil
o
t sub
c
a
rri
ers, and
X
p
(k
)
i
s
the tran
smitted pilot
sub
c
a
rri
ers. Estimated dat
a (
()
Xk
) can be o
b
tained
with the followi
ng e
quation:
1
(
)
(
)
.
(
)
,
1
,
2
,
.
....
Xk
H
k
Y
k
k
(
1
0
)
The output o
f
the channel
compe
n
sato
r pas
se
s
through signal demap
ping, and
it
is
decode
d by the turbo
cod
e
(S
CCC or P
C
CC) d
e
code
r.
Figure 3. Block di
agram of
the tur
bo-co
ded OF
DM b
a
se
d on DM
WCST
syste
m
4. Simulation Resul
t
s an
d Discus
s
io
n
In this se
ctio
n, the BE
R p
e
rform
a
n
c
e
o
f
uncode
d O
F
DM
-DM
W
CST and
code
d OF
DM
-
DM
WCST using
SCCCs and
P
C
CCs is
comp
are
d
for
differe
nt cha
nnel co
nd
itions,
in
cludi
ng
ou
tpu
t
da
t
a
in
put
da
t
a
In
sert Pi
l
o
t
symb
ol
ID
MWCS
Cha
n
nel
Estimation
S/P
Mult
ipat
h c
h
an
ne
l
P/S
S/P
DMW
C
ST
Cha
n
nel
Com
p
ens
a
tio
n
P/S
S
CCC
or
PC
CC
enco
der
dem
a
pp
ing
Mapp
in
g
AW
G
N
S
CCC
or
PC
CC
deco
der
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TELKOM
NIKA
ISSN:
1693-6
930
Enhan
cem
e
n
t
the Perform
ance of OFDM base
d
on
Multiwa
v
elet
s Usin
g …
(S
a
m
eer A. Dawood)
1230
0
2
4
6
8
10
12
14
16
18
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
P
e
r
f
o
r
m
a
nc
e
of
D
M
W
C
S
T
-
O
F
D
M
in
A
W
G
N
a
t
4
-
Q
A
M
S
NR (
d
B)
BE
R
Un
c
o
de
d
O
F
DM
S
CCC-
O
F
D
M
P
CCC-
O
F
D
M
0
2
4
6
8
10
12
14
16
18
20
22
24
26
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
P
e
rf
o
r
m
a
nc
e
of
D
M
W
C
S
T
-
O
F
D
M
in
A
W
G
N
a
t
1
6
-
Q
A
M
SN
R (
d
B)
BE
R
Un
c
o
de
d
O
F
D
M
SC
C
C
-
O
F
D
M
PC
C
C
-
O
F
D
M
Figure 5. Performa
nce of OFDM
-DM
W
CST
in the AWG
N
cha
nnel at 16
-QAM.
Figure 4. Performa
nce of OFDM
-DM
W
CST
in the AWG
N
cha
nnel at 4-QAM.
AWG
N
, Rayl
eigh flat fadin
g
, and Raylei
gh freq
uen
cy
sele
ctive fadi
ng. The pe
rfo
r
man
c
e of the
s
e
system
s
wa
s analy
z
ed
u
s
i
ng MAT
L
AB
versio
n 7.
8.
Table
1,
sho
w
s the
pa
ra
meters a
nd t
heir
values for the
system u
s
ed
in the simula
tion.
Table 1. Simulation Para
meters
Parameter
Value
S
y
stem band
w
i
dt
h
10 MHz
Number of
DMW
C
ST points (
N
)
64
Number of
useful data subcarriers
48
Modulation t
y
pe
4-QAM, a
nd 16
-
Q
AM
Turbo code
rate
1/3
PCCC encode
r g
enerato
r
Encoder 1: [1,5/7
]
oc
tal
, d
fr
e
e
=5
Encoder 2: [1,5/7
]
oc
tal
, d
fr
e
e
=5
SCCC encode
r g
enerato
r
Outer:
[7,5]
oc
ta
l
, d
fr
e
e
=5
Inner: [1, 0,
7/3; 0
,
1,2/3]
oc
ta
l
, d
fr
e
e
=3
Number of
decod
ing iteration
5
Figures 4, an
d 5, illustrate
a com
pari
s
o
n
of PCCC-OF
D
M, SCCC-O
F
DM, and
un
cod
e
d
OFDM over an
AWGN ch
annel usin
g 4-QAM,
a
nd
16-QA
M, re
spectively. Th
ese fig
u
re
s
show
that the perfo
rman
ce of th
e OFDM
syst
em wa
s
imp
r
oved by usin
g turbo
cod
e
s
. In addition,
the
perfo
rman
ce
of
PCCC-OF
D
M wa
s better
th
an
th
at
of SCCC-OF
D
M. Fig
u
re 4
sh
ows that,
at a
BER = 10
-3
, t
he SNR
of th
e PCCC-OF
D
M o
u
tpe
r
formed b
o
th the
SCCC-OF
DM and
un
co
d
ed
OFDM
by
ab
out 1.6
and
6.
