TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 16, No. 1, Octobe
r 201
5, pp. 1 ~ 6
DOI: 10.115
9
1
/telkomni
ka.
v
16i1.846
9
1
Re
cei
v
ed Ma
y 27, 201
5; Revi
sed
Jul 10,
2015; Accept
ed Jul
y
26, 2
015
OFDM PAPR Reduction Using Recurring SLM with
Cyclic and Linear Block Codes Schemes
Pratima Man
h
as*
1
, M. K Soni
2
FE
T
,
ECE Deptt, Manav Rachna Internat
ional Univers
i
t
y
, Faridabad, India
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: pratimame
h
a
k
@gmai
l
.com
1
, ed.fet@mriu.edu.in
2
A
b
st
r
a
ct
Orthogon
al F
r
e
que
ncy div
i
sio
n
multip
lexi
ng i
s
a ty
pe of mul
t
icarrier
mo
dul
ation tec
hni
qu
e
w
h
ich i
s
used i
n
vario
u
s
w
i
reless & te
leco
mmu
n
ic
ati
on stand
ards.
In OF
DM, high
er data rate is
split into seve
ral
narrow
b
a
nd
d
a
ta strea
m
th
at is trans
mitt
ed si
multan
eo
usly ov
er a n
u
mber
of
subc
arriers. One
ma
jo
r
disa
dvant
age
of using OF
DM is high Pe
a
k
to Average
pow
er ratio. T
h
is pa
per pres
ents the simul
a
tio
n
result w
h
ich c
o
mpar
es the
PAPR usi
ng S
L
M w
i
th Cycli
c
& Lin
ear
blo
ck codes. Th
e
simul
a
tion st
u
d
y
verifies that the
PAPR reducti
on by pro
pos
e
d
met
hod is b
e
tter than the ex
isting tech
ni
qu
e (SLM).
Ke
y
w
ords
:
orthog
on
al fre
que
ncy d
i
visi
o
n
multi
p
lex
i
n
g
(OFDM), selective
m
a
pp
ing (SLM), peak-to-
avera
ge-p
o
w
e
r
-ratio (PAPR), line
a
r block co
d
e
s, cyclic code.
Co
p
y
rig
h
t
©
2015 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Orthog
onal
Freq
uen
cy Divisio
n
Mult
iplexi
ng (OF
D
M)
is
a multica
rrie
r
modulatio
n
method
whi
c
h is wi
dely u
s
ed in
wirele
ss
comm
uni
cation. It is used in mobil
e
comm
uni
cati
on
,
Digital terre
s
trial mobile
comm
uni
cati
on, Digital
Audio Broa
d
c
a
s
ting (DA
B
), Digital Vide
o
Broad
ca
sting
terre
strial
(DVB-T), wi
rele
ss
asyn
ch
ro
n
ous
t
r
an
sfer mode (WAT
M
),
Mod
e
m/ADSL.
The transmit sign
als i
n
an
orthog
onal
freque
nc
y-division multiplexi
ng (OF
D
M)
system can h
a
v
e
high
pea
k va
lues in the
time do
main
sin
c
e m
any
sub
c
a
rri
er
co
mpone
nts
are ad
ded via
an
inverse fast Fourie
r tran
sfo
r
mation (IFF
T
)
ope
ra
tion [1]. As
a res
u
lt, OFDM s
y
s
t
ems
are k
n
own
to have a high peak
-
to-av
e
rage
power ratio (PAPR) when c
o
mpar
ed to s
i
ngle-carri
er s
y
s
t
ems
.
