Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 1
,
Febr
u
a
r
y
201
6,
pp
. 10
6
~
11
2
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
1.9
338
1
06
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
A P
o
lyn
o
mial Di
gital
Pre-Dist
orti
on Tech
nique Based on
Iterative Architecture
Kw
an
g-P
y
o L
ee, S
o
o
n
-Il
Ho
ng,
E
u
i
-
Ri
m
J
e
on
g*
Department o
f
I
n
formation and
Co
mmunication Engineering,
National Han
Bat Univ
ersity
, 305-7
19, Korea
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 20, 2015
Rev
i
sed
No
v 5, 201
5
Accepted Nov 22, 2015
A digital pred
istortion (DPD) techniqu
e bas
e
d
on an i
t
er
ativ
e
adapt
a
t
i
on
structure is proposed for linearizing
power amplifiers (PAs).
To obtain
proper DPD par
a
meters, a feedb
ack path
th
at co
nverts the PA’s
output to
a
baseband sign
al
is required
,
and
m
e
m
o
ry
is
als
o
needed
to s
t
or
e t
h
e bas
e
b
a
nd
feedback signals. DPD parameters
ar
e usually
found b
y
an adaptive
algorithm
b
y
using the tr
ansm
itted signals
and
the corr
espondi
ng feedback
signals. However, for the ad
aptive algorithm
to converge to a reliab
l
e
solution, long f
eedback samples are
requir
e
d, which incr
eases hardware
com
p
lexit
y
and cos
t
. Cons
ider
in
g that th
e conv
e
r
gence
tim
e of t
h
e adap
tive
algorithm highly
dep
e
nds on the ini
tial cond
ition, we propo
se a DPD
techn
i
que that
requires rela
t
i
vel
y
shorter fe
edba
c
k
sam
p
les. Spec
ific
all
y
,
th
e
proposed DPD
iter
a
tiv
ely
utilizes the s
hort feedback samples
in memor
y
while k
eeping
and using th
e DPD paramete
rs fo
und at th
e form
er iteration
as
the in
itial
condition at
the n
e
xt
iterati
on. Computer simulation
shows that th
e
proposed techn
i
que performs better
than
the co
nvention
a
l
techn
i
que, as
the
form
er requir
e
s
m
u
ch s
horter f
e
e
dback m
e
m
o
r
y
t
h
an th
e
lat
t
er
.
Keyword:
Dig
ital pre-d
i
sto
r
tion
Indirect learning
Iterative st
ruct
ure
pol
y
n
o
m
i
al
Power am
p
lifie
rs
(PAs)
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
:
Eui
-
R
i
m
Jeong
,
Depa
rt
m
e
nt
of
In
fo
rm
at
i
on an
d C
o
m
m
uni
cati
on
En
gi
nee
r
i
n
g,
H
a
nb
at
N
a
tio
nal U
n
i
v
er
sity 12
5 Don
g
s
eod
a
er
o,
Y
u
seon
g-g
u
,
D
aej
eon
,
30
5-7
1
9
,
Kor
e
a,
Em
a
il: erj
e
on
g@h
a
nb
at.ac.k
r
1.
INTRODUCTION
A p
o
w
er
am
pli
f
i
e
r (P
A
)
i
s
a
n
esse
nt
i
a
l
co
m
ponent
t
o
t
r
a
n
sm
i
t
si
gnal
s
t
o
a
rem
o
t
e
dest
i
n
at
i
on i
n
wireless co
mm
u
n
i
catio
n
s
. Unfortun
ately, th
e PA is t
h
e m
a
j
o
r so
urce o
f
non
linearities in
a
wireless
co
mm
u
n
i
catio
n
system
, resu
ltin
g
no
t on
ly in
sp
ectral re
growth, nam
e
ly strong i
n
terfe
rence for t
h
e a
d
jace
nt
com
m
uni
cat
i
on c
h
an
nel
s
,
b
u
t
al
so i
n
-
b
a
n
d
d
i
st
ort
i
o
n
s
, i
f
i
t
i
s
dri
v
en
cl
ose
t
o
t
h
e
sat
u
rat
i
o
n
poi
nt
[
1
]
.
