Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 3
,
Ju
n
e
201
6, p
p
. 1
096
~ 11
05
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
3.1
032
8
1
096
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
Effici
ent
Low-Complexit
y
Digit
a
l Predist
o
rtion for Power
Amplifier Linearization
Siba Mon
t
her
Yousif
1,4
,
Ros
lina M. Side
k
1
, Anwer S
a
b
a
h Me
kki
2
, Nas
r
i
Sulaim
a
n
1
, Po
ori
a
V
a
ra
h
r
am
3
1
Departm
e
nt
of
Ele
c
tri
cal
and
E
l
ectron
i
c
Engin
e
e
r
ing, Univ
ersiti
Putra Mal
a
y
s
ia
(
U
PM), Mala
y
s
ia
2
Functional
Devi
ces L
a
borator
y
,
I
n
stitute of Adv
a
nced
Te
chnolog
y
,
Universi
ti
Put
r
a Mal
a
y
s
ia (UPM), Malay
s
i
a
3
Department of Electronic Engin
eering
,
May
noo
th University
, May
nooth
,
Co
. Kild
are, Ireland
4
Department
of
Electronic and
C
o
mmunication Engineer
ing, Al-
N
ah
rain Univ
ers
i
ty
, Baghdad
,
Iraq
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Feb 9, 2016
Rev
i
sed
May 11
, 20
16
Accepted
May 20, 2016
In this pape
r,
a
low-com
p
lexit
y
m
odel is prop
osed for lin
earizing power
am
plifiers with
m
e
m
o
ry
effe
c
t
s us
ing the d
i
gita
l pred
istort
ion (DPD)
techn
i
que. In th
e proposed model,
the
linear,
lo
w-order nonlinear and high
-
order nonlinear
memory
effects are
computed separately
to provide
flexibi
lit
y
in con
t
rolling
the m
odel par
a
m
e
ters so that both high p
e
rform
anc
e
and low model complexity
can be
achi
e
ved.
The perform
a
n
ce of the
proposed model is assessed based on
exp
e
rimental measurem
ents of
a
com
m
e
rcial c
l
as
s AB power amplifie
r b
y
apply
i
ng a single-carrier wideband
code division m
u
ltipl
e
ac
cess (W
CDMA) signa
l. The lin
ear
it
y
perform
ance
and the model
complexity
of
the proposed model ar
e
compared with th
e
memory
poly
n
o
m
ial (MP) mode
l and th
e DP
D with s
i
ngle-fe
ed
back m
odel
.
The exp
e
rimental results show that
the proposed
model outperfor
m
s the latter
m
odel b
y
5 dB
in term
s
of
adja
cent
chann
e
l
le
a
k
age power
ra
ti
o (ACLR)
with com
p
arabl
e
com
p
lexit
y
. Co
m
p
ared to M
P
m
odel, the prop
os
ed m
odel
shows improved
ACLR performance b
y
10.8 d
B
with a r
e
duction in th
e
complexity
b
y
1
7
% in terms of numbe
r of floatin
g-point oper
a
tio
ns (FLOPs)
and 18%
in
terms of number of
model coef
ficien
ts.
Keyword:
Dig
ital Pred
ist
o
rtion
M
e
m
o
ry
Ef
fects
M
e
mo
r
y
P
o
l
y
n
o
mi
a
l
Mo
d
e
l C
o
m
p
le
x
ity
Power Am
p
lifiers
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
:
Si
ba
M
ont
her Yo
usi
f
,
Depa
rtm
e
nt of
Electrical an
d Electronic
Engineering,
Un
i
v
ersiti Pu
tra Malaysia (UPM),
Serd
ang
,
434
00
,
Selang
or
, Malaysia.
Em
a
il: sib
a
m
o
n
t
h
e
r200
0@yah
o
o
.
co
m
1.
INTRODUCTION
Power am
p
lifier (PA) is a maj
o
r so
urce of
n
o
n
lin
ea
rity in
a co
mm
u
n
i
cat
io
n
system
sin
ce it is o
f
ten
dri
v
en cl
ose t
o
t
h
e sat
u
rat
i
o
n
regi
on t
o
achi
e
ve hi
gh
p
o
we
r
effi
ci
ency
. T
h
e
no
nl
i
n
ea
ri
t
y
incl
u
d
es
out
-
o
f-
ban
d
em
i
ssi
on w
h
i
c
h ca
uses a
d
jac
e
nt
cha
n
nel
i
n
t
e
rfe
rence
an
d
i
n
-
b
an
d
di
st
o
r
t
i
on t
h
at
de
g
r
a
d
es t
h
e
bi
t
err
o
r
rat
e
per
f
o
r
m
a
nce. I
n
m
oder
n
hi
g
h
s
p
ee
d c
o
m
m
uni
cat
i
o
ns,
t
r
a
n
sm
i
ssi
on sch
e
m
e
s wi
t
h
hi
g
h
s
p
ect
ral
e
ffi
ci
ency
su
ch
as
Ort
h
og
on
al Freq
u
e
ncy Div
i
sion
Mu
ltip
lex
i
ng
(OFDM) and
W
i
d
e
b
a
nd
C
o
d
e
Div
i
sion
Mu
ltip
le
Access (WCDMA) are m
o
re sen
s
itiv
e to
PA n
o
n
lin
earity
an
d
m
e
m
o
ry
effects. Th
is issu
e can
b
e
so
lv
ed
b
y
backi
n
g
-
of
f t
h
e ope
rat
i
ng re
g
i
on o
f
t
h
e PA i
n
t
o
a l
i
n
ear m
ode at
t
h
e expe
n
s
e of t
h
e de
g
r
a
d
at
i
on
of t
h
e
p
o
we
r
a
m
plifier efficiency. T
o
overcom
e
th
e confl
i
ct betwee
n the powe
r e
ffici
en
cy and t
h
e li
nearity of t
h
e
powe
r
a
m
p
lifier, a linearizatio
n
techn
i
qu
e is
requ
ired
.
On
e
o
f
t
h
e
m
o
st co
st-effectiv
e lin
earizatio
n
tech
n
i
q
u
e
s is th
e
d
i
g
ital pred
ist
o
r
tio
n (D
PD
) [1].
Man
y
DPD stru
ctures
h
a
v
e
been
p
r
esen
ted
in
th
e literature, con
t
ain
i
ng
t
h
e
Vo
lterra-b
a
sed
m
o
d
e
ls
[2]
-
[
6]
, t
h
e p
o
l
y
nom
i
a
l
-
base
d m
odel
s
[
7
]
,
t
h
e ne
ural
-net
wo
rk
m
odel
s
[
8
]
,
[
9
]
,
an
d t
h
e
LUT
-
ba
sed
m
odel
s
[10],[11]. Eve
n
though th
e
Volterra m
ode
l is gene
rally the m
o
st
accurate struct
ure
in com
p
ensati
ng the
n
o
n
lin
earity with
m
e
m
o
ry effects
o
f
th
e
p
o
wer am
p
lif
i
e
r, it is
m
a
in
ly restricted
to
co
m
p
en
sate
m
ild
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Efficien
t
Lo
w
Co
mp
lexity Di
g
ita
l Pred
isto
rt
io
n
f
o
r Po
wer
Amp
lifier Lin
e
a
r
iza
tion
(
S
iba Mon
t
h
e
r Yo
usif
)
1
097
nonlinea
rity with
m
e
m
o
ry effects of
the PA. T
h
is is because of its hi
gh com
p
lexity in
extracting Volterra
kernels. T
h
ere
f
ore, se
veral s
p
ecial cases of Volterra
m
o
del were proposed, s
u
ch as t
h
e dynam
i
c deviation
redu
ction
m
o
del [12
]
.
