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
310
~232
1
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
5.1
087
8
2
310
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
PAPR Reduction
for Imp
r
oved Ef
ficien
cy of OFDM
Modulation for Next Generati
on Communication S
y
st
ems
Shatru
g
hn
a P
r
as
ad Yadav
1
,
Sub
has
h
Ch
andra Bera
2
1
Electr
i
cal
and
Electronics Eng
i
neering
Depar
t
ment
, Indus University
, Ahme
dab
a
d, Gujar
a
t, Ind
i
a
2
Satcom & Navigation
S
y
stems
Engineering Div
i
sion, Space A
pplications C
e
ntre,
Indian Space Research Org
a
nization,
Ahmedabad, Ind
i
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Apr 15, 2016
Rev
i
sed
Ju
l 1
,
2
016
Accepte
d
J
u
l 18, 2016
Highly
lin
ear po
wer amplifiers are requir
e
d for
tr
ansferring
larg
e amount of
data for
future com
m
unication.
Ort
hogonal freq
u
ency
div
i
sion
m
u
ltiplexing
(OFDM)
provides high data rate transm
ission capability
with r
obustness to
radio ch
annel
impairments. It has
been widely
accepted
for future
communication f
o
r different serv
ices. Bu
t, it suffers from high value of peak-
to-aver
a
ge power ratio (PAPR). High
value of PAPR drives
high power
am
plifiers in
sat
u
ration
and
caus
e
s it
to oper
a
te
i
n
the non
line
a
r
region.
In
this paper
,
com
p
arative stud
y
o
f
four
differ
e
nt
PAPR reduction
techn
i
ques:
clipping and filtering (CF), selectiv
e mapping
method (SL
M
), partial
transmit sequen
ce (PTS) and DFT- sp
read technique have
been done.
M
a
them
ati
cal m
odeling
and M
a
tl
ab s
i
mulation
s
have been performed to
arrive
at th
e resu
lts with 4 QAM
m
odulation format and 1024 number of sub
carri
ers
.
At 0.0
1
% of com
p
l
e
m
e
nt
ar
y
cumulativ
e distributio
n function
(CCDF) significant reduction of 11.3, 3.5
,
3.4 an
d 1.0 dB have been obtain
e
d
with DFT
-
spread,
SL
M, PT
S
an
d CF techniques
respectively
.
Keyword:
Clip
p
i
ng
an
d Filterin
g
DFT Sp
rea
d
OF
DM
PAPR
Partial Tran
smit Seq
u
e
n
c
e
Selectiv
e Mapp
ing
Method
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
:
Shat
r
u
gh
na Pra
s
ad Ya
dav
,
Electrical and
Electronics
E
n
gi
nee
r
i
n
g Depa
rt
m
e
nt
,
Indus Uni
v
ersi
ty,
Ahm
e
daba
d, G
u
ja
rat
,
In
di
a.
Em
a
il: sp
yad
a
v
68@g
m
ail.co
m
1.
INTRODUCTION
Th
e fu
ture g
e
neratio
n
co
mm
u
n
icatio
n
requ
ires h
i
gh
d
a
ta rate. Bu
t d
ealin
g with
th
e h
i
gh
d
a
ta rate in
an
unp
red
i
ctable wireless ch
an
n
e
l is a d
i
fficu
lt task
. In
o
r
d
e
r t
o
exc
h
a
n
ge
l
a
rger am
ou
nt
of i
n
f
o
rm
at
i
on hi
g
h
l
y
lin
ear p
o
wer am
p
l
ifiers are req
u
i
red.
W
ith
th
e ap
p
licatio
n o
f
o
r
t
h
ogo
n
a
l
frequ
en
cy d
i
visio
n
m
u
ltip
le
x
i
ng
(OFDM) power am
p
lifier no
n
lin
earities b
e
comes
m
o
re vu
lnerab
le
owing
t
o
th
ei
r h
i
g
h
p
e
ak
to av
erage
p
o
wer
ratio (PAPR
)
c
a
use
d
due to la
rge
fluc
tuations in their signa
l
envelope.
OF
DM is desira
bl
e because of se
veral
adva
ntage
s
ass
o
ciated
with it, suc
h
as, to
leran
ce to in
ter-sy
m
b
o
l
in
terfere
nce,
good s
p
e
c
tral efficiency
, bes
t
p
e
rform
a
n
ce of freq
u
e
n
c
y sel
ectiv
e fad
i
ng
i
n
m
u
ltip
ath
env
i
ro
n
m
en
t, robu
stn
e
ss to ch
an
n
e
l
im
p
a
ir
m
e
n
t
s etc.
OFDM is efficien
tly u
s
ed
to
co
m
b
at th
e u
npred
ictab
ility o
f
wireless
ch
ann
e
l and
prov
id
e
h
i
gh
data rate
co
mm
u
n
i
catio
n
s
[1
].
Wh
en
co
m
p
ared
with
t
r
ad
ition
a
l co
mm
u
n
i
catio
n
syste
m
s, it
h
a
s several ad
v
a
n
t
ag
es o
v
e
r
it. It turns t
h
e freque
ncy-selec
tive fa
di
ng cha
nnel i
n
to a
flat
fadi
ng c
h
a
n
ne
l and he
nce
use
s
sim
p
le receiver.
It
is sp
ectrally efficien
t and
is id
eal fo
r m
u
lti
med
i
a co
mm
u
n
icatio
n system
s. On
th
e o
t
her
h
a
nd
, it is sen
s
itiv
e t
o
t
i
m
i
ng a
n
d
f
r
e
que
ncy
sy
nch
r
oni
zat
i
o
n e
r
r
o
r
s
an
d
has
hi
g
h
val
u
e
o
f
P
A
PR
[
2
]
.
OF
DM
sy
st
em
s has
m
a
ny
appl
i
cat
i
ons a
n
d
are wi
del
y
use
d
i
n
hi
gh
-bi
t
-
r
a
t
e
di
gi
t
a
l
su
b
s
cri
b
e
r
l
i
n
es
(HDSL),
d
i
g
ital au
d
i
o
b
r
o
a
dcastin
g
(DAB
), d
i
g
ital v
i
d
e
o b
r
o
a
d
casti
n
g
(DVB) along
with
h
i
gh-d
e
fi
n
itio
n
t
e
l
e
vi
si
on
(H
DTV
)
,
t
e
rre
st
r
i
al
br
oadcast
i
n
g
, et
c.
It
is
co
nsid
ered
as a b
e
tter cand
i
d
a
te
for th
e fu
t
u
re
gene
rat
i
o
n co
m
m
uni
cat
i
on s
y
st
em
s [3]
.