High value of PAPR will cause clip
ping in OFDM si
gnal and enabl
e an amplifi
e
r to operate in
nonlin
ear
se
ction. Due to p
r
esen
ce of thi
s
nonli
nea
rity it will result in in-b
and di
st
ortion a
nd ou
t-
band
radiatio
n. The
in
–ba
nd di
sto
r
tion
will le
ad
to
d
egra
d
e
the
p
e
rform
a
n
c
e
o
f
the
system
and
out-ba
nd radi
ation re
sult in
cau
s
ing inte
rferen
ce am
o
ng adja
c
e
n
t chann
el. Thus this addition
al
interference i
n
the
system
will
results i
n
increasi
ng
Bit Error Rate. One
way t
o
overcom
e
t
h
is
situation i
s
to use hig
h
dyn
a
mic
rang
e linear
power a
m
plifier, but u
t
ilization of this sol
u
tion is
n
o
t
effective, and
too expensiv
e.
1.1.
Ortho
gonal
Freque
nc
y
Div
i
sion Multiplexing Mod
e
l
OFDM
can
b
e
viewed
as
both mo
dulati
on &
m
u
ltiple
xing techniqu
e.Modulatio
n
can
be
viewed a
s
a relation bet
we
en input & ou
tput while the
multiplexing
can b
e
viewe
d
as the o
u
tp
ut
whi
c
h is a lin
ear sum of input. OFDM d
i
ffers fr
om F
D
M. In FDM, entire band
width is u
s
ed
by
use
r
, while i
n
OF
DM
ba
ndwi
d
th i
s
di
vided into
m
any na
rrow
band
chan
ne
ls a
nd
ea
ch
is
allocated to u
s
er.
He
nce O
F
DM
sup
p
o
r
ts mo
re
sub
scribe
r
s/
cha
nne
ls compa
r
e to
FDM. In F
D
M
system
s the
carrie
rs are f
a
r a
part
with
respe
c
t
to
e
a
c
h other
and
in
OF
DM syst
ems ca
rri
ers are
den
sely pa
cked an
d a
r
e o
r
thogon
al to th
e othe
r ca
rrie
rs. O
r
thog
on
al mean
s
pea
k of on
e
carri
e
r
occurs
at null
of the othe
r.
He
n
c
e
OF
DM
system i
s
ba
ndwi
d
th effici
ent as compa
r
ed to th
e F
D
M
system. The
OFDM m
odel
for both tran
smitter & re
ceiver is sho
w
n in Figure 1 and 2.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 16, No. 1, Octobe
r 2015 : 1 – 6
2
Figure 1. OF
DM Tran
smitter
Figure 2. OF
DM Re
ceive
r
The
data i
s
first
conve
r
te
d into
serial
to p
a
rall
el f
o
rm
and
the
n
ea
ch
sub
c
arri
er is
modulated by Quadrature Phase
shi
ft modul
ator (QPSK) m
odulation and then IFF
T
is
perfo
rmed.
T
he received
sign
al fed
to
seri
al to
pa
ra
llel converte
r and
FFT
is
perfo
rmed
to
get
the
ori
g
inal
data sign
al. The OFDM system
ha
s
variou
s a
d
va
ntage
s
su
ch
as have
m
o
re
resi
stant to selective fading, ability to recover fr
om t
he interference and
inter
symbol and i
n
ter
frame inte
rfe
r
en
ce
(ISI), effective and
suitabl
e
util
ization of
a
v
ailable spe
c
trum, cha
n
nel
equali
z
ation
i
s
e
a
sie
r
[2,
3]. The m
a
jo
r d
r
a
w
ba
ck i
n
OF
DM m
e
thod i
s
hi
gh
pea
k to ave
r
age
power
ratio (PAPR), c
o
mmonly the PAPR value for s
o
me t
r
ans
m
itted s
i
gnal is
muc
h
larger t
h
an
the usual values. Thi
s
PAPR factor
enables the
am
plifier to work in nonli
n
ear section which
results in de
g
r
adin
g
the pe
rf
orma
nce of OFDM
syste
m
s.
1.2.