Ho
we
ver
,
hi
g
h
com
p
l
e
xi
t
y
D
P
D i
s
u
n
d
esi
r
abl
e
be
cause
i
t
l
eads t
o
hi
g
h
po
we
r c
ons
um
pt
i
on a
n
d
lo
ng
-tim
e d
e
la
y d
u
e
to
in
tensiv
e p
r
o
cessi
ng
. Moreov
er, th
e m
a
in
j
u
stifi
catio
n
fo
r th
e
DPD tech
n
i
q
u
e is to
g
a
in
m
o
re p
o
wer-efficien
t PA,
wh
ich
is th
e
m
o
st
p
o
w
er con
s
u
m
in
g
d
e
v
i
ce in
tran
sm
itters [1
3
]
-[15
].
Th
erefo
r
e, it is essen
tial th
at th
e p
o
w
er sav
e
d, b
y
u
s
ing
DPD, is no
t sp
en
t on
a hig
h
co
m
p
lex
ity DPD
alg
o
rith
m
.
In
deed
, t
h
e MP
m
o
d
e
l pro
posed
in
[2
] is well-kno
wn
for PA lin
earizatio
n
.
Th
is
m
o
d
e
l
co
m
p
en
sates fo
r
no
n
lin
earities with
m
e
m
o
ry effects
u
s
ing
con
s
i
d
erab
ly lo
wer m
o
d
e
l d
i
m
e
n
s
io
n
s
than
the
m
o
d
e
ls repo
rted
in
[4
]. Howev
e
r, th
e lin
earity p
e
rfor
m
a
nce of t
h
e P
A
usi
n
g t
h
e M
P
m
odel
i
s
gene
ral
l
y
l
o
we
r
than the
perform
ance whe
n
using the models
prese
n
te
d
in
[3
],
[4
].
Th
er
efo
r
e,
ac
hieving
high linearity
p
e
rform
a
n
ce an
d sim
u
ltan
e
o
u
sly
m
i
n
i
mizin
g
th
e
DPD m
o
del co
m
p
lex
ity i
s
cru
c
ial.
In
t
h
is p
a
p
e
r, a lo
w-co
m
p
lex
ity DPD m
o
d
e
l is p
r
op
o
s
ed
an
d ex
p
e
rim
e
n
t
all
y
v
a
lid
ated
fo
r
lin
earizing
p
o
wer am
p
lifie
rs with
m
e
m
o
ry effects. Th
e
p
r
op
o
s
ed
m
o
d
e
l
i
s
const
r
uct
e
d by
se
p
a
rating
th
e lin
ear from th
e
nonlinea
r m
e
mory effects to e
nha
nce
lin
earizatio
n
.
Th
e low-ord
e
r
n
o
n
lin
ear
m
e
m
o
ry effect is then se
parate
d
fro
m
its h
i
g
h
-o
rd
er term
s to
redu
ce t
h
e m
o
d
e
l co
m
p
u
t
ation
a
l co
m
p
lex
ity. Con
s
eq
u
e
n
tly, th
is al
g
o
rithm
wil
l
p
r
ov
id
e
flex
ib
i
lity in
co
n
t
ro
llin
g
t
h
e d
i
m
e
n
s
io
n
s
of th
e m
o
d
e
l t
h
at can
i
m
p
r
o
v
e
th
e linearity p
e
rforman
ce
whi
l
e
re
duci
n
g
t
h
e com
put
at
ional
c
o
m
p
l
e
xi
ty
of t
h
e D
P
D
m
odel
.
Theref
ore
,
t
h
e m
a
i
n
cont
ri
b
u
t
i
on
of
t
h
i
s
pape
r is that the propose
d m
o
del gives a better expe
ri
m
e
nta
lly adjacent channel leaka
g
e powe
r ratio (ACLR
)
perform
a
nce than the MP m
o
d
e
l [2
] with
a co
n
s
i
d
erab
le red
u
c
tion
in
th
e
m
o
d
e
l co
m
p
u
t
atio
n
a
l co
m
p
l
e
x
ity.
M
o
re
ove
r,
t
h
e
expe
ri
m
e
nt
al
resul
t
s
s
h
o
w
t
h
at
t
h
e
pr
op
ose
d
m
odel
out
pe
rf
orm
s
t
h
e D
P
D m
odel
wi
t
h
si
ngl
e-
f
eedb
a
ck
[3
] in ter
m
s o
f
A
C
LR p
e
rfo
r
m
an
ce with a
com
p
arable m
odel com
p
lexity.
2.
MO
DEL DE
S
CRI
PTIO
N
In t
h
i
s
sect
i
o
n, t
h
e m
e
m
o
ry
pol
y
n
o
m
i
al
m
odel
i
s
present
e
d a
nd t
h
e
pr
op
ose
d
m
odel
wi
t
h
i
t
s
id
en
tificatio
n alg
o
rith
m
is clarified
.
2.
1.
Mem
o
ry Pol
y
nomi
al Model
Th
e b
a
seb
a
nd p
r
ed
isto
r
t
er
can
b
e
m
o
d
e
lled
u
s
i
n
g
t
h
e
MP
m
o
d
e
l, wh
ich
is a good
m
o
d
e
l as
con
s
i
d
ere
d
i
n
[
2
]
,
as s
h
ow
n i
n
Eq
uat
i
o
n (
1
):
(1
)
whe
r
e
z(n)
and
x(n)
are t
h
e com
p
l
e
x out
p
u
t
an
d i
n
put
si
gnal
s
of t
h
e
M
P
pre
d
i
s
t
o
rt
er m
odel
,
respe
c
t
i
v
el
y
.
,
K
, a
n
d
Q
are th
e m
o
d
e
l coefficien
ts, non
lin
earity o
r
d
e
r, an
d m
e
m
o
ry len
g
t
h
,
resp
ectiv
ely.
In [
2
]
,
t
h
e M
P
m
odel
,
w
h
i
c
h was
use
d
as
a di
gi
t
a
l
pred
i
s
t
o
rt
er,
of
fers
a go
od t
r
a
d
e
-
of
f bet
w
een
p
e
rf
or
m
a
n
ce an
d co
m
p
lex
ity. I
t
h
a
s a
g
ood adv
a
n
t
ag
e
since its p
a
r
a
m
e
t
e
r
s
(
i
.e. t
h
e M
P
’
s
co
ef
f
i
cien
t
s
)
can
easily be extracted using least square s
o
lut
i
ons wit
h
an
indi
rect learning arc
h
itect
ure pr
o
pose
d
i
n
[
1
6]
as
sho
w
n i
n
Fi
g
u
r
e 1
.
H
o
weve
r
,
t
h
e M
P
m
o
d
e
l
uses t
h
e
sa
m
e
hi
gh
n
onl
i
n
eari
t
y
o
r
de
r i
n
al
l
of
t
h
e m
e
m
o
ry
bra
n
c
h
es,
w
h
i
c
h
resul
t
s
i
n
a
n
ove
rsi
zed
m
odel
and
an
i
n
crease in
t
h
e co
mp
u
t
ation
a
l co
mp
lex
ity of its mo
d
e
l.
Fi
gu
re 1.