In
or
der
t
o
o
v
e
r
com
e
t
hos
e
pr
obl
em
s cause
d
by
no
nl
i
n
eari
t
y
, t
h
e
PA is g
e
n
e
rally b
ack
ed off to
o
p
e
rate
within
th
e
lin
ear p
o
rtion
o
f
its op
erating
cu
rv
e.
Howe
ver,
whe
n
operated at a l
o
we
r po
wer t
h
an the satu
ration
power of
th
e PA, it will h
a
v
e
l
o
w power-efficien
c
y
aro
und
1
0
%.
Thu
s
, v
a
riou
s lin
earizatio
n
tech
n
i
q
u
e
s h
a
v
e
b
een
pr
o
pose
d
t
o
ac
hi
eve
hi
gh
p
o
w
er
-ef
f
i
c
i
e
ncy
o
f
t
h
e
P
A
[2]
.
Am
ong
t
h
ese
t
echni
q
u
es
,
di
gi
t
a
l
pre
-
di
st
or
t
i
on i
s
kn
o
w
n
t
o
be
t
h
e m
o
st
cost
- a
n
d
pe
rf
o
r
m
a
nce-ef
fect
i
v
e t
e
c
hni
que
.
It
ad
ds
a
pre
d
i
s
t
o
rt
e
r
(PD
)
i
n
t
h
e
ba
seba
nd
digital stage t
o
create a
distorted sign
al that
is com
p
le
m
e
ntary to t
h
e c
o
mp
ressi
ng
ch
aracteristic o
f
t
h
e
PA.
A
t
y
pi
cal
DPD s
y
st
em
, as sho
w
n i
n
Fi
g
u
re
1
consi
s
t
s
of
d
i
gital
p
r
ed
istorter
(DPD), DPD en
g
i
n
e
, DAC
(d
ig
ital-
t
o
-a
nal
o
g co
nv
ert
e
r)
, A
D
C
(a
nal
o
g-t
o
-d
ig
ital co
nv
erter),
up
conv
erter and
d
o
wnconv
erter. Th
e tran
sm
it
sig
n
a
l
is p
r
e-d
i
sto
r
ted b
y
t
h
e
DPD in th
e
d
i
g
ital stag
e
b
e
fo
re
it is
co
nv
erted
t
o
an
an
alog
si
g
n
a
l
,
up-
conv
er
ted
to
th
e
t
a
rget
R
F
ban
d
,
an
d fe
d t
o
t
h
e PA.
I
n
t
h
e
D
P
D e
ngi
ne
, an
ad
ap
tiv
e algo
ri
th
m
fin
d
s
th
e
DPD p
a
ram
e
te
rs fo
r
t
h
e i
n
vers
e f
u
nct
i
o
n
o
f
t
h
e
PA,
w
h
i
c
h
re
q
u
i
r
es a
fee
d
ba
ck
pat
h
t
o
c
o
n
v
ert
t
h
e P
A
’
s
out
put
t
o
a
ba
seba
nd
si
gnal
a
n
d
m
e
m
o
ry
t
o
st
ore
t
h
e fee
dba
ck
s
i
gnal
s
. B
y
usi
n
g
t
h
e
param
e
ters, t
h
e P
D
ca
n
gene
rat
e
a
p
r
o
p
erl
y
di
st
ort
e
d si
g
n
a
l
for l
i
n
ea
ri
zi
n
g
t
h
e P
A
. H
o
w
e
ver
,
f
o
r t
h
e a
d
apt
i
v
e al
g
o
ri
t
h
m
t
o
conve
r
g
e t
o
a rel
i
a
bl
e so
l
u
t
i
on,
long feedbac
k
sam
p
les
are
re
qui
red, whic
h
i
n
crease
s
hard
ware co
m
p
lex
ity
and
co
st
d
u
e
to
th
e larg
e m
e
m
o
ry.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
10
6 – 11
2
10
7
To s
o
l
v
e t
h