7 dB,
re
spe
c
ti
vely. Figure
5
,
sho
w
s th
at, for a
BER = 1
0
-3
, the SNR
of
the PCCC-O
FDM outp
e
rf
orme
d the SCCC-OF
D
M and un
co
ded
OFDM by a
bout 4.3 and
9 dB,
r
e
spec
tively.
Figures 6, a
n
d
7, illustrate
the BER perfo
rman
ce of
cod
ed OF
DM
and un
cod
e
d
OFDM
system
s
over Raylei
gh flat
fading
chan
n
e
l for
4-QAM, and
16
-QAM
, re
spe
c
tively. The
s
e fig
u
res
sho
w
that, the perfo
rman
ce of the cod
ed syst
em
was mu
ch bett
e
r than that
of the unco
d
e
d
system. Fig
u
r
e 6
sho
w
s that, the perf
o
rma
n
ce
of the co
ded
OF
DM sy
stem u
s
ing P
C
CC a
nd
SCCC code
s
provide
d
a coding gain of
6.7
and
5 dB
, respe
c
tively, for achievin
g a BER
of 1
0
-3
.
Figure 7 sho
w
s that, the perfo
rman
ce
of the
coded
OFDM syste
m
using PCCCs an
d SCCCs
provide
d
a
co
ding g
a
in of 8
.
5 and 5.1
dB
, respe
c
tively, for a
c
hievin
g
a BER of 1
0
-3
. Als
o
, these
figure
s
indi
ca
tes that the perform
an
ce o
f
the
PCCC-
OFDM
syste
m
was bette
r
than that of
the
SCCC-OFDM
system. Th
e
PCCC-OFD
M
system a
c
hi
eved a BER
of 10
-3
at SNR =
10 an
d 1
4
.8
dB for 4-QA
M an
d 1
6
-QA
M
, re
spe
c
tive
ly, whe
r
ea
s, t
he
sam
e
e
r
ro
r p
e
rfo
r
man
c
e was a
c
hiev
ed
by the SCCC-OF
D
M sy
ste
m
at SNR = 1
1
.6 and
18.2
dB for 4-QAM
and 16-QAM
,
respe
c
tively.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No
. 4, Decem
b
e
r
2015 : 122
5 – 1232
1231
0
2
4
6
8
10
12
14
16
18
20
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
P
e
r
f
o
r
m
a
n
ce o
f
D
M
W
C
ST
-OF
D
M
i
n
fl
at f
a
d
i
n
g
at
4-QA
M
S
NR (
d
B)
BE
R
Un
c
o
d
e
d O
F
D
M
SC
C
C
-O
FD
M
PC
C
C
-O
FD
M
Figure 6. Performa
nce of OFDM
-DM
W
CST
in the flat fading ch
ann
el at 4-QAM.
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
P
e
r
f
o
r
m
a
n
c
e o
f
D
M
W
C
ST
-O
F
D
M
i
n
fl
at
fad
i
n
g
at
16-
Q
A
M
S
NR (
d
B
)
BE
R
Unc
o
de
d
O
F
DM
SC
C
C
-
O
F
D
M
PC
C
C
-
O
F
D
M
Figure 7. Performa
nce of OFDM
-DM
W
CST
in the flat fading ch
ann
el at 16-QAM.
0
2
4
6
8
10
12
14
16
18
20
22
24
26
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
P
e
r
f
o
r
m
a
nc
e
of
D
M
W
C
S
T
-
O
F
D
M
in
f
r
e
q
ue
n
c
y
s
e
le
c
t
iv
e
f
a
d
i
n
g
a
t
4
-
Q
A
M
S
NR (
d
B)
BE
R
Un
c
o
de
d
O
F
DM
S
CCC-
O
F
D
M
P
CCC-
O
F
D
M
Figure 8. Performa
nce of OFDM
-DM
W
CST in
the sele
ctive fading
cha
nne
l at 4-QAM.