PAPR of O
F
DM Sy
stem
The
OFDM
signal
co
nsi
s
ts of multiple
modulate
d
ca
rrie
r
s an
d a
b
l
e
to g
ene
rate
a hi
gh
peak to
average
power ration (PAPR
), when
these coherent carri
ers are
added up [4, 5]. If N
carrie
r si
gnal
s which are adde
d togeth
e
r con
s
titu
te same
pha
se
then they ge
nerate
a pe
a
k
power
whi
c
h is
N times t
he average
power. Thus
, this increased value
of
PAPR will i
n
turn
respon
sibl
e f
o
r
clippi
ng n
o
i
se, n
on–lin
e
a
r di
sto
r
ti
on o
f
power
ampli
f
iers, BER pe
rforma
nce [6,
7]
deba
sem
ent,
energy spillin
g into a
d
jace
nt cha
nnel
s, i
n
ter mo
dulati
on effect
s o
n
the su
b
carrie
rs,
warping of si
gnal co
nstell
ation in each
and ev
ery sub ch
annel,
enha
nced the
complexity factor
in analog to
digital or di
gi
tal to analog conv
ertor .T
he PAPR is
defined as the ratio of Peak
power to the average power.
Equation (1) represents t
he PAPR of
transmitted si
gnal.
(
1
)
The cumulati
ve distributio
n function
(CDF) of
the P
APR is one o
f
the most frequ
ently
us
ed performance measures
fo
r PAPR
reduc
t
ion techniques
. Th
e CCDF of the PAPR denot
es
the probabilit
y that the PAPR of a dat
a block exceeds a
given threshol
d.
The pap
er i
s
orga
nized in
different secti
ons. Sectio
n
2 rep
r
e
s
ent
s the introd
uct
i
on of
Cycli
c
&
Lin
ear Block
co
des. A
bri
e
f introd
uctio
n
to SLM te
chniqu
e & m
odified SL
M
is
pre
s
ente
d
in
se
ction 2. Th
e com
pari
s
o
n
of both
prop
ose
d
method
(cycli
c & line
a
r blo
c
k co
de
s)
and existin
g
method is p
r
e
s
ente
d
in se
ction 3. Lastly results a
r
e co
nclu
ded in section 4.
2. Proposed Method
A linea
r Blo
ck co
de i
s
a
co
de in
which e
x
clusive
O
R
of the t
w
o vali
d code
words create
s
anothe
r co
de
word. It is rep
r
esented a
s
i
n
Equation (2
).
C=
U.G
(2)
Whe
r
e,
U= u
n
code
d informatio
n word with K bit
s
C=
Corre
s
p
o
nding
cod
e
word for the inf
o
rmatio
n
G= G
ene
rato
r matrix of n
×
k
wh
ere
n i
s
the
Colum
n
(output bit
s
) & k is the
ro
w (in
put
bits)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
OFDM PAPR Reduction Usi
ng Recurring SLM
wit
h
Cycli
c
and
Linear… (P
ratim
a
Manhas)
3
Let us
tak
e
an example if the generator matrix is
G=
Her
e
n ×
k =(
7×3
)
C= u
0
.(11
010
01)+u1.
(10
1
0
011)+u
2.(1
11
0100
)
In
Linea
r
bl
o
ck co
de
s
the addition used
is
mo
dul
o
2
or
the exclu
s
i
v
e
OR additi
on.
Supp
ose we
want to find the co
de word
s from c0 t0 c7, then is given as:
U0
=(0
0
0
)
, then C0
=0.(110
1001
)+0.(1
01
0011
) +0.
(
11
1010
0)
C0
=(0
000
000
)
U1
=(0
0
1
)
, then C1
=0.(110
1001
)+0.(1
01
0011
) +1.
(
11
1010
0)
C1
=(1
110
100
)
U2
=(0
1
0
)
,then C2
=0.(110
1001
)+1.(1
01
0011
) +0.
(
11
1010
0)
C2
=(1
010
011
)
U3
=(0
1
1
)
,then C3
=0.(110
1001
)+1.(1
01
0011
) +1.
(
11
1010
0)
C3
=(0
100
111
)
U4
=(1
0
0
)
,then C4
=1.(110
1001
)+0.(1
01
0011
) +0.
(
11
1010
0)
C4
=(1
101
001
)
U5
=(1
0
1
)
,then C5
=1.(110
1001
)+0.(1
01
0011
) +1.