i
s
di
ffi
c
u
l
t
y
, we
pr
o
pose a
DP
D t
ech
ni
q
u
e t
h
at
re
qui
res r
e
l
a
t
i
v
el
y
short
e
r fee
d
b
a
c
k
sam
p
l
e
s, whi
l
e t
h
e l
i
n
ea
ri
za
t
i
on
per
f
o
rm
ance i
s
si
m
i
l
a
r t
o
t
h
e c
o
nve
nt
i
onal
m
e
t
hod
wi
t
h
l
o
n
g
f
eedbac
k
sam
p
les. Sp
ecifically, th
e p
r
o
p
o
s
ed
DPD i
t
erativ
ely u
tili
zes th
e short feed
b
a
ck
sam
p
les in
m
e
m
o
ry
wh
ile
k
eep
i
n
g an
d usin
g th
e DPD p
a
ram
e
ters fou
nd at th
e
fo
rmer iteratio
n
as th
e in
itial co
nd
itio
n at t
h
e n
e
x
t
iteratio
n
.
In
g
e
n
e
ral, t
h
e ad
aptiv
e alg
o
rith
m
co
nv
erg
e
s
qu
ick
l
y if th
e in
itial p
a
ram
e
ter is
clo
s
e to
th
e so
l
u
tio
n.
At each iteration, the
param
e
ter approac
h
e
s
the sol
u
ti
on
m
o
re closely, since the initial param
e
ter becom
e
s
clo
s
e to th
e solu
tio
n
,
as
well. Co
m
p
u
t
er simu
latio
n shows
th
at th
e
p
r
op
osed
tech
n
i
q
u
e
perfo
r
m
s
b
e
tter
th
an
the conventi
onal techni
que
, a
s
the
form
er re
qui
res
m
u
ch s
h
orter fee
d
back
me
m
o
ry than t
h
e latter.
Fi
gu
re
1.
Tra
n
s
m
i
t
t
e
r arc
h
i
t
ect
ure
em
pl
oy
i
ng
DP
D
2.
D
P
D STR
UCTU
R
E
AN
D SIGNA
L
M
O
DEL
Let
and
b
e
t
h
e inp
u
t
an
d
ou
tpu
t
of th
e PA, resp
ectiv
ely
,
and
let
G
den
o
t
e
s t
h
e PA
’s
ch
aracteristic.
Th
e PA
ou
tpu
t
can
b
e
written
as
fo
llo
ws:
n
(1
)
Si
m
ilarly, if
x
(n
) an
d
y
(n)
are the input and
output
of t
h
e PD, re
spectively, and
pre
F
is th
e PD’s
ch
aracteristic, th
en th
e
PD ou
t
p
u
t
can
b
e
written
as
fo
llows:
y
n
(2
)
Th
e i
d
eal pred
isto
rter shou
ld
satisfy
n
n
(3
)
whe
r
e
is
th
e
PA’s id
eal linear
g
a
in
.
W
e
assu
m
e
th
at
=1 h
e
reafter.
In th
is
pape
r, a
p
o
l
y
nom
i
a
l
-
bas
e
d
DP
D i
s
em
pl
oy
ed, an
d i
t
s
pa
ram
e
t
e
rs are est
i
m
a
t
e
d by
an i
ndi
rect
l
earni
n
g
m
e
t
hod, as s
h
o
w
n i
n
Fi
gu
r
e
2 [
3
]
.
Sp
ecifically, the po
lyn
o
m
ial c
o
efficien
ts are
foun
d
b
y
lin
earizin
g
PA – postd
isto
rter, an
d th
en th
e
p
a
rameters
o
f
th
e po
st
d
i
sto
r
ter are co
p
i
ed
t
o
t
h
e
DPD
in
th
e Tx
p
a
th.