Indi
rect learning a
r
chitecture
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
. 3,
J
u
ne 2
0
1
6
:
10
9
6
– 11
05
1
098
2.
2.
Prop
osed
M
o
del
To re
duce t
h
e
com
p
l
e
xi
t
y
of t
h
e DP
D m
o
del
and e
nha
n
ce t
h
e com
p
ensat
i
ng pe
rf
orm
a
nce o
f
t
h
e
n
o
n
lin
earities
with
m
e
m
o
ry
effects of th
e po
wer am
p
lifier, a DPD m
o
d
e
l is d
e
riv
e
d
from th
e Vo
lterra-series
m
odel
repre
s
en
t
e
d i
n
c
o
m
p
l
e
x
base
ba
nd
[
17]
as sh
o
w
n
i
n
Eq
uat
i
o
n
(
2
):
(2
)
whe
r
e
and
ar
e t
h
e com
p
l
e
x
base
ban
d
out
p
u
t
an
d i
n
put
si
gnal
s
of t
h
e V
o
l
t
e
rra
-seri
e
s
p
r
edi
s
t
o
rt
er,
respectively.
is th
e
no
n
lin
earity o
r
d
e
r,
i
s
t
h
e m
e
m
o
ry
de
pt
h,
are the
th
-o
rd
er
V
o
lterr
a
ker
n
el
s, a
n
d t
h
e sy
m
bol
d
e
n
o
tes th
e co
m
p
le
x
co
nju
g
a
te
operato
r.
If t
h
e
Volterra
kernels a
r
e e
q
ual to zer
o e
x
ce
pt along the
di
agonal
whe
r
e
onl
y
are co
n
s
i
d
ered, th
is
will red
u
c
e th
e m
o
del co
m
p
lex
ity with
ou
t si
g
n
i
fi
can
t
redu
ction
in the lin
earity p
e
rfo
r
m
a
n
ce. Th
us, th
e exp
r
ession
in Eq
u
a
tion
(2
) is redu
ced to
Equ
a
tio
n (3
):
(3
)
By co
m
b
in
in
g
th
e term
s o
f
t
h
e lin
ear m
e
m
o
ry effects
(i.e.
wh
en
k
= 1) and
sep
a
rating
t
h
e
m
fro
m
th
e
ot
he
r t
e
rm
s, w
h
i
c
h
re
prese
n
t
t
h
e dy
nam
i
c nonl
i
n
ea
ri
t
y
effe
cts. Conse
que
ntly, the linear
me
m
o
ry effect
s can
be e
ffi
ci
ent
l
y
c
o
m
p
ensat
e
d as
sho
w
n i
n
E
qua
t
i
on
(4
):
(4
)
Th
en
, for prop
erly con
t
ro
llin
g
t
h
e co
m
p
en
sation
of th
e n
o
n
lin
earity with
m
e
m
o
ry
effects and
r
e
du
cing
at th
e sam
e
ti
me
th
e co
m
p
u
t
atio
n
a
l
co
m
p
lex
ity o
f
th
e pr
opose
d
m
odel, the effects of t
h
e dy
na
m
i
c
lo
w-ord
e
r are
sp
lit fro
m
th
e
h
i
gh
-o
rd
er no
nlin
earity e
ffects b
y
so
rting
ou
t th
e no
n
lin
earity ter
m
s o
f
fro
m
th
e h
i
gh
er
n
o
n
lin
earity
o
r
d
e
r as illu
strated
in
Equ
a
tion
(5):
(5
)
By changing t
h
e m
odel coe
f
ficients
,
, and
to
,
, and
r
e
sp
ectiv
ely, the pr
opo
sed m
e
t
h
od
can
b
e
expr
essed
as i
n
Equ
a
tio
n (6
)
:
(6
)
whe
r
e
and
are the c
o
m
p
lex coefficients
of the
first a
n
d
seco
nd
b
r
a
n
c
h
es
of t
h
e
pr
o
pos
ed m
odel
,
respectively, a
nd the
v
a
lu
es in
clu
d
e
th
e co
m
p
lex
m
o
d
e
l co
efficien
ts
of th
e th
ird
b
r
an
ch.
and
rep
r
ese
n
t
the
m
e
m
o
ry
dept
h
fo
r t
h
e fi
rst,
seco
nd
, a
n
d
third
branc
h
es
, res
p
ectively, and
de
not
es
t
h
e
n
o
n
lin
earity o
r
d
e
r
for the th
i
r
d
b
r
an
ch
.
It is wo
rth no
ting th
at th
e th
ird
term
starts wit
h
non
lin
earity
o
r
d
e
r
to
av
o
i
d
r
e
dund
an
cy
w
ith
t
h
e
f
i
r
s
t an
d second
ter
m
s.
As m
o
d
e
rn
wireless syste
m
s u
tilize wid
e
r b
a
ndwid
t
h
s with
h
i
gh
er sp
eed, th
e d
e
si
g
n
for an
accurately DP
D m
odel m
u
st take i
n
to a
c
c
o
unt t
h
e lin
ea
r m
e
m
o
ry effe
cts and the
dynam
i
c nonline
a
rities.
Th
us, t
h
e
p
r
o
p
o
se
d p
r
edi
s
t
o
rt
er sh
o
w
n i
n
Fi
gu
re
2 has a
n
i
m
port
a
nt
pr
o
p
e
rt
y
,
w
h
i
c
h i
s
separat
i
n
g t
h
e
pu
rel
y
linear m
e
m
o
ry effects
(re
presente
d in the first
br
a
n
c
h
) f
r
om
t
h
e l
o
w-
or
de
r n
o
n
l
i
n
eari
t
y
dy
nam
i
c one
(co
n
si
de
re
d i
n
t
h
e secon
d
br
anch
) an
d fi
na
l
l
y
adds t
h
ese bra
n
c
h
es to the high-o
rd
er no
n
lin
earity
m
e
m
o
ry
effect
s bra
n
c
h
.
C
o
n
s
eq
ue
nt
l
y
,
t
h
e pr
op
ose
d
m
odel
pr
ovi
de
s
an
e
ffi
ci
ent
way
t
o
pre
s
ent
an
e
ffect
i
v
e
di
st
ort
i
o
n
com
p
ensation approach for powe
r
am
p
lifi
e
r lin
earization
.
M
o
reo
v
er, t
h
e pro
p
o
s
ed
m
o
d
e
l also
allo
ws for
m
o
re flexibilit
y in
m
odelling the
m
e
m
o
ry effects in
which the m
odel di
m
e
nsions of each branch are
co
n
t
ro
lled separately, wh
ich redu
ces th
e
m
o
d
e
l co
m
p
le
x
ity wh
ile en
han
c
ing
th
e linearity p
e
rforman
ce
of
PAs.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Efficien
t
Lo
w
Co
mp
lexity Di
g
ita
l Pred
isto
rt
io
n
f
o
r Po
wer
Amp
lifier Lin
e
a
r
iza
tion
(
S
iba Mon
t
h
e
r Yo
usif
)
1
099
Fi
gu
re 2.
B
a
si
c
arc
h
i
t
ect
ure of
t
h
e pr
o
pose
d
m
odel
2.
3.
Mo
del Ide
n
tifi
cati
on Pr
oced
ure
The
pr
op
ose
d
pre
d
i
s
t
o
rt
er ha
s t
h
e p
r
o
p
ert
y
of l
i
n
earity in
m
o
d
e
l p
a
ram
e
t
e
rs as sh
own
in
Equ
a
tion
(6),
wh
ich
m
ean
s that th
e m
o
d
e
l
ou
tpu
t
is
lin
ear
with
its
coefficients, si
nce it wa
s derived
from
Vol
t
erra-
seri
es m
odel
.
