TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 11, Novembe
r
2014, pp. 77
5
8
~ 776
3
DOI: 10.115
9
1
/telkomni
ka.
v
12i11.60
07
7758
Re
cei
v
ed Ma
rch 2
3
, 2014;
Re
vised Ma
y 29, 2014; Accepted June 1
5
, 2014
An Improved Tone Reservation Scheme in OFDM
Systems for Adaptive Amplitude Clipping
Yang Song*,
Chaos
h
i Cai
，
Jianping L
i
Schoo
l of Information En
gi
ne
erin
g, Commu
nicati
on
Un
iver
sit
y
of Chi
na, B
e
iji
ng 1
0
0
024,
Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: ic
y
s
o
n
g
y
a
n
g
@
16
3.com
A
b
st
r
a
ct
Orth
og
on
al
freq
ue
ncy d
i
vi
si
on
mu
l
t
i
p
l
e
xin
g
(OFD
M) su
ffe
rs from
a
hi
gh
p
e
a
k
to
ave
r
ag
e
po
w
e
r
rati
o (P
APR).
T
o
n
e
r
e
se
rvat
i
o
n
(T
R)
tec
h
n
o
l
ogy
i
s
c
ons
i
der
ed
as
on
e
of th
e
most
pr
o
m
is
in
g
met
h
o
d
s
b
e
c
au
se
o
f
no
a
d
d
i
ti
on
al
d
i
storti
on
, n
o
side
i
n
fo
rm
a
t
i
o
n
,
a
n
d
l
o
w im
pl
emen
ta
ti
on
cost. H
o
we
ve
r, in
al
l
PAPR
re
du
ction
scheme
s
，
det
er
mi
n
i
n
g
the
opt
i
m
a
l
target c
l
i
p
p
i
ng
lev
e
l i
s
diff
icu
l
t. In this p
a
p
e
r
,
w
e
consi
d
er
an
ad
apt
ive
a
m
pl
itud
e l
e
ast s
q
u
a
re
s a
ppr
o
x
i
m
at
io
n (AA
L
AS-T
R
) a
l
g
o
r
i
th
m. Ad
just
ad
apt
ive
opt
i
m
al
conv
er
genc
e f
a
ctor
for
initial c
l
ipping t
h
reshold.
That is
res
u
lts
an
a
ppr
ox
im
at
ely
PAPR reduction
perf
o
r
m
anc
e w
i
t
h a
l
o
w
co
mpu
t
atio
n
a
l c
o
mpl
e
xity. Si
mu
lati
o
n
res
u
lts
sh
ow
that t
he
pr
op
os
ed
al
g
o
rit
h
m c
a
n
achieve
better PAPR r
e
duction as th
at differ
e
nt clipping t
h
reshold.
Key
w
ords
:
hi
gh
pe
ak-t
o-av
era
ge
p
o
w
e
r r
a
tio
(PAP
R), ton
e
re
serv
ati
o
n (T
R), a
d
apti
v
e a
m
pl
itu
d
e
l
e
a
s
t
squ
a
r
e
s a
ppr
ox
i
m
at
io
n (AA
L
A
S
-T
R), OF
DM, cli
p
p
i
n
g
c
ontr
o
l
Copy
right
©
2014 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
frequ
en
cy div
i
sion
multipl
e
xing (OF
D
M) i
s
o
ne
of the mo
st
pop
ular
t
e
chn
o
logie
s
in cu
rre
nt
h
i
gh-
rat
e
wi
rel
e
s
s
c
o
mmu
n
i
cat
i
on
sy
st
e
m
s w
h
ic
h is
f
o
r mult
i-
car
r
ier
modulatio
n t
e
ch
niqu
es [1
], However,
OFDM
sy
ste
m
s h
a
ve hi
g
h
pe
ak to a
v
erage
po
we
r
ratio(PAPR)
probl
em
whi
c
h is i
nefficient requi
res
a li
near high power amplifier
(HPA). T
o
study
this p
r
obl
em,
variou
s PAP
R redu
ction
tech
niqu
es ha
ve bee
n p
r
op
ose
d
. Such a
s
clippi
ng a
n
d
filtering [2-4],
coding [5
-6], compa
ndin
g
sch
eme [7
], active co
nstel
l
ation extensi
on [8] and tone
reservatio
n [
9
-10]. A
s
o
n
e
of ton
e
re
servation
(T
R) tech
niqu
es,
clippi
ng
cont
rol (CC-T
R
) [11]
method i
s
to repe
atedly gene
rate pe
ak-ca
n
ce
ling
signal
s by
clippi
ng, but
CC-TR m
e
thod
requi
rem
ent
of many ite
r
a
t
ions
to
redu
ction PAP
R.