Deno
ting
as
t
h
e
p
o
st
di
st
or
t
e
r o
u
t
put
,
i
t
i
s
written
as fo
llows:
1
ˆ
()
(
)
()
H
pos
t
o
yn
F
a
n
n
K
wa
(4
)
whe
r
e
pos
t
F
is th
e ch
aracteristic
fun
c
tio
n of t
h
e
po
st
di
st
o
r
t
e
r i
n
t
h
e
feed
bac
k
pa
t
h
, a
n
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A Pol
y
no
mi
al
Di
gi
t
a
l
Pre
-
Di
st
ort
i
o
n
Tec
hni
que
B
a
sed
o
n
I
t
erat
i
ve Archi
t
ect
ure
(
E
ui
-Ri
m
Je
on
g)
10
8
w
,
,⋯,
(5
)
a
n
1
,
1
1
,⋯
,
1
1
(6
)
2P+
1
i
s
t
h
e
m
a
xi
m
u
m
nonl
i
n
ear o
r
der o
f
t
h
e p
o
st
di
st
o
r
t
e
r, an
d
w
is th
e
p
o
l
yno
m
i
a
l
co
e
fficient vector of the
post
d
i
s
t
o
rt
er.
The p
r
edi
s
t
o
rt
er and
post
d
i
s
t
o
rt
er
have t
h
e
sam
e
pol
y
n
o
m
i
a
l st
ruct
ure
,
and t
h
ei
r p
o
l
y
nom
i
a
l
coefficients a
r
e
the sam
e
, as well. Conse
q
ue
n
t
l
y
, t
h
e PD
o
u
t
put
ca
n
be e
x
pr
essed a
s
:
y
n
∗
|
|
∗
,
∗
,…,
∗
x
n
|
|
⋮
n
|
|
(7
)
G
()
en
x
y
()
pre
F
()
post
F
a
ˆ
y
Fi
gu
re
2.
I
ndi
r
ect
l
earni
n
g
st
r
u
ct
u
r
e
3.
PROP
OSE
D
PD ALGO
RI
THM
To
o
b
t
ain
th
e op
ti
m
a
l
w
th
at li
n
earizes t
h
e PA, it is g
e
n
e
rally
found
via adaptive
algorithm
s
, such as
th
e least m
ean
sq
uar
e
(
L
MS)
[
4
]
o
r
th
e r
e
cur
s
iv
e least
squ
r
es (
R
LS)
cr
itertio
n
[
5
]-[6
].
the pr
op
sed
alg
o
r
ith
m
was de
vel
o
pe
d
based
on R
L
S cri
t
e
ri
o
n
. T
h
e p
r
o
p
o
sed a
l
go
ri
t
h
m
i
s
present
e
d i
n
Ta
bl
e 1.
We de
n
o
t
e
t
h
e
tran
sm
it
ted
sign
al (or th
e PD
in
pu
t) as
n
, th
e DPD ou
tpu
t
sig
n
a
l as
y
n
, the fe
edbac
k
signal
as
an
, and
as
the
DPD
coefficient
vec
t
or. T
h
e
P
1
P
1
matr
i
x
is d
e
fin
e
d
as th
e inv
e
rse correlation
matrix
, an
d t
h
e fo
rg
etting
fact
o
r
is d
e
fin
e
d as
λ
. F
i
r
s
t,
and
are in
itialized
with
an all-zero
v
ect
o
r
an
d the
P
1
P
1
id
en
tity m
a
trix
,
resp
ectiv
el
y. Assu
m
e
that th
e feedb
a
ck
sign
al len
g
t
h
is
N, i.e., t
h
e
m
e
m
o
ry
size for st
ori
n
g
the
f
eedbac
k
si
gnal
is N.