Hence
,
t
h
e c
o
e
ffi
ci
ent
s
of t
h
e
pr
op
ose
d
m
o
d
e
l
can be e
x
t
r
a
c
t
e
d i
n
a di
r
ect
way
usi
n
g t
h
e
l
east
squ
a
res
(LS
)
t
echni
que
. T
h
e
i
d
ent
i
f
i
cat
i
o
n
of t
h
e
pr
op
os
ed m
odel
i
s
an o
ffl
i
n
e p
r
oc
edu
r
e a
n
d
al
l
of t
h
e
bra
n
c
h
es
of
Eq
uat
i
o
n
(
6
)
are
i
d
ent
i
f
i
e
d si
m
u
l
t
a
neo
u
sl
y
as s
h
ow
n i
n
E
q
uat
i
o
n
(7
):
(7
)
whe
r
e the
vect
or i
s
t
h
e o
u
t
p
ut
of t
h
e t
h
ree
dy
nam
i
c branc
h
es base
d
on E
quat
i
o
n (
6
), t
h
e
m
a
trix
in
clu
d
e
s
t
h
e basi
s f
u
nc
t
i
ons o
f
t
h
e t
h
ree
p
o
l
y
nom
ial
bra
n
ches
, a
nd t
h
e
vector contains the
coefficients of the
pr
o
pose
d
m
o
d
e
l
.
The
vect
o
r
s
and
are de
fi
ned in E
q
uations (8) and
(9)
respectively,
where
N
i
s
th
e
in
p
u
t
sam
p
les len
g
t
h u
s
ed
for t
h
e iden
tificatio
n
:
(8
)
(9
)
Th
e m
a
trix
is an
alysed
i
n
to
su
b-m
a
tri
ces as sho
w
n i
n
E
qua
t
i
on
(1
0):
(1
0)
whe
r
e the s
u
b-matrices,
, are com
posed
from
the basis
f
unct
i
o
ns
of t
h
e l
i
n
ear m
e
m
o
ry
effects, low-ord
e
r non
lin
earity with
dy
nam
i
c effect
s, and
dy
nam
i
c
hi
g
h
-
o
r
d
e
r
n
o
n
l
i
n
eari
t
y
bra
n
che
s
,
respectively. T
h
e indi
rect learning ar
c
h
itecture is used for
extracting the
coefficients of
the propose
d
m
odel
as sh
o
w
n
i
n
Fi
gu
re
1.
Acc
o
r
d
i
ngl
y
,
a
ne
w se
que
nce i
s
de
fi
n
e
d i
n
E
quat
i
o
n
(1
1):
(1
1)
whe
r
e
i
s
t
h
e c
o
m
p
l
e
x base
ba
nd
i
n
put
si
gnal
of
t
h
e
pre
d
i
s
t
o
rt
er
du
ri
n
g
i
d
e
n
t
i
f
i
cat
i
on
pr
o
cess,
is the
com
p
l
e
x baseb
a
nd
out
put
si
g
n
al
of t
h
e P
A
,
and
is th
e g
a
in
o
f
th
e
line
a
rized PA. The vector
can
be
exp
r
esse
d i
n
E
quat
i
o
n
(
1
2
)
:
(1
2)
The s
u
b-m
a
trices
are e
x
p
r
esse
d i
n
E
quat
i
o
ns
(1
3)
,
(1
4)
, a
n
d
(1
5)
res
p
ect
i
v
e
l
y
:
(1
3)
(1
4)
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
. 3,
J
u
ne 2
0
1
6
:
10
9
6
– 11
05
1
100
(1
5)
Fin
a
lly, th
e co
efficien
ts of th
e p
r
op
o
s
ed
m
o
d
e
l in
Eq
uatio
n
(6
) can
b
e
d
e
term
in
ed u
s
ing
least-
squ
a
res s
o
l
u
t
i
on
fo
r E
quat
i
on
(7
) as s
h
o
w
n i
n
Eq
uat
i
o
n (
1
6
)
,
whe
r
e
(.
)
H
represent
s
com
p
lex conjugate
trans
p
ose:
(1
6)
3.
E
X
PERI
MEN
T
AL SETUP
To
d
e
m
o
n
s
trat
e th
e lin
earizatio
n
ab
ility o
f
t
h
e
p
r
o
p
o
s
ed
p
r
ed
isto
rter, m
easu
r
em
en
ts was p
e
rfo
rm
ed
usi
n
g t
h
e e
x
pe
ri
m
e
nt
al
set
up sh
ow
n i
n
Fi
g
u
re
3.
It
co
nsi
s
t
s
of a
pe
rso
n
al
com
put
er
(
P
C
)
,
Agi
l
e
nt
-
EX
G
v
ector
sign
al gen
e
r
a
t
o
r
N
5172
B, Ag
ilen
t
–
PXA
sign
al analyzer
N
9
0
30A
, ATM atten
u
a
tor
–
PN
R A
V
08
4-
30
, a
nd
PA
u
nde
r t
e
st
. T
h
e
PC
co
nt
ai
ns
t
h
ree s
o
ft
ware
,
w
h
i
c
h a
r
e A
g
i
l
e
nt
Sy
st
em
Vue
2
0
1
5
.
0
1
,
M
a
t
l
a
b
20
1
4
a, a
n
d
Ag
i
l
e
nt
89
6
0
0
V
S
A s
o
ft
ware
. T
h
e com
p
l
e
x i
n
p
u
t
ba
seba
n
d
si
gnal
was
ge
ner
a
t
e
d i
n
M
a
t
l
a
b
.
The
n
,
by
usi
ng
Sy
st
em
Vue sim
u
l
a
tor
,
t
h
i
s
si
g
n
al
was
do
w
n
loa
d
ed, t
h
rough L
o
cal Area
Netwo
r
k
(LAN), in
t
o
th
e
EXG i
n
or
de
r
t
o
exci
t
e
t
h
e PA u
n
d
er t
e
st
by
t
h
e R
F
i
nput
si
g
n
al
. T
h
en, t
h
e R
F
o
u
t
put
fr
om
t
h
e
po
we
r
a
m
p
lifier was
atten
u
a
ted
b
y
1
0
d
B
and
receiv
ed
b
y
th
e PXA. Th
is PXA was
u
tilized
to
d
o
wn
-con
vert and
dem
odulate the RF output si
gnal t
o
baseba
nd signal cooperating with
t
h
e VS
A
89600
soft
ware
. T
h
en, the
base
ban
d
i
n
put
and o
u
t
p
ut
w
a
vef
o
rm
s were
used t
o
ext
r
ac
t
t
h
e coeffi
ci
ent
s
of t
h
e
pre
d
i
s
t
o
rt
i
on
fu
nct
i
ons i
n
Matlab
.
After
th
at, syn
t
h
e
sizin
g
th
e pred
ist
o
rted
sig
n
a
l an
d
d
o
wn
lo
ad
in
g
th
is sign
al
in
to
th
e EXG were
carried out
usi
n
g System
Vue
soft
ware
.
The PA under test used
was
the HMC-C
0
74 si
ngle
stage class AB power am
p
lifier, fro
m
Hitt
it
e
M
i
crowa
v
e C
o
rp
orat
i
o
n,
w
h
i
c
h
pr
ovi
des
13
dB
g
a
i
n
a
n
d
2
9
.