In
t
h
e OF
DM
tran
sm
it
ter th
e d
i
g
itally
m
a
p
p
e
d
4-QAM si
g
n
a
l is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
PAPR Re
duction for
Impr
ove
d
Efficiency
of
OFDM M
o
dul
ation for
Next .... (
S
hatrughna Pras
ad Yadav
)
2
311
di
vi
de
d i
n
t
o
N
num
ber of s
u
bcar
ri
ers wi
t
h
t
h
e hel
p
of se
ri
al
t
o
paral
l
e
l
(S/
P
) co
n
v
ert
e
r
.
Then eac
h su
bcar
ri
er
is
m
u
ltip
lied
with
a co
m
p
lex
sig
n
a
l
e
and a
d
d
e
d t
o
get
h
e
r
t
o
get
t
h
e O
F
DM
si
gnal
.
Thi
s
i
s
eq
ui
val
e
nt
t
o
i
nve
rse di
scret
e
Fou
r
i
e
r t
r
an
sfo
r
m
(IDFT)
operat
i
on an
d i
s
im
pl
em
ent
e
d t
h
r
o
ug
h
i
nve
rse fast
F
o
u
r
i
e
r
trans
f
o
r
m
(IFF
T
)
[4]
.
The
tim
e
-d
om
ain signa
l,
r
i
s
gi
ve
n as i
n
e
quat
i
o
n
(
1
).
r
∑
X
n
e
0
t
T
u
0
otherwise
(1
)
After
fre
q
u
enc
y
- to tim
e
-dom
ain co
nve
rsio
n,
the sig
n
al is summed up, and the cyclic prefix is a
dde
d
as gi
ven
i
n
e
q
u
a
t
i
on
(2
).
s
r
t
T
u
T
g
,
0
t
T
g
r
t
T
g
,
T
g
0
otherwise
(2
)
Whe
r
e, T
u
i
s
t
h
e use
f
ul
sy
m
bol
pe
ri
o
d
, T
g
is cyclic
p
r
efix d
u
r
ati
o
n
(gu
a
rd
in
terv
al) and T
s
= T
u
+ T
g
is
th
e
t
o
t
a
l
OFDM
s
y
m
bol
du
rat
i
o
n. T
h
e t
r
a
n
s
m
i
t
t
e
d base
ba
nd si
g
n
al
i
s
fo
rm
ed by
l
i
nki
ng t
oget
h
er al
l
OF
DM
sy
m
b
o
l
s in
time do
m
a
in
as in
eq
u
a
tion
(3
).
s
t
∑
s
ts
T
(3
)
Cyclic prefix is added to reduce effect of inter
sy
m
b
o
l
in
te
rferen
ce and
in
te
r carrier inter
f
erence and
to
m
a
in
ta
in
o
r
th
og
on
alit
y b
e
t
w
een
th
e two
sig
n
a
ls. No
rm
ally, so
me p
a
rt o
f
th
e fron
t p
o
rtio
n
o
f
t
h
e sign
al is
copied a
nd
pa
sted in the empty space usua
lly provi
ded for the
guard band in
the
normal co
mmunic
a
tion
s
y
s
t
em
s
.
Thi
s
si
gnal
i
s
fi
n
a
l
l
y
up con
v
e
r
t
e
d t
o
a car
r
i
er fre
que
ncy
t
h
r
o
u
g
h
ba
nd
p
a
ss
m
odul
at
i
o
n an
d
tran
sm
it
ted
as g
i
v
e
n
i
n
eq
uatio
n
(4).
Wh
ere,
u
(
t
)
is the tran
sm
itted
RF sign
al and f
c
is t
h
e RF
carrie
r
fre
que
ncy
.
u
t
R
e
s
t
e
п
(4
)
M
a
t
l
ab sim
u
l
a
ti
on has bee
n
p
e
rform
ed at
2 GHz carri
er f
r
e
quency
wi
t
h
10
24
num
ber of su
bcarri
ers
(N),
5.
12
μ
s
of
usef
ul
sym
bol
peri
od
(
Tu
)
,
0.16
μ
s o
f
guar
d
i
n
t
e
rval
(cy
c
l
i
c
prefi
x
) an
d
5.2
8
μ
s of to
tal OFDM
sym
bol
peri
od [
5
]. 4
-
Q
A
M
baseban
d
m
odul
at
i
on wi
t
h
IFFT of l
e
ngt
h
204
8 (
2
L)
has been consi
d
e
r
ed.
T
o
achi
e
ve over
sam
p
l
i
ng zeroes
are pad
d
ed t
o
t
h
e si
gnal
.
2.
PEAK T
O
A
V
ER
AGE
PO
WER
RATI
O
OF THE
OF
DM
SIG
N
AL
PAPR is a m
e
a
s
u
r
e
u
s
ed
to quan
tify th
e flu
c
tu
atio
n
s
i
n
t
h
e
envel
ope
o
f
m
u
lt
i
carri
er si
gnal
s
[6]
.
For
a
gi
ve
n sam
p
l
e
{x
m
} the average power a
n
d peak power for an OF
DM
sy
st
em
i
s
gi
ven by
equat
i
o
n (
5
) and
(
6
)
respectively.
P
∑
x
(5
)
P
x
(6
)
Peak -
to –
Average Power ra
tio
(P
A
P
R)
i
n
O
F
D
M
syste
m
i
s
defi
ned as the rat
i
o
of m
a
x
i
m
u
m
(peak)
powe
r
to ave
r
age power
of the com
p
lex passband di
scret
e
t
i
m
e
si
gnal
as given
by
equat
i
o
n (
7
).
PA
P
R
(7
)
It
i
s
al
so expre
ssed i
n
t
e
rm
s o
f
crest
fact
or (
C
F) gi
ven
by
equat
i
on (
8
).
CF
√
PA
P
R
(8
)
For a l
a
r
g
e n
u
m
ber of subca
rri
ers, t
h
e
baseband
OF
DM
s
i
gnal
can be a
ppr
oxi
m
a
t
e
d b
y
a com
p
lex
Gaussi
an di
st
ri
but
i
on. C
u
m
u
lat
i
v
e di
st
ri
but
ion
fu
nct
i
on (C
DF)
of t
h
e am
pl
i
t
ude of t
h
e
sam
p
l
e
s i
s
used t
o
m
easure percent
a
ge of t
h
e sa
m
p
l
e
s whi
c
h are affect
ed by
t
h
e cl
i
ppi
ng o
p
e
rat
i
on [7]
.