If
N
is no
t
sufficien
tly larg
e,
t
h
e a
d
aptive algorithm
cannot
con
v
e
r
ge
. I
n
t
h
e
pr
op
ose
d
m
e
t
hod,
h
o
w
e
v
er
,
and
are fo
u
n
d
by
u
s
i
ng t
h
e
N fe
edbac
k
s
a
m
p
les
rep
e
titiv
ely. No
tin
g (1)
and
(2
)
in
Tab
l
e 1
,
th
e
co
efficien
t v
ector
an
d th
e inv
e
rse co
rrelatio
n
m
a
trix
ar
e
f
oun
d fo
r
n1
,
⋯
,
N
.
At
n=
N,
b
o
t
h
pa
ram
e
t
e
rs are c
l
oser t
o
th
e op
ti
m
u
m
so
lu
tio
n.
Howev
e
r,
wh
en
t
h
e
l
e
ngt
h
o
f
t
h
e
f
eedbac
k
sam
p
l
e
s, N
,
is no
t su
fficien
tly lo
ng
, it lead
s to
t
h
e d
e
grad
ation o
f
t
h
e lin
eari
zatio
n
per
f
o
r
m
a
nce.
To
res
o
l
v
e t
h
i
s
p
r
o
b
l
e
m
,
t
h
e pr
o
pose
d
m
e
t
hod
kee
p
s
t
h
e l
a
st
and
acqui
red at n=
N. Then,
th
o
s
e p
a
ram
e
t
e
rs
b
e
co
m
e
th
e in
itial p
a
rameters
and
,
resp
ectiv
ely, and
t
h
e ad
ap
tiv
e algo
rith
m
is ru
n
again
with t
h
e sam
e
feedback sam
p
les.
This
proce
d
ure can
be
re
pe
ated se
veral ti
mes. Since t
h
e RLS
alg
o
rith
m
co
nv
erg
e
s m
o
re
q
u
i
ck
ly wh
en th
e in
itial p
a
ram
e
ters are clo
s
er t
o
th
e
so
lu
tion
,
t
h
e
p
r
o
p
o
s
ed
alg
o
rith
m
u
t
i
l
i
zes th
is ch
aracteristic to
co
n
v
erg
e
th
e algorith
m with
sh
ort feedb
ack
sam
p
les. Fin
a
lly, th
e PD
uses
ob
tain
ed
at th
e fi
n
a
l iteratio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
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08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
10
6 – 11
2
10
9
Tab
l
e
1
.
Th
e Pr
opo
sed algo
r
i
t
h
m
4.
COMPUTER SIMULATION
To ve
ri
fy
t
h
e
p
e
rf
orm
a
nce of
t
h
e pr
o
p
o
s
ed
m
e
t
hod, si
m
u
l
a
t
i
on was ca
rri
ed o
u
t
by
usi
n
g M
A
TL
AB
.
The sim
u
lation environm
ents that
were use
d
are as follows
. The tran
sm
itted signal is LTE Downlink
signal
wi
t
h
20M
Hz
b
a
nd
wi
dt
h. T
h
e
PD
’s m
a
xim
u
m
pol
y
nom
i
a
l
or
der
i
s
5
(
P
2
. Th
e forg
etting
facto
r
λ
fo
r
th
e
RLS algo
r
ith
m
is 0.999
99
. For
th
e non
lin
ear
PA
m
o
d
e
l,
Sal
e
h’s
m
odel
i
s
e
m
pl
oy
ed [7]
,
w
h
i
c
h i
s
gi
ven
b
y
G
y
n
1
|
|
|
|
|
|
1
.
1
,
0
.
3
,
1
,
1
(8
)
Fi
gu
re
3 s
h
ow
s t
h
e
PA
m
odel
’
s AM
-AM
an
d
AM
-PM
res
p
o
n
ses
.