In [12]
，
ue
s a
optim
al co
nverge
nce
fa
ctor
scale the filt
ered
frist
-
iteration cli
ppin
g
noi
se to co
mpen
sate fo
r pea
ks th
at
are
above the
threshold
and c
an
achieve a lager PAPR reduc
t
ion,
but als
o
need high iterat
ion c
o
mplexity. In
[13], based on the least squares
approximation
with fast convergenc
e reduction PAPR, only
need
a fe
w iteration
s
can
achieve
the
sa
me
perfo
rman
ce
and
re
du
ce
d computatio
nal
compl
e
xity. The LSA-T
R
schem
e is
em
ployed to ca
l
c
ulate th
e op
timal con
s
tan
t
P but different
c
lipping threshold A
res
u
lts
in
different
PAPR redu
c
t
ion. In other
words
,
Eac
h
iteration s
h
ould
corre
s
p
ond to
an optimal consta
nt P but not the same
P.
In this letter, a clipping algorithm
i
s
developed to obt
ain good PAPR reduction
perfo
rman
ce
rega
rdl
e
ss of
the initial target c
lip
ping l
e
vel. This i
m
proved
TR
m
e
thod b
a
sed
on
the adaptive
amplitude
least squa
re
s app
roxi
ma
tion (AALAS-TR) alg
o
rit
h
m. The fa
st
c
onvergence fac
t
or P
wit
h
the iterative c
h
anges
obtain a good PAPR reduc
tion
with low
compl
e
xity.
And different clipping thres
hol
d have an approximat
ely PAPR reducti
on
perfo
rman
ce.
The paper is organized as
fo
llows
. In
Sec
t
ion II, the s
y
s
t
em model bas
e
d on the TR
method
and
the ad
aptiv
e
lea
s
t s
qua
r
e
s
app
rox
i
m
a
tion(LAS
-
TR
) alg
o
rithm
i
s
intr
odu
ce
d
III,
prop
oses th
e
novel sche
me the ada
p
t
ive amp
litud
e least
squa
res ap
proximation(AALAS-TR)
algorith
m
. In
Section IV, th
e sim
u
lated
result
s
a
r
e sh
own and
the conve
r
ge
nce of
su
ch a
nov
el
algorith
m
is compa
r
ed
with
the other me
thods. In the end, a co
ncl
u
sion i
s
given.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
An Im
proved
Tone Reservation Schem
e in OF
DM System
s for Adapt
ive... (Yang Song)
7759
2. OFDM Sy
stems an
d T
one Re
serv
a
tion Tech
nique
2.1. OFDM Sy
stems and PAPR Ton
e-Res
e
rv
ation Techniqu
e
I
n
OFDM
sy
stem
s, the transmitted
si
g
nal co
n
s
ist
s
of a great n
u
mbe
r
of o
r
thogo
nal
sub
c
a
rri
ers. The ba
seb
and
sampl
e
s of
a
n
OFDM
sym
bol ca
n be written as:
1
2/
0
1
,0
1
N
jn
k
N
nk
k
xX
e
k
N
N
(1)
Where
N is the sub
c
arrie
r
number of an OFDM syst
em, X
k
is the
modulated data carried by
the
k
th subcarrier, is
the nth sa
mp
le of a
time-domain symbol.
The tone-Reservation techni
que reserves Nr
tones for PAP reduction and don’t carry
any data info
rmation ,the
remai
n
ing (N- Nr) tone
s f
o
r data tran
smissi
on. Obvi
ously, the to
ne
-
reservatio
n ration R= Nr
/N is small. The pe
ak-ca
n
celi
ng si
gna
l c(t) i
s
ge
ne
rated b
a
sed
on
reserve
d
tone
, and the pea
k-re
d
u
ced si
g
nal is given b
y
:
T
kt
j
N
N
k
k
k
e
C
X
N
t
c
t
x
t
x
/
2
1
2
/
2
/
)
(
1
)
(
)
(
)
(
~
(2)
2.2. Propose
d
LSA-T
R
Sc
heme
The LSA
-
T
R
algorith
m
i
s
e
m
ployed to
calcul
at
e the
o
p
timal con
s
ta
nt P, the o
b
je
ctive of
optimizatio
n probl
em is formulated a
s
[13]:
}
]
)
(
[
{
min
2
,
n
n
A
p
n
f
c
p
P
(3)
For the lea
s
t squ
a
re
s ap
proximat
ion (LS
A
) algorith
m
, we defin
e:
2
]
[
)
(
n
n
n
f
c
p
p
g
(4)
Then,
p
f
c
p
p
p
g
n
n
n
2
]
[
)
(
p
f
c
p
f
c
p
n
n
n
n
n
]
2
[
2
2
2
(5)
n
n
n
n
n
f
c
c
p
2
-
2
2
Make
0
)
(
p
p
g
，
we have:
n
n
n
n
n
c
f
c
P
2
(
6)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 11, Novem
ber 20
14: 77
58 – 776
3
7760
From the a
b
o
v
e we can
kn
ow,
)
(
)
(
n
pc
n
x
approximates to
)
(
)
(
n
f
n
x
, and the
good PAPR reduction coul
d be achi
eved
after the first servers iter
ations. But
when P is
uniquel
y
determi
ned,
i
n
the iterative pro
c
e
s
s
，
d
i
fferent clippi
ng thre
shol
d
A results in
different PAPR
redu
ction
pe
rforman
c
e
s
.