C
u
m
u
l
a
ti
ve di
st
ribut
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
:
231
0
–
23
21
2
312
funct
i
on (C
DF)
of
z
i
s
gi
ven as
i
n
equat
i
on
(9)
.
Fz
z
P
z
Pz
.
Pz
…….P
z
1
e
(9
)
Whe
r
e,
Pz
=
fz
u
du,
n
0,
1,2,
…
…
.
N
1
(1
0)
Co
m
p
le
men
t
ary cu
m
u
lat
i
v
e
d
i
strib
u
tio
n
fun
c
tio
n
(CCDF) is u
s
ed
to find
ou
t th
e p
r
o
b
a
b
ility
th
at th
e
PAPR (crest fa
ctor) exceeds a
particul
ar value as given in e
q
uation (11).
F
z
z
P
z
1
P
z
z
1
Fz
z
1
1
e
(1
1)
PAPR
val
u
e o
f
t
h
e OFDM
sy
st
em
i
s
pl
ot
t
e
d i
n
Fi
gure 1
and 2 f
o
r
QPS
K
and
4 QAM
m
odul
at
i
on
respect
i
v
el
y
for di
ffere
nt
num
ber o
f
su
bcarri
ers. At
0.
01%
of C
C
D
F, P
A
P
R
val
u
es for
Q
PSK m
odul
at
i
on are
10.
5, 1
0
.7,
10.
9, 11
.2 an
d 11
.4 dB
for N =
64, 1
28, 2
5
6
,
512 an
d 10
24
respect
i
v
el
y
.
Sim
i
l
a
rly
for QAM
m
odul
ati
on t
h
ese val
u
es are 11.5,
11.
7, 1
2
.
0
,
12.
2, and
12.
5
dB
respect
i
v
ely
.
It
i
s
evi
d
ent
from
t
h
e fi
gure t
h
at
val
u
e o
f
P
A
PR
i
n
creases wi
t
h
i
n
crease i
n
nu
m
b
er of su
bcar
ri
ers and
4
-
Q
A
M
m
odul
at
i
on
has ap
pr
oxi
m
a
t
e
l
y
1.0
dB
hi
g
h
er
PAPR
t
h
an t
h
a
t
of QPS
K
m
odul
at
i
on form
at
.
Fig
u
re
1
.
PAPR o
f
th
e
orig
inal OFDM system
with
QPSK
b
a
seb
a
nd
m
o
du
latio
n
Fi
gu
re
2.
P
A
P
R
of
t
h
e
o
r
i
g
i
n
al
OF
DM
sy
st
em
wi
t
h
4 Q
A
M
base
ba
nd
m
odul
at
i
o
n
3.
PA
PR
R
E
DUC
TION
TECHNIQUES
There are di
ffe
rent
t
echni
ques
used f
o
r P
A
P
R
reduct
i
on.
I
n
t
h
i
s
paper we
have i
nvest
i
g
at
ed fol
l
o
wi
n
g
fou
r
t
echni
que
s:
cl
i
ppi
ng and
fi
lt
eri
ng, sel
e
ct
i
v
e
m
a
ppi
ng m
e
t
hod (SLM
), part
i
a
l t
r
ansm
i
t
sequence (PTS) and
7
8
9
10
11
12
13
14
10
-3
10
-2
10
-1
10
0
O
F
DM
sy
s
t
e
m
w
i
th Q
PSK Base
band
M
o
d
u
latio
n
N-point
FFT
PAPR
[
dB
]
CCDF
N=
2
5
6
N=
5
2
8
N
=
102
4
N=
6
4
N=
1
2
8
7
8
9
10
11
12
13
14
10
-3
10
-2
10
-1
10
0
OFDM sy
st
e
m
w
i
t
h
QAM
Bas
e
band Modul
at
i
o
n
N-
poi
nt
FFT
PAPR
[
d
B]
CC
DF
N=
64
N=
128
N=
256
N=
51
2
N=
102
4
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
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208
8-8
7
0
8
PAPR Re
duction for
Impr
ove
d
Efficiency
of
OFDM M
o
dul
ation for
Next .... (
S
hatrughna Pras
ad Yadav
)
2
313
discrete Fourier transf
orm
(DFT) sprea
d
techniq
u
e. E
ach
r
e
duct
i
on t
echni
que i
s
ha
vi
ng c
e
rt
ai
n advant
ag
es and
di
sadvant
ages
associ
at
ed wi
t
h
i
t
over anot
her
t
echni
que.
Ap
pl
i
cati
on of par
t
i
c
ul
ar
t
echni
que depen
d
s u
p
on t
h
e
val
u
e o
f
P
A
PR
desi
red
and
c
o
m
put
ati
onal
com
p
l
e
xit
y
i
nvol
ved. It
ca
n
be
obser
ved
fr
om
t
h
e resul
t
s
o
b
t
a
i
n
ed
th
at th
e DFT sp
read
tech
n
i
q
u
e g
i
v
e
s lo
west
PAPR v
a
lu
e
bu
t its i
m
p
l
e
m
e
n
tatio
n
is d
i
fficu
lt. On
th
e
o
t
her h
a
nd
,
clipping and filtering
m
e
thod is s
i
m
p
le
st from
application point of view
but gives distorti
ons and spectral
regr
owt
h
.
3.
1.
Clipping
and Filtering Method
PAPR
can be r
e
duced
by
cl
i
ppi
ng t
h
e pea
k
a
m
p
l
it
ude of t
h
e
t
r
ansm
it
t
e
d si
g
n
al
and passi
n
g
i
t
t
h
rough
a lo
w
p
a
ss filter [8
].
In case o
f
ov
er sam
p
l
e
d
sig
n
a
l
b
a
n
d
p
a
ss filter is
req
u
i
red to
redu
ce th
e ou
t of b
a
nd
r
a
d
i
atio
n
.
Bu
t
f
o
r
th
e
b
a
nd
l
i
mited
sig
n
a
l clip
p
e
d
at N
yquist sa
m
p
l
i
n
g
r
a
te all th
e d
i
sto
r
tio
n
s
lies w
ith
in
th
e
b
a
n
d
, h
e
n
ce a lo
w
p
a
ss filter is su
fficien
t [9
],[10
]
. Bu
t
th
e lo
w p
a
ss filt
er u
s
ed
after clip
p
i
n
g
op
eratio
n
m
o
d
e
rate
ly en
l
a
rg
es th
e PAPR. PAPR can
b
e
also
red
u
c
ed
b
y
clip
p
i
ng
an
d
frequ
en
cy d
o
m
ain
filter
i
n
g
as
show
n i
n
Figur
e
3
.