It
i
s
o
b
ser
v
e
d
t
h
at
t
h
e n
onl
i
n
ear
di
s
t
ort
i
o
n
is no
tab
l
e in that th
e PA inpu
t m
a
g
n
itu
d
e
b
e
co
m
e
s larg
er.
Figu
re 3.
(a
) A
M
/AM
res
p
o
n
s
e
Fi
gu
re
3.
(
b
)
A
M
/
P
M
resp
o
n
s
e
Fi
gu
re 4
(
a) s
h
ows t
h
e co
nve
nt
i
onal
DPD
’
s
l
earni
n
g
curve for 5,000
feedback
sam
p
les. The learni
ng
cur
v
e s
h
ow
s
m
ean sq
ua
re e
r
r
o
r
(M
SE
),
E
[
|e(n
)|
2
] in
Tab
l
e I fo
r tim
e
n
.
It is ob
serv
ed th
at t
h
e ad
ap
tiv
e
al
go
ri
t
h
m
conv
erges t
o
1
0
-4
at
n=5
,
0
0
0
. Fi
g
u
r
e 4
(
b
)
sh
o
w
s t
h
e l
earni
n
g
cu
r
v
e o
f
t
h
e
pr
op
o
s
ed m
e
t
hod wi
t
h
1
0
iteratio
n
s
.
At t
h
e en
d
of th
e
fin
a
l iteratio
n, the MSE conv
erg
e
s to 10
-5
. The MSE is 10-fold
b
e
tter t
h
an th
at of
th
e conv
en
tional tech
n
i
qu
e.
Th
is resu
lt in
d
i
cates th
at
th
e DPD
p
a
ram
e
ters are clo
s
er to
t
h
e op
tim
u
m
so
lu
tio
n
as th
e nu
m
b
er
o
f
iteration
s
increases, and
b
e
tter lin
eari
zat
i
on pe
rf
o
r
m
a
nce i
s
expect
e
d
by
usi
n
g t
h
e
pr
o
p
o
se
d
technique.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
A Pol
y
no
mi
al
Di
gi
t
a
l
Pre
-
Di
st
ort
i
o
n
Tec
hni
que
B
a
sed
o
n
I
t
erat
i
ve Archi
t
ect
ure
(
E
ui
-Ri
m
Je
on
g)
11
0
Figu
re
4.
(a
) L
earni
ng
Cu
rve
fo
r the
co
n
v
ent
i
onal P
D
(itera
tion =
1
)
Fi
gu
re
4.
(
b
)
L
earni
ng
C
u
rve
fo
r t
h
e
p
r
op
ose
d
P
D
(i
t
e
rat
i
o
n
= 1
0
)
Fi
gu
re 5 sh
o
w
s
t
h
e pow
er spe
c
t
r
um
at t
h
e PA o
u
t
p
ut
. The
gra
p
hs rep
r
ese
n
t as follo
ws: (a) Tx sig
n
al;
(b
) PA
out
put
wi
t
h
o
u
t
DP
D
;
(c) PA o
u
t
p
ut
wi
t
h
co
n
v
e
n
t
i
onal
D
P
D
(
m
ax_i
t
e
r = 1)
and 5
,
0
0
0
fe
edbac
k
sam
p
l
e
s (N =
5,
00
0
)
;
(d
) PA
out
p
u
t
wi
t
h
p
r
o
p
o
sed
DP
D (m
ax_i
t
e
r = 10
) an
d 5,
0
00 fe
edbac
k
sam
p
l
e
s (N
=
5,
00
0
)
;
and
(e
) PA
out
put
wi
t
h
co
nv
ent
i
onal
D
P
D
(m
ax_i
t
e
r = 1
)
a
nd
17
0,
0
00
fe
edbac
k
sam
p
l
e
s (N =
17
0,
0
0
0
)
. C
o
m
p
ari
ng (c) a
nd (
d
), i
t
i
s
seen t
h
at
t
h
e pr
o
pose
d
m
e
tho
d
pe