5
dB
m
out
pu
t
po
wer
at
1
d
B
gai
n
c
o
m
p
ressi
o
n
and ca
n
ope
rat
e
fr
om
10 M
H
z t
o
6
GHz
. T
h
e P
A
was
o
p
e
r
ated at 2.14
GHz with a
n
inpu
t p
e
ak
pow
er
b
ack-
of
f o
f
1
dB
and t
e
st
ed
u
nde
r 5
-
M
H
z
ban
d
w
i
d
t
h
of a si
n
g
l
e
-car
ri
er
W
C
DM
A si
g
n
al
wi
t
h
pea
k
-t
o-
avera
g
e
p
o
w
e
r
r
a
tio (PA
P
R) of
8
.
7
dB and
th
e signal w
a
s sam
p
led at 25
M
H
z.
Fi
gu
re
3.
M
eas
urem
ent
set
u
p
use
d
f
o
r t
h
e
p
r
op
ose
d
DP
D
v
a
l
i
d
at
i
o
n
The c
o
m
p
l
e
x i
n
p
u
t
a
n
d
o
u
t
p
ut
base
ba
n
d
w
a
vef
o
rm
s, f
r
o
m
t
h
e real
P
A
,
co
nt
ai
ni
n
g
20
00
0 sam
p
l
e
s
were
utilized to e
x
tract the c
o
effi
cients of t
h
e MP m
odel
according to
Equation
(1) a
n
d the
proposed m
odel
base
d
on
Eq
u
a
t
i
on
(6
)
usi
n
g t
h
e
t
r
ai
ni
ng
pat
h
s
h
o
w
n i
n
Fi
gu
re
1.
T
h
e
di
m
e
nsi
ons
o
f
t
h
e
m
odel
s
we
re
appropriately selected to m
a
ke a
su
itab
l
e trad
e-off
b
e
tween
co
m
p
lex
ity and acc
uracy. The c
o
m
putational
com
p
lexity will be discuss
e
d in section
5
and t
h
e
m
odel accuracy
of t
h
e propose
d a
nd MP m
odels
were
eval
uat
e
d
usi
n
g t
h
e
n
o
r
m
a
li
zed m
ean sq
uar
e
d e
r
r
o
r
(
N
M
S
E) c
r
i
t
e
ri
o
n
,
w
h
i
c
h i
s
desc
ri
b
e
d i
n
E
quat
i
o
n
(1
7):
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8-8
7
0
8
Efficien
t
Lo
w
Co
mp
lexity Di
g
ita
l Pred
isto
rt
io
n
f
o
r Po
wer
Amp
lifier Lin
e
a
r
iza
tion
(
S
iba Mon
t
h
e
r Yo
usif
)
1
101
(1
7)
whe
r
e y
i
s
t
h
e desi
re
d o
u
t
p
ut
wave
f
o
rm
,
i
s
t
h
e m
easured o
u
t
p
ut
wa
vef
o
r
m
, and
N
i
s
t
h
e num
ber
o
f
sam
p
les u
tilized
in
t
h
ese
ou
tpu
t
wav
e
form
s.
The calculated
NMS
E
an
d m
odel
di
m
e
nsi
ons
of t
h
e
pr
o
pose
d
an
d M
P
m
odel
s
are l
i
s
t
e
d i
n
Tabl
e 1 a
s
well as th
e
NM
S
E
an
d m
odel
di
m
e
nsi
ons o
f
t
h
e
m
odel
pr
o
p
o
se
d i
n
[3]
.
Fr
om
Tabl
e 1, i
t
can be o
b
se
rve
d
t
h
a
t
t
h
e p
r
o
p
o
se
d
m
odel
has hi
g
h
er acc
u
r
acy
t
h
an
t
h
e acc
ur
acy
of t
h
e M
P
m
odel
by
2
.
1
dB
a
nd
sl
i
ght
l
y
com
p
arable ac
curacy
w
ith
resp
ect to
t
h
e
p
r
op
o
s
ed m
o
d
e
l in [3
].
Table 1
.
C
o
m
p
ari
s
o
n
of
m
odel
di
m
e
nsi
ons a
n
d
NM
S
E
of
di
ffe
rent
DP
D m
odel
s
4.
MEASUREMENT RESUL
T
S
In
order t
o
ass
e
ss the effectivene
ss of the
propos
ed
p
r
ed
isto
rter, th
e PA was lin
earized
u
s
i
n
g
t
h
e
w
e
ll-
kno
wn
M
P
m
o
d
e
l b
a
sed
on
Equ
a
tion (
1
)
w
ith
Q
=3
and
K
=7
,
an
d
t
h
e pr
oposed
m
o
d
e
l b
a
sed
on
Eq
uat
i
on
(6
)
w
i
t
h
M
= 3, L =
3,
K = 7
,
an
d
Q = 2
.
The m
easure
d
out
put
s
p
ect
ra
of t
h
e
p
o
we
r am
pl
i
f
i
e
r bef
o
re
and a
f
t
e
r a
ppl
y
i
ng t
h
e
p
r
o
p
o
s
e
d an
d M
P
DP
Ds are s
h
ow
n i
n
Fi
g
u
r
e 4 a
n
d
l
i
s
t
e
d i
n
Tabl
e
2 wi
t
h
t
h
e m
e
asure
d
resul
t
s
o
f
t
h
e DP
D m
odel
i
llust
rat
e
d i
n
[3]
.
B
e
fore a
ppl
y
i
ng
DP
D, t
h
e A
C
LR
of t
h
e PA
out
p
u
t
was -
4
0.
5 dB
c
wh
ile after app
l
yin
g
MP m
o
d
e
l, th
e co
m
p
en
sation
of
dy
n
a
m
i
c nonl
i
n
ea
r
i
t
y
was -51
.
3
dB
c. M
o
reo
v
e
r
, t
h
e
m
odel
prese
n
t
e
d i
n
[
3
]
an
d l
i
s
t
e
d i
n
Ta
bl
e
2
has m
o
re re
d
u
c
t
i
on i
n
AC
LR
t
h
an t
h
e M
P
m
odel
where
-
5
7
dB
c
was o
b
t
a
i
n
e
d
.
Ho
we
ver
,
f
u
rt
h
e
r AC
LR
i
m
provem
e
nt
can b
e
achi
e
ve
d w
h
en usi
ng t
h
e p
r
op
ose
d
m
odel
and t
h
e
ACLR p
e
rfo
r
man
ce was
-62
.
1
d
B
c. Therefore, th
e e
xperim
e
n
t
al resu
lts illu
strate a
b
e
tter lin
eari
zation
per
f
o
r
m
a
nce u
s
i
ng t
h
e
pr
o
p
o
s
ed m
odel
t
h
a
n
t
h
e
pe
rf
o
r
m
a
nce ac
hi
eve
d
by
t
h
e
M
P
m
odel
and t
h
e
m
odel
pr
o
pose
d
i
n
[3
]
by
1
0
.
8
dB
a
n
d
5
dB
,
res
p
e
c
t
i
v
el
y
.
Thi
s
a
c
hi
evem
ent
wa
s o
b
t
a
i
n
e
d
bec
a
use
of
a
d
d
r
es
si
ng
t
h
e
linear m
e
m
o
ry effects and se
parately com
p
ensating the ef
fect
s of t
h
e l
o
w-
or
de
r and t
h
e hi
gh
-o
r
d
er n
onl
i
n
ea
r
m
e
m
o
ry
effect
s i
n
t
h
e
pr
op
os
ed m
odel
.