T
o
red
u
ce peak regr
ow
t
h
caused by
fi
l
t
eri
ng recursi
v
e/
i
t
e
rat
i
v
e cli
ppi
ng an
d fi
l
t
eri
n
g
t
echni
ques are
al
so used [
11]
.
Fig
u
re 3
.
Clip
pin
g
and
filtering
with
o
v
e
r
sam
p
l
i
n
g
factor
The L-t
i
m
e
s oversam
pl
ed di
scret
e
-t
im
e si
gnal
x’ [m
]
is g
e
n
e
rated
fro
m
th
e IFFT
o
p
e
ration
.
Th
en
it is
m
odul
ated wi
t
h
carri
er
freq
u
e
ncy
f
c
t
o
y
i
eld a
passban
d
si
gnal
x
m
, whe
r
e
x
m
den
o
t
e
t
h
e
cl
i
pped
versi
on of
si
g
n
a
l
x
m
and i
s
exp
r
essed as gi
ven
i
n
equat
i
on
(1
2
)
.
x
m
A
x
m
A
x
m
x
m
A
x
m
A
(1
2)
PAPR
al
so dep
e
nds u
p
o
n
cl
i
ppi
ng rat
i
o
(C
R
)
whi
c
h i
s
defi
ned as t
h
e cli
ppi
ng l
e
vel
norm
a
l
i
zed by
t
h
e
RMS v
a
lu
e
σ
of
OFDM
si
gnal
gi
ven as i
n
e
q
u
a
t
i
on (13
)
.
CR
(1
3)
3.1.1.
PAP
R
of
Cl
i
p
ped
and
Fi
l
t
er
ed si
gn
al
When
ba
nd
pa
ss OFDM
si
g
n
al
i
s
passed
t
h
ro
ug
h a
cl
i
pper ci
rcui
t
i
t
s
PAPR
val
u
e decreases
si
gni
fi
cant
l
y
. Fi
gure 4 sh
ows
t
h
e C
C
D
Fs of PAPR
val
u
e fo
r t
h
e cl
i
pped OFDM
si
gnal
s
for 1
0
2
4
n
u
m
b
er o
f
sub carri
ers at
2 GHz o
f
carri
er freque
ncy
wi
t
h
4-QAM
m
o
dul
at
i
on form
at
. It
can be no
t
e
d from
t
h
e figur
e
t
h
at
at
0.01%
of C
C
D
F wi
t
h
cl
i
ppi
ng rat
i
o
of 0
.
8,
1.
0, 1
.
2
,
1.4
and
1.
6 t
h
e PAPR
val
u
es
are 4.6
,
5.
0,
5.
5, 5.
9
and 6
.
5 dB
res
p
ect
i
v
el
y
.
From
t
h
e fi
gure i
t
i
s
observed t
h
at
t
h
e PAPR
val
u
e of t
h
e OF
DM
si
gnal
decreases
si
gni
fi
cant
l
y
af
t
e
r cl
i
ppi
ng. It
has al
so bee
n
obser
ved t
h
at
s
m
all
e
r t
h
e cl
i
p
pi
ng
rat
i
o
(C
R
)
great
er i
s
t
h
e
PAPR
reduction effect [12]. But this decrease
in PAPR is at the
cost of increas
e in
th
e b
it erro
r rate an
d
spectral
regr
owt
h
[1
3]
.
Sim
i
l
a
rly
Fi
gure 5 shows P
A
P
R
val
u
e of cl
i
pped OF
DM
si
gnal
when i
t
i
s
al
l
o
wed t
o
pass t
h
rou
gh a
filter cicu
i
t
. Fo
r th
e sam
e
p
a
ramet
e
rs as
m
e
n
t
io
n
e
d
ab
ov
e the PAPR v
a
lu
es are 10
.7
, 11
.0, 1
1
.
2
,
1
1
.4
an
d 1
1
.
7
dB
wi
t
h
cl
i
ppi
ng
rat
i
o
of
0.8,
1.0,
1.
2,
1.4 a
n
d 1.
6 res
p
ect
i
v
el
y
.
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
:
231
0
–
23
21
2
314
Fi
gu
re
4.
P
A
P
R
of
cl
i
ppe
d
si
gnal
s
f
o
r
N=
1
0
2
4
Wh
en
it is com
p
ared
with
PAPR
v
a
lu
e
o
f
clip
p
e
d
si
g
n
al
,
i
t
s
val
u
e
has i
n
crease
d
by
a
p
pr
o
x
i
m
at
ely
2
.
0
d
B
after fil
t
erin
g pro
c
ees. Bu
t t
h
e
b
it erro
r rate
an
d sp
ectr
a
l regr
owth
h
a
s
b
een de
craesed signifi
cantly
[14]
.
Fig
u
re
5
.
PA
PR o
f
clip
p
e
d
and
filtered
si
g
n
a
l for
N
=
1
024
3.
1.
2.
Bit Error
Rate Perform
a
nc
e of
Clipped and
Filtered
Si
gnal
Fig
u
r
es
6
,
7 and
8
sh
ows th
e
BER p
e
rfo
rm
a
n
ce for un
clip
ped
,
clip
p
e
d
o
n
l
y an
d
clip
p
e
d
an
d
filtered
si
gnal
respect
i
v
el
y
.
The B
E
R
val
u
e fo
r u
n
cl
i
pped
si
gnal
at
10
dB
of
si
gnal
po
wer i
s
0.
00
0
7
.
Fi
gu
re 6.
B
E
R
Perf
o
r
m
a
nce
o
f
uncl
i
p
pe
d
si
g
n
al
It
can be o
b
ser
v
ed f
r
om
Fi
gure 7 t
h
at
B
E
R
perform
ance i
s
a funct
i
on
of c
l
i
ppi
ng rat
i
o
(
C
R
)
. For t
h
e
cl
i
pped si
gnal
it
i
s
observe
d fr
om
t
h
e fi
gure that
at
10 dB
of si
gnal
power
and wi
t
h
C
R
val
u
e of 0.8,
1.0
,
1.2
,
1.4 an
d 1.
6 t
h
e B
E
R
val
u
es ar
e 0.04
1, 0.
02
7,
0.0
19,
0.0
10 an
d 0.0
07
respect
i
v
el
y
.
It can be
obser
ved t
h
at
as t
h
e
value of clipping ratio decreases BER performance beco
me
s wo
rse. Th
is in
crease in
BER v
a
lu
e
is
d
u
e
to
di
st
ort
i
ons cau
sed d
u
ri
ng
t
h
e
process
of cl
i
p
pi
ng
[1
5]
.