rf
orm
s
m
u
ch bet
t
e
r than t
h
e
con
v
e
n
t
i
onal
t
echni
que
wi
t
h
t
h
e sam
e
feedback
sam
p
l
e
s. The s
p
ect
ral
re
gr
owt
h
i
s
re
d
u
ced by
a
n
ad
di
t
i
onal
13~
1
4dB
by
usi
n
g t
h
e
pr
o
pos
ed
t
ech
ni
q
u
e. C
o
m
p
ari
n
g
(d
) a
n
d (
e
),
t
h
e
pr
o
p
o
s
ed
m
e
t
hod s
h
o
w
s nea
r
l
y
id
en
tical p
e
r
f
or
m
a
n
ce w
ith
t
h
e co
nv
en
tio
nal D
P
D
techn
i
q
u
e
u
s
i
n
g 170,00
0 f
e
edb
ack sam
p
les, w
h
i
l
e th
e
pr
o
pose
d
m
e
t
h
od re
q
u
i
r
es o
n
l
y
5,0
00 fee
d
ba
ck sam
p
l
e
s. Thi
s
resul
t
i
ndi
ca
t
e
s t
h
at
t
h
e pro
pos
ed t
ech
ni
q
u
e
can
rel
i
e
ve t
h
e
re
q
u
i
r
em
ent
on
t
h
e fee
dbac
k
m
e
m
o
ry
si
ze wi
t
hout
l
i
n
ea
ri
zat
i
o
n
per
f
o
r
m
a
nce l
o
ss.
Figure
5. Spectrum
com
p
arison at PA
output
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
10
6 – 11
2
11
1
5.
CO
NCL
USI
O
N
A
pol
y
n
o
m
i
al DP
D t
e
c
hni
q
u
e
base
d
on
a
n
i
t
e
rat
i
o
n st
r
u
ct
u
r
e
was
pr
op
ose
d
.
Si
nce
t
h
e a
d
a
p
t
i
v
e
alg
o
rith
m
h
i
g
h
ly d
e
p
e
nd
s
o
n
th
e in
itial co
n
d
itio
n
,
it is p
o
s
sib
l
e to
o
b
t
ai
n
perfo
r
m
a
n
ce u
s
i
n
g
i
n
sho
r
t m
e
m
o
ry
sim
ilar to that accom
p
lished with
l
o
ng m
e
m
o
ry by
kee
p
ing a
n
d itera
tively using t
h
e c
o
nve
r
ge
d DPD
p
a
ram
e
ters at th
e form
er iteratio
n
as t
h
e i
n
itial co
nd
itio
n at
th
e curren
t
iteratio
n
.
C
o
m
p
u
t
er sim
u
latio
n
resu
lts
show t
h
at a
DPD technique that re
quire
s
relativel
y sh
or
t f
e
edb
ack sam
p
les
can achieve
linea
rization
p
e
rform
a
n
ce similar to
th
at im
p
l
e
m
en
ted
u
s
in
g
l
o
ng
m
e
m
o
ry.
ACKNOWLE
DGE
M
ENTS
Thi
s
re
searc
h
was s
u
pp
ort
e
d
by
t
h
e
Wo
rl
d C
l
ass
300
R&D
projects funded by t
h
e Sm
all and
M
e
di
um
B
u
si
n
e
ss A
d
m
i
ni
st
rat
i
on
of
K
o
rea
(
S
2
3
1
8
1
0
9
)
.
REFERE
NC
ES
[1]
S
.
C. Cripps
, Ada
v
anced
t
echniqu
es
in
RF
POWE
R AM
PL
IFIE
R
DESIGN
. Artech
House, 2002
.
[2]
P.B. Kenning
ton
,
High
Linearity RF Amplifiers
Design
. R
ead
ing,
MA: Artech
House, 2000
.