Ho
wever,
th
e optim
al target cli
ppin
g
l
e
vel o
r
clippi
ng
ratio
not
be
pred
etermi
ne
d at the initial stage. In th
e next
se
ctio
n, prop
oses
a nov
el sch
e
m
e the ada
ptive
amplitude
lea
s
t squa
re
s ap
proximatio
n(AALAS-TR
) a
l
gorithm. T
o
i
dentify differe
nt P
depen
di
ng
on the initial clipping ration
R.
3. Proposed
AALS
A
-TR S
c
heme
In this secti
on, we
prop
ose
an a
d
a
p
tive amplitu
de lea
s
t sq
uare
s
a
p
p
r
o
x
imation
algorith
m
for
TR-ba
s
ed
OF
DM sy
stem
s. The mai
n
obj
ective is to
control b
o
th th
e target
clippi
ng
level A and converg
e
n
c
e factor P at ea
ch iteratio
n. that is:
}
{
min
2
)
(
)
(
）
（
，
n
i
n
i
n
i
p
A
f
c
p
P
(7)
）
（
2
)
(
)
(
）
（
)
(
i
n
i
n
i
n
i
p
f
c
p
p
p
g
)
(
)
(
)
(
)
(
2
)
(
2
)
(
2
）
（
2
i
n
i
n
i
n
i
i
n
i
n
i
p
f
c
p
f
c
p
n
i
n
n
n
i
n
i
f
c
c
p
)
(
2
)
(
)
(
2
-
2
(8)
Make
p
p
g
)
(
0
，
we have:
2
)
(
)
(
)
(
)
(
ˆ
i
n
i
n
i
n
i
c
f
c
p
(
9
)
Whe
r
e
.,.
repre
s
ent
s the re
al
inner-produ
ct. This implie
s that the calculation of P involves real
domain,
rath
er th
an
co
mplex d
o
ma
in. Fro
m
th
e ab
ove
we can
kno
w
,
)
(
ˆ
)
(
n
c
p
n
x
approximate
s
to
)
(
)
(
n
f
n
x
. For the
complexity co
mpari
s
o
n
, in the CC-TR
m
e
thod n
eed t
w
o
FFT/IFFT o
peratio
ns d
u
ring
eve
r
y iteratio
n.
Thus,
CC-T
R m
e
thod
co
mplexity is
))
1
2
(
)
log
(
(
2
2
K
LN
LN
T
，
the LSA-TR method ju
st need few i
t
eration
s
whi
c
h we
set T
can achieve the
sam
e
PAPR reduction. In [
13],
We LSA-T
R
m
e
thod
compute com
p
l
e
xity
is obtain
ed
)
log
(
2
2
LN
LN
I
. The AALSA-TR alg
o
rithm
is
modifi
ed
in the
iteration p
r
ocess
step
size a
nd
the
thre
sh
old v
a
lue A,
so t
he
com
put
ati
onal
co
mple
xity of the
algorithm
is t
h
e
s
a
me with
LS
A-TR
.
4. Simulation Resul
t
s
To
sho
w
th
e
advanta
ge
of the n
o
vel
ALSA-TR
alg
o
rithm, com
p
uter simul
a
tions
are
perfo
rmed
in
Chin
a Mo
bile
Multimedi
a
Broad
ca
sting
(CMMB) sy
stem. In this simulation, 4
0
96
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
An Im
proved
Tone Reservation Schem
e in OF
DM System
s for Adapt
ive... (Yang Song)
7761
sub
c
a
rri
ers
are p
e
rfo
r
me
d for FFT/IF
FT ope
ration
. This di
stri
bution me
an
s that all d
a
ta
sub
c
a
rri
ers a
r
e symm
etric about the central fr
e
que
ncy and th
e reserve
d
ton
e
s is
ran
d
o
m
ly
generated. Quadratur
e Phase Shift Keying (QPSK) is used for
the simulation system. The
PAPR reduc
t
ion performanc
e is
evaluat
ed by the PA
PR
CCDF func
tion.
4
time overs
a
mpling is
used in all si
mulations.