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
10
-2
10
-1
10
0
PAPR
(
d
B)
CDF
PAP
R
O
F
CL
I
P
PED
S
I
G
N
AL;
N
=
1
0
2
4
CR =
0.8
CR =
1.0
CR =
1.2
CR =
1.4
CR =
1.6
2
3
4
5
6
7
8
9
10
11
12
10
-2
10
-1
10
0
PAP
R
(dB)
C
CDF
PAP
R
OF CLIP
PED AND
FILTERED
SIGNAL;
N
=
1024
CR=
0.8
CR=
1.0
CR=
1.2
CR=
1.4
CR=
1.6
0
1
2
3
4
5
6
7
8
9
10
10
-4
10
-3
10
-2
10
-1
10
0
SIG
N
A
L
PO
W
E
R
(
dB
)
BE
R
B
E
R
O
F
U
N
C
L
I
PPED
SIG
N
A
L
,
N
=
1
0
2
4
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
PAPR Re
duction for
Impr
ove
d
Efficiency
of
OFDM M
o
dul
ation for
Next .... (
S
hatrughna Pras
ad Yadav
)
2
315
Fig
u
r
e
7
.
BER
Per
f
or
m
a
n
ce of
clipp
e
d sign
al f
o
r
N
=
1
024
Wh
en
th
e clip
p
e
d
sig
n
a
l is p
a
ssed
th
ro
ug
h
filter c
i
rcu
i
t
i
t
s
BER
v
a
lu
e i
m
p
r
ov
es. At 1
0
d
B
o
f
sig
n
a
l
p
o
w
er an
d at CR v
a
lu
e o
f
0.8
,
1
.
0
,
1
.
2, 1.4 an
d 1.6 th
e B
E
R v
a
lu
es of clip
p
e
d
and
filte
red
sign
al are
0
.
0
1
9
,
0
.
0
1
3
,
0
.
0
0
7
,
0
.
0
0
5
and
0
.
0
0
3
resp
ectiv
el
y
.
Th
e im
p
r
o
v
e
m
en
t in
BER in
clip
p
e
d
and
filtered
signal i
s
appr
oxi
m
a
t
e
ly
0.0
14 at
C
R
va
l
u
e of
1.0 t
h
a
n
t
h
at
of o
n
l
y
cl
ipped
si
gnal
.
Fig
u
re 8
.
BER Perform
a
n
ce
with
clip
p
e
d
and
filtered
sign
al for N
=
1
024
3.
2.
Sel
ecti
v
e M
a
p
p
i
n
g Me
th
od
Sel
ect
i
v
e m
a
ppi
n
g
m
e
t
hod
(
S
LM
) i
s
o
n
e
of
t
h
e i
m
port
a
nt
m
e
t
hod
fo
r
red
u
ci
n
g
PA
P
R
of
O
F
DM
sy
st
em
. It
has
m
a
ny
advant
ages o
v
er
ot
h
e
r m
e
t
hods
, s
u
ch as:
si
m
p
le i
n
im
pl
em
ent
a
t
i
on, a
b
se
n
ce of
d
i
sto
r
tion
s
in
t
h
e tran
sm
itted
sig
n
a
l, and
si
gn
ifican
t
red
u
c
ti
o
n
in
PAPR [16
]
. In
t
h
is m
e
t
h
od
t
h
e
o
r
i
g
in
al d
a
ta
bl
oc
k i
s
co
nve
r
t
ed i
n
t
o
se
veral
i
nde
pen
d
e
n
t
si
gnal
s
. Di
fferent p
h
a
se
ro
tation
s
are app
lied
to
p
a
rallel b
a
seb
a
nd
m
odul
at
ed si
g
n
al
s. T
h
e p
h
as
e rot
a
t
i
o
n w
h
i
c
h gi
ves m
i
nim
u
m
PAPR
val
u
e of t
h
e t
i
m
e signal
i
s
sel
ect
ed [
17]
.
A l
a
rge set
of
dat
a
vect
o
r
s, a
l
l
represent
i
ng
t
h
e sam
e
i
n
for
m
at
i
on i
s
generat
e
d d
u
ri
ng t
h
i
s
proces
s. The
dat
a
v
ector wh
ich
gen
e
rates lowest PAPR v
a
l
u
e is selected
for tran
sm
issio
n
.
Sid
e
in
form
at
i
o
n
is tran
sm
it
t
e
d
t
o
the recei
ver ha
ving inform
ation about th
ese
data vect
ors. T
h
is e
x
tra informa
tion is an overhea
d
to the
channe
l
wh
ich
redu
ces
th
e ov
erall d
a
t
a
rate [18
]
.
Fi
gu
re
9 sh
o
w
s
t
h
e bl
oc
k
di
ag
ram
of sel
ect
i
v
e
m
a
ppi
n
g
(
S
L
M
) t
echni
que
.
Here
, t
h
e i
n
p
u
t
dat
a
bl
oc
k
X =
[X
[
0
]
,
X
[
1
]
,…..X
[
N
-
1
]
i
s
m
u
l
t
i
p
l
i
e
d wi
t
h
U
di
ffe
re
nt
p
h
ase se
q
u
ence
s
as
gi
ve
n i
n
eq
uat
i
o
n
(
1
4).
P
P
,
P
,……P
(1
4)
Whe
r
e,
P
e
and
φ
∈
[0,
2
π
]
fo
r v
= 0, 1,
…..
,
N
-
1 and u
= 1, 2,
…
…
U whi
c
h
p
r
o
duce
a
m
odi
fi
ed
dat
a
bl
ock
as i
n
e
quat
i
o
n
(
1
5
)
.
X
X
0
,
X
1
,……..X
N
1
(1
5)
0
1
2
3
4
5
6
7
8
9
10
10
-3
10
-2
10
-1
10
0
SIG
N
A
L
P
O
W
E
R
(
d
B
)
BE
R
BER OF
CL
I
P
PED
SI
GNA
L
;
N
=
1024
CR =
0.
8
CR =
1.
0
CR =
1.
2
CR =
1.
4
CR =
1.
6
0
1
2
3
4
5
6
7
8
9
10
10
-3
10
-2
10
-1
10
0
SI
GN
A
L
POWER
(
dB
)
BE
R
BE
R
O
F
CLI
P
P
E
D
AND
FILT
E
R
E
D
S
I
G
N
A
L
;
N=
10
24
CR =
0.
8
CR
=
1
.
0
CR
=
1
.
2
CR
=
1
.
4
CR
=
1
.