[3]
Young-Doo Ki
m, Eui-Rim Jeong, and Y
ong H. Lee. "Adaptive compensation
f
o
r power amplif
ier nonlin
ear
ity
in
the presen
ce of
quadratur
e modul
ation
/
demodu
lation errors",
I
EEE Transactio
ns on Signal P
r
ocessing
, 55(9)
(2007): 4717-47
21.
[4]
Chang B
y
ong-
Kun, Jeon Chang-Dae, Song
Dong-Hy
uk
, “P
erformance Improvement
in
Alternate Mainbeam
Nulling b
y
Adap
tive
Estimation
of Convergen
ce
Paramete
rs in
Linearly
Constr
ain
e
d Adaptiv
e Arr
a
y
s
”,
Journal of
information
and
communication
convergen
c
e
eng
i
neering
, pp
.392
–398, vol. 7
,
no
.
3,
2009.
[5]
Roman Marsalek, Pascale Jardin, a
nd Genev
i
ève Baudoin
.
"From post-dist
ortion to pre-disto
r
tion for power
am
plifiers line
a
r
i
za
tion",
Communications
Letters, IEEE
7(7) (200
3): 308-310.
[6]
Sungho Choi,
Eui-Rim Jeong, and Yong H.
Lee. "A direct
learn
i
ng struct
ur
e for ad
aptiv
e
poly
nomial-based
predistortion
for
power am
plifi
e
r line
a
riz
a
t
i
on",
Vehicular Techn
o
logy Conferen
ce, 2007
. VTC20
07-Spring. IEEE
65th
. I
E
EE, 200
7.
[7]
A.
A.
M.
Saleh,
“Fre
quency
-
independent and fr
eque
ncy
-
dep
e
ndent nonlinear mode
ls of TW
T am
plifiers”,
IE
EE
Trans. Commun
., vol. COM-29,
no. 11
, (Nov 198
1): 1715-1720.
BIOGRAP
HI
ES OF
AUTH
ORS
Kwang-P
y
o L
e
e
receiv
e
d the B.
S
.
degree from
the Departm
e
nt
of Radio W
a
ve Engine
ering at
Hanbat National University
, Daejeo
n
,
Korea, in
2014. He is cu
rrently
pursuing
the master’s
degree
in th
e Department o
f
Radio Wave Eng
i
n
eeri
ng
at Hanb
at National University
, Daejeon
,
Korea. His
r
e
s
e
arch in
ter
e
s
t
s
in
clude
the
are
a
s
of
digital sign
al processing, pre-distortion
,
and
modem design.
Soon-il Hong received th
e B.S
.
degree from the
Department of
Radio
Wave Engineer
ing at
Hanbat National University
, Daejeo
n
,
Korea, in
2014. He is cu
rrently
pursuing
the master’s
degree
in th
e Department o
f
Radio Wave Eng
i
n
eeri
ng
at Hanb
at National University
, Daejeon
,
Korea. His
r
e
s
e
arch in
ter
e
s
t
s
in
clude
the
are
a
s
of
digital sign
al processing, pre-distortion
,
and
modem design.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A Pol
y
no
mi
al
Di
gi
t
a
l
Pre
-
Di
st
ort
i
o
n
Tec
hni
que
B
a
sed
o
n
I
t
erat
i
ve Archi
t
ect
ure
(
E
ui
-Ri
m
Je
on
g)
11
2
Eui-Rim Jeong received the B.S., M.S., and Ph.D
. degrees from the Department of Electr
i
cal
Engineering
at the Korea Advanced Institute
o
f
Scien
c
e and
Technolog
y
(KAIST),
Daejeon
,
Korea, in 1995, 1997, and 2001, respectively
.
He
is currently an associate pr
ofessor in the
Department o
f
I
n
formation and
Communication
E
ngineering, Hanbat Nati
onal U
n
iversity
, since
2009. His resear
ch interests
inclu
d
e th
e ar
eas of
communication signal pro
cessing, pre-distortion,
and modem design.
Evaluation Warning : The document was created with Spire.PDF for Python.