Figure
4. Meas
ure
d
s
p
ectra
of the PA
with
5-MHz
W
C
DM
A sign
al ex
citatio
n
.
(a)
W
i
t
h
ou
t DPD (b
)
W
i
th
MP
m
odel
(K=
7 a
n
d
Q=
3)
.
(c)
W
i
t
h
pr
o
pose
d
m
odel
(M
=3,
L=3,
K=
7
,
a
n
d
Q=2
)
Tabl
e 2.
C
o
m
p
ari
s
on
o
f
AC
LR
pe
rf
orm
a
nce o
f
t
h
e
P
A
DPD
m
odel
M
odel dim
e
nsions
NM
SE (
d
B)
MP [
2
]
(
K
,
Q
)
= (7
,3
)
-3
4
.
7
DPD m
odel
[
3
]
(
K
odd or
de
r
,
Q
)
=
(
11,
3)
-
37.
1
Pr
oposed m
odel
(
M
)(
L
)(
K
,
Q
) =
(3
)
(
3
)(7
,2
)
-3
6
.
8
DPD m
odel
ACLR (dBc)
-5
M
H
z
+5
MHz
W
ithout DPD
-
40.
5
-
41
M
P
m
odel
[2]
-
51.
3
-
50.
5
DPD m
odel
[3]
-
57
-
56
Pr
oposed m
odel
-
62.
1
-
61
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I
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:
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088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
10
9
6
– 11
05
1
102
To furt
her
de
m
onstrate the effective
n
ess
of
th
e p
r
op
osed
pr
ed
isto
r
t
er, dy
nam
i
c
AM/AM and
AM/PM ch
aracteristics o
f
the p
o
wer am
p
lifier, dr
ive
n
by a single-ca
rrier
W
C
DMA sig
n
a
l with
5-MHz
ban
d
w
i
d
t
h
, be
f
o
re an
d aft
e
r a
ppl
y
i
n
g
t
h
e pr
op
ose
d
an
d M
P
pre
d
i
s
t
o
rt
e
r
s are sh
ow
n i
n
F
i
gu
re 5 an
d Fi
gu
re 6
,
respectively.
From
these figures, the dis
p
ersions a
n
d
bending
of the PA cha
r
acteristi
cs are s
h
own
before
ap
p
l
ying
th
e
propo
sed
and
M
P
m
o
d
e
ls d
u
e
t
o
th
e electri
cal
m
e
m
o
ry effects an
d
no
n
lin
earities, resp
ectiv
ely.
Fi
gu
re
5 s
h
o
w
s
t
h
at
t
h
e di
s
p
er
si
ons
wi
t
h
be
n
d
i
n
g o
f
t
h
e
actual PA cha
r
act
eristics are bett
er com
p
ensate
d afte
r
ap
p
l
ying
th
e
pro
p
o
s
ed
m
o
d
e
l th
an
t
h
e MP mo
d
e
l.
Wh
ile
, Fi
g
u
re
6
,
illu
strates th
at th
e linearizatio
n
cap
a
b
ility
on the
dy
nam
i
c AM/PM c
h
a
r
acteristics of t
h
e
real PA
of
bot
h t
h
e M
P
a
n
d
pr
op
ose
d
p
r
edi
s
t
o
rt
ers
i
s
m
a
i
n
l
y
th
e sam
e
.
Figure
5. Dy
na
mic AM/AM characteristics
of th
e
real PA
drive
n
by 5-MHz
W
C
DMA si
gnal
Figure
6. Dy
na
mic AM/PM characteristics
of th
e
real PA
drive
n
by 5-MHz
W
C
DMA si
gnal
5.
CO
MP
UTAT
ION
A
L CO
M
P
LE
X
I
TY A
N
A
LYS
I
S
To
ev
alu
a
te t
h
e propo
sed pred
isto
rter in term
s o
f
co
m
p
u
t
atio
n
a
l co
m
p
le
x
ity redu
ction
,
th
e m
o
d
e
l
co
m
p
lex
ity o
f
th
e propo
sed
alg
o
rith
m
is d
e
t
e
rm
in
ed
an
d
co
m
p
ared
with
th
e co
m
p
u
t
ation
a
l co
m
p
lex
ity o
f
bot
h t
h
e M
P
m
odel
[2]
and
t
h
e DPD m
odel
prese
n
t
e
d
i
n
[3]
.
I
n
[1
8
]
, i
t
has been
dem
onst
r
at
ed
t
h
at
co
nsid
eri
n
g even
o
r
d
e
r
n
o
n
lin
earities
g
i
v
e
a b
e
tter m
o
d
e
l p
e
rfo
r
m
a
n
ce
th
an u
s
i
n
g
o
n
l
y o
dd order term
s.
Th
erefo
r
e,
b
o
t
h
ev
en an
d od
d ord
e
rs of
n
o
n
lin
ear
ities in
th
e propo
sed
m
o
d
e
l are con
s
id
ered
i
n
th
i
s
com
p
arison.
The c
o
m
p
l
e
xi
t
y
of t
h
e
DP
D
m
odel
s
i
s
eval
uat
e
d
base
d
o
n
t
h
e
num
ber
o
f
fl
oat
i
n
g
-
poi
n
t
ope
rat
i
o
ns
(FL
O
Ps
) and the num
b
er of
m
odel coefficients, as in
[14],[19]. FLOPs
are an actual
m
easure for
m
odel
co
m
p
lex
ity
th
at g
i
v
e
s th
e n
u
m
b
er o
f
su
b
t
ractio
n
s
, ad
d
ition
s
, and
m
u
ltip
l
i
catio
n
s
u
s
ed
wh
en
th
e ou
tpu
t
o
f
the
DPD
m
odel
is calculated. As explai
ne
d in
[19], the
num
b
er of FL
OPs
re
quire
d
in each
DPD m
odel include
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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ECE
I
S
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:
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8-8
7
0
8
Efficien
t
Lo
w
Co
mp
lexity Di
g
ita
l Pred
isto
rt
io
n
f
o
r Po
wer
Amp
lifier Lin
e
a
r
iza
tion
(
S
iba Mon
t
h
e
r Yo
usif
)
1
103
FLOPs du
ring
th
e co
n
s
t
r
u
c
tion
o
f
th
e
b
a
sis fun
c
tion
s
and
FLOPs when
th
ese b
a
sis functio
n
s
are filtered
by
the m
odel coe
f
ficients.
The
num
ber
of
FLOP
s an
d m
odel
c
o
ef
fi
ci
en
t
s
of t
h
e M
P
,
DP
D m
odel
pr
esent
e
d i
n
[
3
]
,
and
p
r
o
p
o
se
d
m
odel
are re
po
rt
ed i
n
Ta
bl
e 3
.
T
h
e M
P
m
o
d
e
l
has e
q
ua
l non
lin
earity order in
all
o
f
th
e
me
m
o
ry b
r
an
ch
es and
M
P
di
m
e
nsi
o
n
s
were
set
t
o
7
and
3
f
o
r
K a
nd
Q,
res
p
ectiv
ely. Con
s
eq
uen
tly, th
is results in
2
4
4
FLOPs and
28 c
o
e
fficients
according to
Equation
(1).