6
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
:
231
0
–
23
21
2
316
Fi
gu
re
9.
B
l
oc
k
di
ag
ram
of S
e
l
ect
ed M
a
p
p
i
n
g
M
e
t
h
od
Am
ong
whi
c
h
t
h
e o
n
e
S
mi
n
=
S
with
t
h
e l
o
west
PAPR is select
ed f
o
r
t
r
ansm
i
ssi
on a
s
gi
ve
n i
n
equat
i
o
n (
1
6
)
.
S
⎸
S
n
⎸
,
,
…
,
,…
(1
6)
In
or
de
r t
o
re
cove
r t
h
e
o
r
i
g
i
n
al
dat
a
bl
oc
k i
n
fo
rm
at
i
on ab
out
t
h
e
se
l
ect
ed p
h
ase s
e
que
nce i
s
t
r
ansm
i
t
t
e
d as a si
de i
n
fo
r
m
at
i
on. Im
pl
em
ent
a
t
i
on o
f
SLM
t
ech
ni
que
re
qui
res
U I
FFT
ope
r
a
t
i
ons.
Furt
herm
ore,
it re
quire
s lo
g
2
U
bi
t
s
of
si
de i
n
f
o
rm
at
i
on f
o
r
e
ach
dat
a
bl
oc
k.
3.
2.
1.
PAP
R
w
i
th
Se
lective
Ma
ppi
ng
Me
th
od
Matlab
si
m
u
latio
n
h
a
s
b
een car
r
i
ed
ou
t t
o
calcu
late the v
a
lu
e
of
PA
PR for
1024
n
u
m
b
e
r
o
f
su
bcarr
i
er
s.
As show
n in Figu
r
e
10
it can
be ob
serv
ed
t
h
at at
0
.
0
1
p
e
r
c
en
t of
CC
D
F
, PA
PR
v
a
lu
es
o
b
tain
ed
wi
t
h
p
h
ase
ve
ct
ors,
U
=
16
,
8,
4,
2
an
d
1 a
r
e 8
.
2
,
8.
4,
8.
9
,
9
.
7
an
d
1
0
.
6
dB
res
p
ect
i
v
el
y
.
It
i
s
al
so
ev
i
d
ent
fro
m
th
e fig
u
re th
at PAPR
v
a
lu
e is lowest
for larg
er
num
b
er of
phase rotat
i
ons
(U
= 16)
wh
ich
in
creases with
either
inc
r
ease in
num
b
er of s
ubca
rri
e
r
s
or
re
duct
i
o
n i
n
ph
as
e vect
o
r
s.
Fig
u
re
10
.
PAPR red
u
c
tion
with
SLM with N=
10
24
3.
3.
Parti
a
l Trans
m
it Sequence
Th
e p
a
rtial tran
sm
it
seq
u
e
n
c
e (PTS) techn
i
q
u
e
as sho
w
n
i
n
Figu
re
11
p
a
rtitio
n
s
an
inpu
t d
a
ta b
l
ock
of
N
sy
m
bol
s i
n
t
o
M
di
s
j
oi
nt
sub
b
l
o
cks
as
f
o
l
l
o
w
s
:
x
x
,
x
,x
,
x
,
……..x
(1
7)
He
re,
x
are the
subbl
ocks
tha
t
are consec
utively lo
cated a
nd a
r
e
of e
q
ua
l size. Unlike
the SLM
technique i
n
which sc
ram
b
ling is a
pplied t
o
all subca
rrie
r
s
in this techni
que
scram
b
ling is a
pplied t
o
each
sub
b
l
o
ck
[
19]
.
4
5
6
7
8
9
10
11
12
10
-2
10
-1
10
0
PA
P
R
(
dB
)
CC
DF
PAPR R
E
DUC
T
I
ON
WI
T
H
SL
M F
O
R N
=
1024
;
4 QAM
P
h
a
s
e vec
t
o
r
=
4
P
h
a
s
e
vec
t
o
r
=
8
Ph
a
s
e
v
e
ct
o
r
=
16
P
h
ase
v
e
c
t
o
r
=
2
P
h
a
s
e
vec
t
o
r
=
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
PAPR Re
duction for
Impr
ove
d
Efficiency
of
OFDM M
o
dul
ation for
Next .... (
S
hatrughna Pras
ad Yadav
)
2
317
Figu
re 1
1
.
Blo
c
k diag
ram
of PTS fo
r
P
A
PR
red
u
ctio
n
Th
en
each
p
a
rtitio
n
e
d
sub
b
l
ock
is m
u
ltip
lied
b
y
a correspo
n
d
i
ng
co
m
p
lex
p
h
a
se
factor
b
=
e
whe
r
e,
n =1,
2,
…N
.
Subse
q
uently taking its IFF
T
to yield
xI
F
F
T
∑
b
X
∑
b
.
I
FFT
X
∑
b
x
(1
8)
Whe
r
e {
x
} is referred
t
o
as
p
a
rtial tran
smit seq
u
e
n
ce
(PTS)
and the
phase
vector is c
hose
n
s
o
that t
h
e PAPR
can be m
i
nim
i
zed. T
h
e c
o
r
r
e
s
po
n
d
i
n
g t
i
m
e-
dom
ai
n si
gnal
wi
t
h
t
h
e l
o
wes
t
PAPR
v
ect
or
can be e
x
pres
sed a
s
in
equ
a
tion
(19).
s
∑
b
x
(1
9)
Sel
ect
i
on of
t
h
e pha
se
f
act
ors
b
is lim
i
ted to a set
of ele
m
ents to
reduce t
h
e se
arc
h
com
p
l
e
xi
t
y
. The P
T
S t
e
c
hni
que
re
q
u
i
r
es
M
IFFT
o
p
e
r
a
t
i
ons
fo
r eac
h
dat
a
bl
ock
an
d
l
o
g
X
b
its of si
d
e
i
n
f
o
rm
at
i
on [2
0]
. The
P
A
PR
per
f
o
r
m
a
nce of t
h
e PT
S t
echni
que
de
pe
n
d
u
p
o
n
m
a
ny
fact
or
s, s
u
c
h
a
s
t
h
e
n
u
m
b
e
r of subb
lo
ck
s,
n
u
m
b
e
r o
f
allowed
ph
ase factors,
an
d
su
bb
l
o
ck
p
a
rtitio
n
i
ng
. Su
bb
lo
ck
p
a
rtitio
nin
g
is a
m
e
t
hod o
f
di
vi
di
n
g
t
h
e su
bba
nds i
n
t
o
m
u
l
t
i
p
l
e
of sub
b
a
n
d
s
whi
c
h are di
sj
oi
nt
. The
r
e are
t
h
ree di
ffe
re
nt
t
y
pes
o
f
t
h
e su
bb
lock
p
a
rtitio
n
i
ng
sch
e
m
e
s: a
d
j
acen
t
, i
n
terl
eav
ed and
p
s
eu
do-ran
d
o
m
. Th
e
p
s
eu
do-rando
m
p
a
rtitio
n
i
n
g
sch
e
m
e
h
a
s b
een
kn
own
to
prov
id
e th
e
b
e
st p
e
rfo
r
m
a
n
ce an
d
h
a
s b
e
en co
n
s
i
d
ered
for th
e
sim
u
lation purpos
e [21]
. In the interleave
d
m
e
thod, e
v
ery
subba
n
d signal
s
spaced at th
e interval of N
apart is
allocated the s
a
m
e
subband.