Figure 1. Comparis
on of PAPR Reduction
between AALSA-TR,
LSA-TR
and CC-TR with
Different Cli
p
ping Th
re
shol
d
In Figure
1 ,
we compare the PAPR
reduc
t
ion
perf
o
rmance of t
he
CC-TR
，
LSA-TR
method with
our AALSA-T
R
method, th
e maximum
numbe
r of iteration
s
is 1
0
, and the clip
ping
threshold A
=
1.2,1.4,1.6. Whe
n
CCDF
=
10
-5
, when
A=1.2, AALSA-TR
m
e
thod have 0.5dB
PAPR
redu
ction
with LSA-TR. As A=1.6, hav
e 0.3dB gai
n
s
. Obviou
sly, the LSA-TR algorithm is in
different c
l
ipping threshold hav
e different PAPR reduc
t
ion perf
ormanc
e.
Contrary to our
new
meth
od,
can
be in
diff
erent
cli
ppin
g
thre
shold,
CCDF
curve
s
wa
s bette
r, a
nd no i
n
cre
a
se in
comp
utationa
l complexity.
Figure 2. Comparis
on of PAPR Redu
ction with Different Step Size p
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 11, Novem
ber 20
14: 77
58 – 776
3
7762
In Figure 2,
the pro
p
o
s
ed AALSA-T
R
sch
e
me
redu
ction PA
PR pe
rform
a
nce
with
different ste
p
si
ze, We
cho
s
e
ste
p
size
re
sp
ectively
from
0.1 to
1
ra
nge.
When
p=
0.1,0.2,0.3,0.4, the PAPR are 9.8dB to 6.5dB. Fo
r
the other choic
e
s
on p the different of t
h
e
PAPR are v
e
ry
s
m
all
and that is
about
6dB. Moreover, that is
the s
m
aller p
c
a
n not
effec
t
ively
adjust the clipping level A,
and choose a bigger
step size p to gain
better PAPR performance
for
the AALSA-TR algo
rithm.
Figure 3. BER Perfo
r
man
c
e of OF
DM System
over AWG
N
with CC-T
R, LSA-TR , AALSA-TR
Method
In Figure 3,
the bit-erro
r-rate (BE
R
)
perfo
rman
ce
evaluate wi
th CC-TR, L
SA-TR,
AALSA-TR
method,
we
con
s
id
er a
d
d
i
tive white G
aussia
n
noi
se (AWGN)
with hig
h
po
wer
amplify (HPA
). The input backoff (IBO) is set to
be 5 dB. The number of iterat
ions i
s
15. The
prop
osed AA
LSA-TR sche
me can offe
r
better BER
p
e
rform
a
n
c
e compa
r
e with origin
al
meth
od.
More
over, th
e AALSA-T
R
sche
me
ca
n
offer
nea
r
l
y
th
e
sa
me BER
pe
r
f
or
manc
e
w
i
th CC
-TR
scheme
a
nd
LSA-TR meth
od.Wh
en th
e
BER=1
0
-6
, the SNR
ca
n g
e
t 0.2dB
gain
s
the
AALSA-T
R
scheme com
pare with
LSA-TR scheme
.
5. Conclusio
n
In this
paper,
the tone reserv
ation
scheme for PAPR reduction i
s
investigated i
n
this
pape
r. With
the introdu
ctio
n of the
ada
p
t
ive am
plitud
e
lea
s
t squa
res app
roxima
tion
(AALSA-TR)
algorith
m
. Th
e Pro
p
o
s
ed
AALSA-TR
schem
e m
a
ke
s the
am
plitu
de of th
e g
e
n
e
rated
ne
w p
eak-
can
c
eli
ng si
g
nals a
pproximate to
that of the original
clippin
g
noi
se. simultane
o
u
sly, the AALSA-
TR sc
heme
can have a
better PAPR gains
c
o
mp
are with
LSA-TR s
c
hem
e. AALSA-TR method
in different cli
pping
threshold have an
approxim
atel
y PAPR reduction perform
ance. Simulated
results a
r
e shown that re
quire
a l
a
rg
e
step si
ze to
get the st
ea
dy CCDF curve. Throug
h the
OFDM
sy
ste
m
, the AALSA-TR
schem
e ca
n offer n
early the
sa
m
e
BER p
e
rfo
r
mance
with L
SA-
TR sch
e
me i
n
the same
computation
a
l compl
e
xity.
Ackn
o
w
l
e
dg
ements
This pa
pe
r is funded by the key proj
ect
of
Chinese Ministry of
Education (No.
106042
)
and the
proj
e
c
t sp
on
sored
by the Scie
ntific Re
se
arch Fo
und
atio
n for the
Ret
u
rne
d
Ove
r
seas
Chin
ese Sch
o
lars, State Educat
ion Mini
stry (20
07 [24
]
).
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
An Im
proved
Tone Reservation Schem
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