Conversely, the use of three
dynam
i
c branc
h
es in the
propos
ed
p
r
ed
istorter m
a
k
e
s it p
o
ssi
b
l
e to
redu
ce th
e
me
m
o
ry d
e
p
t
h
o
f
th
e th
ird
bran
ch
to
b
e
app
lied
with
flex
ib
i
lity
in
t
h
e ot
he
r t
w
o
bra
n
c
h
es as sh
ow
n i
n
Fi
gu
re 2. Acc
o
rdi
ngl
y
,
t
h
e di
m
e
nsi
ons o
f
t
h
e p
r
o
p
o
se
d pre
d
i
s
t
o
rt
er wer
e
set
t
o
3
,
3,
7,
an
d 2
f
o
r
M
,
L,
K st
art
e
d
fr
om
3, an
d
Q,
res
p
ect
i
v
el
y
.
Th
us, t
h
e F
L
OPs
an
d
nu
m
b
er o
f
coef
fi
ci
ent
s
are
red
u
ce
d t
o
20
4 an
d
23
, res
p
e
c
t
i
v
el
y
,
based
on
Eq
uat
i
o
n (
6
). T
h
ere
f
o
r
e, as
sho
w
n i
n
Ta
bl
e 3, i
t
can be co
ncl
u
d
e
d t
h
at
t
h
e pr
o
pos
ed m
odel
h
a
s com
put
at
i
o
n
a
l
co
m
p
l
e
xi
t
y
reduct
i
o
n o
f
ap
pr
o
x
i
m
at
el
y 17
% i
n
term
s o
f
FLOPs and
18
% in term
s o
f
m
o
d
e
l d
i
m
e
n
s
io
n
s
with
resp
ect t
o
th
e MP m
o
d
e
l. Th
ese co
m
p
lex
ity
reduction re
sul
t
s were
achie
ved
because the
MP m
odel
is
an
ove
rsized
m
odel since it uses
the sam
e
high
n
o
n
lin
ear
ity o
r
d
e
r
i
n
all o
f
t
h
e
m
e
m
o
r
y
b
r
an
ch
es. In
the
D
P
D
m
o
d
e
l with
sin
g
l
e-
f
e
edb
ack, 11
th odd-
or
d
e
r
no
nl
i
n
ea
ri
t
y
and m
e
m
o
ry
dept
h o
f
t
h
ree we
re
em
pl
oy
ed, as
rep
o
rt
e
d
i
n
[3]
.
Hence
,
t
h
e
nu
m
b
er of FL
OP
s a
n
d
coef
fi
ci
ent
s
a
r
e
sl
i
ght
l
y
i
n
c
r
ea
sed t
o
21
0 a
n
d
24
,
resp
ectivel
y, as c
o
m
p
ared with
t
h
e pr
o
p
o
s
ed
m
odel
.
Tabl
e
3. C
o
m
p
ari
s
o
n
of
D
P
D
m
odel
s
’ com
put
at
i
onal
c
o
m
p
l
e
xi
t
y
and
n
u
m
b
er
o
f
c
o
ef
fi
ci
ent
s
In s
u
m
m
ary
,
the p
r
op
ose
d
m
odel
out
pe
rf
orm
s
bot
h t
h
e
DP
D m
odel
prese
n
t
e
d i
n
[
3
]
i
n
t
e
rm
s of
AC
LR
per
f
o
r
m
ance by
5 d
B
wi
t
h
a com
p
ara
b
l
e
com
put
at
i
onal
com
p
l
e
xi
t
y
and M
P
m
odel
i
n
t
e
rm
s of
l
i
n
eari
t
y
perf
o
r
m
a
nce by
10.
8 dB
wi
t
h
a com
p
l
e
xi
t
y
reduct
i
on
of al
m
o
st
17% i
n
t
h
e
FLOP
s as wel
l
as a
reduction of
18% in the num
ber of
m
ode
l coefficien
ts.
These res
u
lts dem
onstrates that a high linearity
per
f
o
r
m
a
nce w
a
s achi
e
ve
d
w
h
i
l
e
t
h
e com
p
u
t
at
i
onal
com
p
l
e
xi
t
y
of t
h
e p
r
op
ose
d
DP
D
m
odel
was m
i
ni
m
i
zed.
Co
n
s
equ
e
n
tly, th
ese im
p
r
ove
m
e
n
t
s will lead
t
o
redu
ctio
n in transm
i
tter po
wer con
s
u
m
p
tio
n and
also
red
u
ct
i
o
n i
n
ha
rd
ware
res
o
urc
e
s re
qui
red
f
o
r
DP
D i
m
pl
em
ent
a
t
i
on.
6.
CO
NCL
USI
O
N
In
th
is
p
a
p
e
r, a DPD m
o
del with
lo
w-co
m
p
lex
i
t
y
was pr
op
ose
d
f
o
r
l
i
n
eari
zat
i
on
of P
A
s. T
h
e
pr
o
pose
d
m
odel
co
nsi
s
t
s
of
t
h
ree
pa
ral
l
e
l
dy
nam
i
c bran
c
h
es
usi
n
g
a l
i
near
m
e
m
o
ry
effect
s,
a l
o
w
-
or
der
no
nl
i
n
ea
ri
t
y
m
e
m
o
ry
effec
t
s, and a
hi
g
h
-
o
r
d
e
r
non
linearity
m
e
m
o
ry effects fu
nctio
n
s
. Th
e lin
earity
per
f
o
r
m
a
nce of
t
h
e
pr
op
ose
d
m
odel
was val
i
dat
e
d
usi
n
g a
class AB
p
o
wer
a
m
p
lifier driv
en
b
y
a sing
le-carrier
WCDM
A si
gnal and c
o
m
p
ared to the
MP m
odel as
well as th
e DPD with sing
le-feed
b
a
ck m
o
d
e
l. The
expe
ri
m
e
nt
al
r
e
sul
t
s
cl
earl
y
il
l
u
st
rat
e
d t
h
at
t
h
e pr
o
pose
d
m
odel
had a b
e
t
t
e
r perf
orm
a
nce t
h
an t
h
e p
r
evi
ous
m
odel
s
i
n
red
u
c
i
ng t
h
e
AC
L
R
by
10
.8
dB
a
nd
5
d
B
,
res
p
ec
t
i
v
el
y
.
M
o
reo
v
e
r, t
h
e c
o
m
put
at
i
onal
com
p
l
e
xi
t
y
of
t
h
e p
r
o
p
o
se
d
m
odel
was re
d
u
ced
by
17
%
and
1
8
% i
n
t
e
rm
s of FL
OPs
and num
b
er of m
odel coeffi
cients,
resp
ectiv
ely, as co
m
p
ared to th
e co
m
p
lex
ity o
f
th
e
M
P
m
odel
.
The e
n
hance
d
pe
rf
or
m
a
nce an
d c
o
m
p
l
e
xi
ty
redu
ction
o
f
th
e p
r
op
osed
pred
istort
er are
expected to im
prove t
h
e
PA
e
fficiency
a
n
d re
duce t
h
e
overall
p
o
wer co
n
s
u
m
p
tio
n in
t
r
an
sm
itters, resp
ectively.
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DPD
m
odel
Nu
m
b
er
of
m
odel
coefficients
No.
of FL
OPs
MP [
2
]
K (
Q
+
1)
= 28
10 + 2(
K
-1
) + 8
K
(
Q
+1)
- 2 = 244
DPD m
odel
[
3
]
K
odd or
de
r
(Q
+
1)
= 2
4
10 + 2(
K
-1
) + 8
K
(
Q
+1)
- 2 = 210
Pr
oposed m
odel
(
M+
1)
+(
L+
1)
+(
K
-2)
(
Q
+1)
= 23
10 + 2(
K
-1
) + 8
[
(
M
+1) +
(
L
+1)+
(
K
-2
)(
Q
+1)]
-
2
= 204
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
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. 3,
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u
ne 2
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9
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05
1
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A
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nom
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k
adem
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.