In the a
d
jacent
m
e
thod in
which
N/M succ
essive subbands are gi
ven t
h
e
sam
e
sub
b
l
o
ck se
q
u
e
nt
i
a
l
l
y
. On t
h
e ot
he
r ha
nd
, i
n
t
h
e
pseu
d
o
-
ran
dom
m
e
t
hod eac
h s
u
b
b
a
nd si
gnal
i
s
as
si
gne
d
into a
n
y one
of the s
u
bbl
ocks ra
ndom
ly. In PTS,
each
subbl
ock is to
be m
odulated
by inde
pende
n
t IFFT
.
Due t
o
re
d
u
ct
i
on i
n
num
ber
of s
u
bbl
ock
s
t
h
e com
put
at
i
o
nal
com
p
l
e
xi
t
y
of
PTS t
e
c
hni
que i
s
c
o
m
p
ar
at
i
v
el
y
less th
an th
at
of SLM m
e
th
od
.
3.
3.
1.
PAP
R
with P
a
rti
a
l Transm
it Sequence
The Matlab si
m
u
lation
using pse
u
do – ra
ndom
m
e
t
hod of bloc
k partitioning ha
s
be
en c
a
rried
out. 4-
QAM
si
gnal
c
onst
e
l
l
a
t
i
on
ha
s bee
n
t
a
ke
n i
n
t
o
c
o
n
s
i
d
erat
i
on
wi
t
h
80
0
0
bl
oc
ks.
Fi
g
u
re
12 s
h
ow
s t
h
e
PAPR
val
u
es
at
0.
01
perce
n
t
of
C
C
D
F
f
o
r
1
0
2
4
n
u
m
b
er o
f
s
u
b
carri
ers
as
8
.
3
,
8.
6,
9.
1,
9.
8
and
10
.6
dB
f
o
r
t
h
e
num
ber
of
su
b
bl
oc
ks,
V =
1
6
,
8
,
4
,
2 an
d
1
r
e
spect
i
v
el
y
.
F
r
om
fi
gure i
t
i
s
cl
ear t
h
at
P
A
P
R
val
u
e i
s
l
o
w
e
st
fo
r
l
a
rge n
u
m
b
er
of s
u
b bl
oc
ks
(V=
16
).
As i
n
t
h
e p
r
e
v
i
o
us
m
e
t
hods i
t
i
n
creases wi
t
h
e
i
t
h
er i
n
crea
se i
n
t
h
e
num
ber
of
s
u
b
carri
ers
o
r
red
u
c
t
i
on i
n
t
h
e
n
u
m
ber of
su
b
bl
ock
s
.
Figure 12. PAPR
re
ductio
n
w
ith
PTS f
o
r
N=
10
24
4
5
6
7
8
9
10
11
10
-2
10
-1
10
0
PA
PR
[d
B]
CCDF
PA
PR
RE
D
U
C
T
I
O
N WI
T
H
PT
S F
O
R
N=
1
0
2
4
;
4
Q
A
M
N
o
of subbl
ocks
=
16
No of s
ubblock
s
=
8
No of s
ubblock
s
=
4
N
o
of subbloc
ks
=
2
N
o
of subbloc
ks
=
1
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
:
231
0
–
23
21
2
318
3.
4.
DFT S
p
read
Technique
Transm
itter of
a DFT s
p
read
syste
m
consists of a
serial
to
p
a
rallel
con
v
e
rto
r
, DFT spread
ing
,
IDFT
d
e
sp
read
ing
,
parallel to
serial co
nv
erter,
ad
d
ition
of
cyclic p
r
efix, d
i
g
ital to
an
alog
conv
erter an
d
R
F
m
odul
at
i
on f
o
r
con
v
e
r
t
i
ng
ba
seba
nd si
gnal
i
n
t
o
pa
ssba
n
d
si
gnal
bef
o
re t
r
ansm
i
t
t
i
ng i
t
t
h
r
o
ug
h t
h
e c
h
annel
[22].
If size of DFT is sam
e
as th
at
of IDFT, the
OFDM
A system
become
s equi
val
e
nt
t
o
t
h
e si
ngl
e
carri
e
r
FDMA (SC
-
FDMA) system beca
use the
DFT a
n
d IDFT
operations
virtually cancel each
othe
r. T
h
en the
tran
sm
it sig
n
a
l will h
a
v
e
t
h
e sam
e
PAPR
as in
a sing
le-carrier system [2
3
]
. Th
e eq
uiv
a
len
ce
o
f
OFDMA
syste
m
with
DFT-sp
read
techn
i
qu
e is sho
w
n in
Fi
g
u
re
13
.
Fi
gu
re 1
3
.
E
q
u
i
val
e
nce of
O
F
DM
A sy
st
em
s
wi
t
h
DFT
-
s
p
re
ad
Wh
en
we consid
er a co
nv
en
tio
n
a
l
OFDM
A system
, su
b
carriers are
p
a
rtitio
n
e
d
and
assig
n
e
d
to
m
u
ltiple
m
obile use
r
s. B
u
t in this
technique
,
each use
r
use
s
a subset
of
s
ubca
rrie
r
s to transm
it its own data.
Th
e sub
carriers wh
ich are not u
s
ed
for t
h
e
d
a
ta tran
sm
i
ssi
o
n
are filled
with
zero
s
[24
]
.
Here, th
e nu
m
b
er of
subcarriers allocated to eac
h user is
assu
m
e
d
to
b
e
M. In
th
e DFT-sp
readin
g
techn
i
qu
e,
M-po
in
t DFT is u
s
ed
fo
r sp
rea
d
i
n
g,
and t
h
e o
u
t
p
ut
of
DFT i
s
ass
i
gne
d t
o
the
s
u
bcarriers of IDFT.