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
P
e
rf
o
r
m
a
nc
e
of
D
M
W
C
S
T
-
O
F
D
M
i
n
f
r
e
q
ue
n
c
y
s
e
l
e
c
t
iv
e
f
a
di
ng a
t
1
6
-
Q
A
M
SN
R
(d
B
)
BE
R
Un
c
o
d
e
d
O
F
DM
S
CCC-
O
F
D
M
P
CCC-
O
F
D
M
Figure 9. Performa
nce of OFDM
-DM
W
CST in
the sele
ctive fading
cha
nne
l at 16-QAM.
Figures 8, a
nd 9,
com
p
a
r
e the
pe
rformanc
e of th
e thre
e
syst
ems i
n
a
fre
quen
cy-
sele
ctive
Ra
yleigh fadi
ng
ch
ann
el u
s
i
ng 4
-
QAM
a
nd 1
6
-QAM,
respe
c
tively. Two
path
s
were
sele
cted, the
se
cond
path
had a g
a
in
of
−
10 dB
an
d a delay of
eight sa
mple
s. Obviou
sly, the
cod
ed sy
ste
m
wa
s more
robu
st in the frequ
en
cy-sele
c
tive fadi
ng ch
ann
el than the un
coded
OFDM. Also, PCCC-OFDM wa
s
better than SCCC-OFDM.
As sh
own in
Figure 8, a B
E
R = 1
0
-3
r
e
sulted in a
7.3
dB impr
ovement for
PCCC-
OFD
M
and 5.8 dB improvem
ent for SCCC-OF
D
M
co
mpa
r
e
d
with the un
cod
ed sy
ste
m
.
Figure 9
sho
w
s th
at, the
BER be
cam
e
con
s
tant
at 8.6*10
-3
after SNR
of app
roximately
36 dB in
the
uncode
d OF
DM, si
nce n
o
CP exi
s
t
e
d
in t
he
ca
se
of
OFD
M
-
D
M
W
CS
T
sy
st
e
m
;
hen
ce, ISI o
c
curred
an
d
resulted i
n
t
he lo
ss of
o
r
thogo
nality
betwe
en
su
b
c
arrie
r
s an
d
the
occurre
n
ce of ICI. Turbo
code
s ca
n eli
m
inate the re
sidu
al ISI and ICI, therefo
r
e
,
offering
better
perfo
rman
ce
in this
cha
n
n
e
l. Also, the
perfo
rman
ce
of OFDM
-DM
W
CST
with t
he PCCC
co
ding
scheme
wa
s better than th
at with the SCCC c
oding
scheme. Th
e
figure sh
ows that, the PC
CC-
OFDM
syste
m
had a BER of 10
-2
at SNR = 1
4
dB. SCCC-OF
D
M
had the
sam
e
BER at SNR =
18.8 dB, and
uncode
d OF
DM had the
same BER at SNR =
34 dB
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Enhan
cem
e
n
t
the Perform
ance of OFDM base
d
on
Multiwa
v
elet
s Usin
g …
(S
a
m
eer A. Dawood)
1232
5. Conclusio
n
In this
work,
turbo
co
de
s are
propo
se
d for the
OF
DM-DM
W
CS
T syste
m
to
achi
eve
highe
r pe
rformance an
d robu
st
ne
ss ag
ainst wirel
e
ss
comm
uni
cati
on
chan
nel. The
p
e
rfo
r
ma
nce
analysi
s
of
th
e
p
r
opo
se
d system wa
s
e
v
aluated by
simulation
s
in
different ch
a
nnel
s,
in
cludi
ng
AWG
N
, Rayleigh flat fading, and Rayl
eigh freq
uen
cy sele
ctive fading. The
simulation re
sults
indicated tha
t
the use of turbo co
de
s with
the OFDM
-DM
W
CST system can eliminate
the
resi
dual
ISI, therefo
r
e
,
offering
a hi
ghe
r
data rate in
wirel
e
ss
com
m
unication. A
l
so, the
PCCCs
system
gives better BE
R
perfo
rman
ce
at low S
N
R
value
s
than
th
e SCCCs
system in all
of the
cha
nnel
s. Th
e goo
d pe
rfo
r
man
c
e
of the PCCCs
sy
stem can b
e
explained
b
y
its better b
u
rst
error correcti
on capability inside codeword's
than the SCCCs
syst
em. Also, the PCCCs
syst
em
provide
d
g
o
o
d
final
estim
a
tion du
e to
ad
dition o
peration of
two
e
s
timations ta
ke
n from
two SI
SO
decode
rs in t
he re
ceive
r
d
e
sig
ned for th
e parall
e
l
gro
up of two ide
n
tical convolu
t
ional en
cod
e
r
s.
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