(
11
1010
0)
C5
=(0
011
101
)
U6
=(1
1
0
)
,then C6
=1.(110
1001
)+1.(1
01
0011
) +0.
(
11
1010
0)
C6
=(0
111
010
)
U7
=(1
1
1
)
,then C7
=1.(110
1001
)+1.(1
01
0011
) +1.
(
11
1010
0)
C7
=(1
001
110
)
2.1. C
y
clic Codes
Cycli
c
code
s
are th
e spe
c
i
a
l type of line
a
r bl
oc
k
cod
e
s
with
on
e ex
tra prope
rty. In cycli
c
cod
e
, if a co
deword i
s
cy
clically shifte
d (rotat
ed), t
he re
sult is
a
nother
co
de
word [8]. It can
b
e
impleme
n
ted
usin
g simpl
e
shift regi
sters. The cycli
c
shift is given as:
Suppo
se x=
1011
0
Π
(x) =01
011
Here in this
example the las
t
bit is
s
h
ifted to the firs
t.
A cyclic
code
has the follo
wing advanta
g
e
s:
1)
It has better
minimum di
stance than oth
e
r linea
r code
s with same p
a
ram
e
ters
2)
Encodi
ng & d
e
co
ding i
s
pe
rforme
d by si
mple feedb
ack ci
rcuit
r
y.
3)
It can be ea
si
ly implement
ed and h
a
s
cost effective electroni
c ci
rcuit.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 16, No. 1, Octobe
r 2015 : 1 – 6
4
2.2. Propose
d
SLM Tech
nique
w
i
th Cy
c
lic/Linear Block
Code
s
In SLM method the tra
n
s
mitter
sele
cts one favo
ra
ble tran
smit
sign
al from
a set of
sufficie
n
tly different sign
al
s whi
c
h all repre
s
e
n
t the same info
rmation[9][10]. The system
atic
diagram for
SLM method
and mo
difie
d
SLM is
sh
own in
Figu
re 3 & 4. The
data stream
after
seri
al to parallel conve
r
si
on is rep
r
e
s
ented by vector X=[X
0
, X
1
----
--
--,X
N-1
]
T
. Then ph
ase
rotated data
due to the ph
ase rotation factor B
(u)
ca
n be written a
s
:
)
(
u
x
= IFFT(x
×
B
(u)
)
Whe
r
e,
B
(u)
=[
B
0
(u
)
,B
1
(u)
,-----
--,B
N-1
(u)
)
T
u=0,1,
----U-1
is the
pha
se
weightin
g seq
uen
ce
wit
h
│
B
n
(u)
│
=1(n=
0
,1,N-1) and is
usu
a
lly sel
e
ct
ed from
{ ±1}
for avoidin
g
t
he complexit
y
for co
mplex
multiplicatio
n. The m
odified
data for the u
th
phase seq
uen
ce is give
n as:
X(u)=
[
X
0
B
u
,
0
,
X
1
B
u
,
1
,
----
--
,X
N-1
B
u
,
N-1
]
T
After that the PAPR c
o
mparis
on among the U
data s
e
quenc
e
)
(
u
x
is do
ne a
nd t
he
optimal map
p
ed one
x
ˆ
with the minimum
PAPR is
s
e
lec
t
ed for transmis
s
i
on.