T
h
e effect of PAPR
reduction
depe
n
d
s o
n
t
h
e way
of assi
g
n
i
n
g t
h
e su
bca
rri
ers t
o
eac
h t
e
rm
i
n
al
. Two
di
ffere
nt
ap
pr
oache
s
of assi
gni
ng
sub
car
ri
ers are
used am
ong
users
,
D
F
DM
A (
D
i
s
t
r
i
b
ut
ed
FDM
A
) an
d
LFDM
A
(L
o
cal
i
zed FDM
A
).
In
DFDMA, M
DFT ou
tpu
t
s are d
i
stribu
ted
o
v
er th
e en
tire
b
a
n
d
o
f
t
o
tal N su
b
c
arriers with zero
s
filled
in N-M
unuse
d
s
u
bcarriers. But i
n
t
h
e L
F
DM
A,
DFT
outputs
are allocate
d
t
o
M c
o
nsec
utive s
ubca
rrie
r
s
in
N
su
bcarriers and rem
a
in
in
g
are filled
w
ith
zero
s
. If d
i
stri
b
u
t
i
o
n
o
f
DFT ou
t
p
u
t
s in
DFDM
A is d
o
n
e
un
ifo
r
m
l
y
with
eq
u
a
l
d
i
st
an
ce then it is
referre
d to
as i
n
terleave
d
FD
M
A
(
I
F
D
M
A
)
[2
5]
.
In
p
u
t dat
a
s[m
]
is DFT-
sprea
d
t
o
ge
ne
rat
e
S(
k
)
si
g
n
al
s i
n
f
r
e
que
ncy
dom
ai
n as
gi
ve
n i
n
eq
uat
i
o
n
(
2
0).
Sk
∑
s
m
e
/
(2
0)
These a
r
e alloc
a
ted as
de
picted in equation
(21).
S
S
,
k
X
.
m
;
m
0
,1,2,3
…
…
,
M
1
0,
o
therwise
(2
1)
The IF
FT o
u
t
p
ut
seq
u
ence s
(
n) wi
t
h
n = M
. x +
m
for x
= 0, 1,
2, …
…
…
., X
-
1 and
m
= 0, 1, 2,
…., M
-
1
can
b
e
ex
pres
sed
as
sho
w
n i
n
e
quat
i
on
(
2
2
)
.
∑
sm
(2
2)
It can be seen from
Equations (22) that the
time-dom
ain LFDMA signal becom
e
s th
e 1/X-scal
e
d
copi
es
o
f
t
h
e
i
n
put
seq
u
e
n
ce.
3.
4.
1.
PAP
R
of DF
T
Spre
a
d tech
nique
PAPR
pe
rf
or
m
a
nces
usi
n
g
DFT
sp
rea
d
t
echni
q
u
e
i
s
s
h
o
w
n
i
n
Fi
g
u
r
e
1
4
fo
r 10
2
4
num
ber of
sub
car
riers ap
p
lied to the IF
D
M
A, LF
DM
A,
and
OFDM
A
sy
stem
s. The PAPR
value f
o
r IF
DM
A
,
LF
DM
A,
and
O
F
DM
A a
r
e
0.
04
,
6.
9 a
n
d
10
.6
dB
res
p
ect
i
v
el
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
PAPR Re
duction for
Impr
ove
d
Efficiency
of
OFDM M
o
dul
ation for
Next .... (
S
hatrughna Pras
ad Yadav
)
2
319
Figu
re 1
4
. PA
PR
pe
rf
orm
a
nces
f
o
r
IF
DM
A
,
LFDM
A,
an
d OF
DM
A f
o
r N
=
1
0
2
4
; 4 QA
M
It
can
be
o
b
se
rve
d
fr
om
Fi
gures
1
4
,
1
5
a
n
d
1
6
t
h
at
t
h
e
PAPR
pe
rf
or
m
a
nce o
f
t
h
e
DFT
-
sp
rea
d
t
echni
q
u
e
va
ri
es wi
t
h
m
odul
at
i
on
o
r
de
r a
n
d
s
ubca
rri
e
r
al
l
o
c
a
t
i
on m
e
t
hod
.
Figu
re
1
5
.
PA
PR pe
rf
orm
a
nces f
o
r
IF
DM
A
,
LFDM
A,
an
d
OF
DM
A
f
o
r
N
=
1
0
2
4
;
16
Q
A
M
For t
h
e case
o
f
4
-
Q
A
M
m
odul
at
ed si
g
n
al
a
t
0.0
1
%
of C
C
DF t
h
e
val
u
e
s
of
PA
PR
s w
i
t
h
IF
DM
A
,
LFDM
A, an
d
LFDM
A are 0
.
4, 6
.
9 a
n
d 1
0
.
6
dB
respect
i
v
el
y
.
B
u
t
for
1
6
-
QAM
m
odul
at
ed si
g
n
al
, t
h
e
val
u
es
are
3.
4,
7.
8 a
n
d
10
.6
dB
res
p
ect
i
v
el
y
.
Si
m
i
larl
y
fo
r
6
4
-
Q
A
M
m
odul
at
ed s
i
gnal
t
h
e c
o
r
r
e
s
po
n
d
i
n
g
val
u
es ar
e
f
oun
d
to
b
e
4
.
6,
7.9
and
10
.6
d
B
r
e
sp
ectiv
el
y.
Figu
re
1
6
.
PA
PR pe
rf
orm
a
nces f
o
r
IF
DM
A
,
LFDM
A,
an
d
OF
DM
A
f
o
r
N
=
1
0
2
4
;
64
Q
A
M
0
2
4
6
8
10
12
10
-2
10
-1
10
0
PA
PR
[dB]
C
CDF
PA
PR O
F
D
FT SPR
EA
D SIG
N
A
L
;
N
=
102
4;
4
Q
A
M
OF
D
M
A
LFD
MA
IFD
M
A
0
2
4
6
8
10
12
10
-2
10
-1
10
0
PAP
R
[dB
]
CCDF
PAPR
OF D
F
T
S
P
R
E
A
D
SIG
N
A
L
;
N
=
1024;
16 Q
A
M
OF
D
M
A
LFDMA
IFDMA
0
2
4
6
8
10
12
10
-2
10
-1
10
0
PA
PR
[d
B
]
CC
DF
PAPR
O
F
DF
T
SPR
EAD SI
G
N
AL
;
N=
1
024;
64 QAM
OF
DM
A
LF
DMA
IF
D
M
A
Evaluation Warning : The document was created with Spire.PDF for Python.