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aiza S
., “
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hy
s
i
c
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ll
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ired neur
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plifier behavior
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n,”
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E
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E
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ans
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h
eor
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ech
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[10]
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w
am
inathan J
.
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a
r P
.
, “
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ign of Efficien
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r
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a
r High P
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wer Am
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[11]
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Ghannouchi F.
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odel for
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ensat
i
on of tr
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itters radio fr
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im
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r
ans
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h
eor
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ech
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unct
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[19]
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BIOGRAP
HI
ES OF
AUTH
ORS
Siba Monther
Yousif receiv
ed B
.
Sc. d
e
gree
in Electronic and
Co
mmunication En
gineer
ing
and M.Sc. degr
ee in Electronic Engineering fr
om
the University
of Technolog
y
,
Ir
aq, in
1992 and 2007, respectiv
ely
.
S
h
e has 12
y
e
ars
of experien
ce in designing and
developin
g
ele
c
troni
c c
i
rcui
ts
for wirel
e
s
s
com
m
unication
s
y
s
t
em
s
.
S
h
e j
o
ined th
e Depa
rtm
e
nt o
f
Electronic and
Communication Engineering in
Al-N
ahrain Uni
v
ers
i
t
y
, Ir
aq, as
an as
s
i
s
t
ant
lecturer in 2007
. She is curr
ently
a Ph.D.
cand
i
date in th
e Department of Electrical
and
Ele
c
troni
c Eng
i
neering
in Univ
ersit
y
Putr
a Ma
la
y
s
ia
(UPM), Mala
y
s
ia
. She
i
s
an IEIC
E
m
e
m
b
er and a
c
ons
ultant m
e
m
b
er of Ir
aqi Eng
i
n
eers
Union.
Her
res
earch
int
e
res
t
s
are in
the
areas
o
f
l
i
ne
ariz
ation
of power
a
m
plifiers
and
wi
reles
s
com
m
unic
a
tion
s
y
s
t
em
s
.
Roslina Mohd
Sidek receiv
ed
B.Sc. d
e
gree in
Electrical Eng
i
neering
from the George
Washington University
, Washin
gton D.C, USA in 1990
. She
received M
.
Sc.
degree in
M
i
croel
ectron
i
cs
S
y
s
t
em
s
Des
i
g
n
and P
h
.D.
deg
r
ee
in M
i
cro
e
le
c
t
ronics
from
Univers
i
t
y
of
Southampton, U
K
. She joined U
n
iversiti Putra
Malay
s
ia (UPM) as a
le
cturer in
1999. She
is
current
l
y
an
as
s
o
cia
t
e prof
es
s
o
r in the Dep
a
rtm
e
nt of Electrical
and
Electronic Engineer
ing,
UPM. Her research in
terests
an
d
her pub
lications
are in
the
areas of semiconductor devices
and fabr
ication
,
integr
ated
circuit (IC) d
e
sign
an
d tes
t
, and
nano
ele
c
troni
cs
. S
h
e
is
an I
E
E
E
member and has
joined
IEEE
Electron Dev
i
ce
s
S
o
cie
t
y and
IE
EE
Circuits
and S
y
s
t
em
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Efficien
t
Lo
w
Co
mp
lexity Di
g
ita
l Pred
isto
rt
io
n
f
o
r Po
wer
Amp
lifier Lin
e
a
r
iza
tion
(
S
iba Mon
t
h
e
r Yo
usif
)
1
105
Anwer Sabah Mekki receiv
e
d B.Sc. degree in
Electron
i
c and Co
mmunication En
gineer
ing
from University
of Technolog
y (U.O.T)
,
Bagh
da
d, Ir
aq in 19
92. He worked
in private
sectors in designing electronic circu
its for
wire
le
ss c
ontrol sy
ste
m
s,
ma
inte
na
nc
e
of
com
puter num
erica
l
control m
achin
es
CN
C a
nd designing infrared sensors for radar
applications. He was the h
ead
of mainten
a
nc
e
department of I
CCB/
Iraqi Cons
ultants
and
Construction Bu
reau
in 2004
. Then, h
e
was
the head
of Electr
onic
and Communication
Department of
Alardh Alkhadr
aa Compan
y
in 2
009.
He is
currently
a Ph.D.
can
didate in
the
Institute of Adv
a
nced
Technolo
g
y
in Universi
t
y
Putra Mal
a
y
s
ia
(UPM), Malay
s
i
a
. He
is an
IEICE member and a consultant
member of Iraqi
Engineers Union. He is interested
in sensor
circu
its
,
m
i
cros
tr
ip t
echniqu
es
,
an
d wirel
e
s
s
com
m
unica
tion s
y
s
t
em
s
.
Nasri Sulaiman received B.Eng. degree from Un
iversity
of Putra Malay
s
ia in 1
994, M.Sc.
degree from University
of
South
a
mpton, UK in
1999, and
Ph.D. degree from Un
iversity
of
Edinburgh, UK in 2007. He h
a
s more than 1
10 journal and
conference papers. He is
current
l
y
a s
e
ni
or lectur
er in th
e Departm
e
nt o
f
Elec
tric
al and
Elec
tronic
Eng
i
neer
ing at
Universit
y
Putra
Mala
y
s
ia
, UPM. His research
in
terests ar
e in th
e
areas of signa
l
processing
and Evolvab
l
e
Hardware (EH
W
). Also, he is
the head of con
t
rol and automation laborato
r
y
as well
as an
e
xpert superv
isor of proj
ects
at I
r
anian
Institu
te
of Advanced
Sc
ienc
e an
d
Techno
log
y
,
S
h
iraz,
Iran
.
P
ooria Varahra
m
received B
.
S
c
. degre
e
in E
l
e
c
t
ric
a
l and
Ele
c
tr
onics
Engine
eri
ng from
the
Khaje Nasir Un
iversity
, Teh
r
an, Iran in 2002
.
He received M
.
Sc. an
d Ph.D.
degrees in
W
i
reless Comm
unications fro
m
Tarbiat Mo
dare
s, Tehran
,
Iran, and Univ
ersity
Putra
Malay
s
ia, in 20
05 and 2010, r
e
spectively
.
He w
a
s a postdoctor
a
l fellow in Univ
ersity
Putra
Malay
s
ia
till Jul
y
2012
. He was senior lecturer
at Universi
t
y
Putra Mal
a
y
s
ia fro
m
2013 to
2015. He
is currentl
y
a sen
i
or postdoctor
a
l
resear
cher
at
Callan
Institu
te, May
noo
th
Universit
y
, Ire
la
nd. He is a m
e
m
b
er of IEEE since 2010. He has m
o
re than
10
y
ears o
f
experience in designing and dev
e
loping a r
a
nge
of elec
troni
c and
tele
com
m
unicat
ion rela
ted
projec
ts
. His
r
e
s
earch
inter
e
s
t
s
are
P
A
P
R
reduction
in OF
DM
s
y
s
t
em
s
,
L
i
n
eari
zat
ion of
power am
plifi
e
rs
, and
m
i
crow
av
e power
amplifier
design.
Evaluation Warning : The document was created with Spire.PDF for Python.