Figure 3. Block di
agram of
SLM techniq
u
e
Figure 4: Block di
agram of
SLM using Li
near Block cod
e
s
3. Proposed
Work
The map
p
ing
sequ
en
ce for both cycli
c
&linear
bl
ock code
s are
sele
cted to de
cre
a
se th
e
peak to average powe
r ratio (PAPR)
of OFDM signal. SLM method have hi
gher
compl
e
xi
ty
factor a
s
it in
clud
es la
rg
e numbe
r of IF
FT ope
ra
tion
s. MATLAB tool is u
s
e
d
to
cal
c
ulate
CCDF
and Power
spectral den
si
ty (PSD) for both ex
isting
SLM and propo
sed SLM
(
usi
ng cy
clic &
Linea
r blo
ck
cod
e
s) [12]. Table 1 sho
w
s
the simulatio
n
para
m
eters.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
OFDM PAPR Reduction Usi
ng Recurring SLM
wit
h
Cycli
c
and
Linear… (P
ratim
a
Manhas)
5
Table1. Simul
a
tion Param
e
ters
Modul
atio
n
QPSK
Number of
data s
ubcarriers(N
)
256
Total numbe
r of
data s
y
mbols
1000
Size of the phase sequence
256
FFT Si
z
e
64
Coding Techniqu
e
C
y
clic& Linear
3. Results &
Analy
s
is
Figure 5 and 7 repres
ents
the
CCDF
pl
ot of PAPR for exis
ting
SLM (QPSK
based
OFDM
) a
n
d
modified S
L
M (b
oth cy
clic &
Linea
r cod
e
s). Fig
u
re 6
and
8
rep
r
e
s
ent
s
the
comp
ari
s
o
n
b
e
twee
n Powe
r spe
c
tral de
nsity of existing SLM and
Propo
se
d SLM (both cy
cli
c
&
Linea
r
cod
e
s) .Then
the
re
sult i
s
com
p
a
r
ed
with
the
existing S
L
M
techni
que
an
d foun
d that
the
prop
osed work ha
s effective outcom
e
than the existin
g
SLM metho
d
.
Figure 5. CCDF plot of PAPR of basi
c
Q
PSK-OF
DM
system with t
he SLM technique and
Propo
se
d Wo
rk (with cy
clic)
By using this phase sequence [1, -1, j, -j] obt
ained PAPR by using proposed SLM method is
nearly
abo
ut 17dB
(Figu
r
e 5)
and
16
dB (Fig
ure
7
)
. On
other
hand th
e PA
PR obtai
ned
by
existing SLM
method is n
early 19dB (i
n Fi
gure 5 and 7). Thu
s
,
by propo
se
d SLM method
enabl
es to
re
duce the PA
PR by ne
arly
2 db a
nd
3
d
B
which i
s
11
.76% & 18.75
% in perce
ntage
improvem
ent over ori
g
inal
method respe
c
tively.
Figure 6. Co
mpari
s
o
n
of PSD betwe
en
original
QPSK-OFDM PAPR with SLM & PAPR with
Propo
se
d Wo
rk (with cy
clic)
Figure 7. CCDF plot of PAPR of bas
ic
QPSK-
OFDM
syste
m
with the SLM techniq
ue
and
Propo
se
d Wo
rk (with line
a
r code
)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 16, No. 1, Octobe
r 2015 : 1 – 6
6
Figure 8. Comparis
on of PSD between orig
inal QPS
K
-OFDM PAPR with SLM
& PAPR with
Propo
se
d Wo
rk (with line
a
r code
)
4. Conclusi
on
The m
odified
SLM meth
o
d
by u
s
ing
b
o
th cy
clic & li
near blo
c
k
code
s
whi
c
h h
a
s
better
perfo
rman
ce
in terms of CCDF a
nd PSD with re
s
pec
t to exis
ting SLM is
s
h
own in this
paper.
Figure 5 and 7 represent
s the result
s obt
ained
by the
proposed met
hod for
reduci
ng PAPR. The
compari
s
on between the modified SLM using
cycl
i
c
code results in
2db re
duction in PAPR while
in case of
m
odified SL
M
usin
g Li
nea
r
block
co
de
re
duces the PA
PR by
3db.
MATLAB tool
is
use
d
to o
b
tai
n
the p
e
rfo
r
mance of PA
PR redu
ct
ion
,
whi
c
h
clea
rly rep
r
esents that there is a
signifi
cant im
provem
ent in performance. The pr
oposed methods
in this
paper will results i
n
reduction of
PAPR by 2dB & 3db which is an im
provement of 11.76 % & 18.75%
in all.
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