TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 8, August 201
4, pp. 6217 ~ 6223
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.562
8
6217
Re
cei
v
ed
Jan
uary 14, 201
4
;
Revi
sed Ma
rch 2
0
, 2014;
Acce
pted April 10, 2014
QR-bas
ed Channel Estimation for Orthogonal
Frequency Division Multiplexin
g
Systems
Peilong Jiang, Honggui
Deng*,
Bin Lei
Dep
a
rtment of Electron
ic Scie
nce an
d
T
e
chnolo
g
y
, C
entral
South Un
iversit
y
,
Lush
an R
oad,
410
08
3 Cha
n
g
s
ha, Chi
na, +
86-07
31-8
8
8
3
6
4
4
3
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: deng
ho
ngg
ui
@16
3
.com
A
b
st
r
a
ct
Cha
nne
l esti
mation is th
e k
e
y techn
o
lo
gy
for Orthogon
al F
r
equ
ency
Divisi
on Mu
ltiplex
i
n
g
(OF
D
M), w
h
ich h
a
s
direct
i
m
p
a
ct o
n
th
e
perfor
m
a
n
ce
o
f
OF
DM. In thi
s
pa
per, w
e
pr
esent
a
nove
l
QR-
base
d
a
l
g
o
rith
m to
up
date
th
e ch
ann
el
i
m
p
u
lse r
e
sp
onse
(CIR) for DF
T
-
base
d
ch
an
nel
esti
matio
n
. T
h
e
discrete F
our
ie
r transform (D
F
T
)
estimatio
n
reduces th
e
n
o
ise p
o
w
e
r tha
t
exists outside
of the CIR pa
rt,
beca
u
se the
e
s
timate
d CIR from
LS has
mo
st of its pow
er
conce
n
trated o
n
the first L sam
p
les. To reduce
the nois
e
pow
e
r
that exists inside of
the first L sampl
e
s, the CIR is fu
rther p
r
ocesse
d by QR deco
m
positi
o
n
in propos
ed
algorithm
. The
simulati
on r
e
s
u
lts show that
the bit-err
o
r-rate(BER) of our estim
a
tor has
reduc
ed
sig
n
if
icantly
co
mp
a
r
ed w
i
th
the
conve
n
tio
nal
DF
T
-
based
ch
ann
el
esti
mat
o
r a
n
d
LS-l
in
ear
estimation.
Ke
y
w
ords
: OF
DM, chann
el e
s
timati
on, QR
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
OFDM i
s
an
efficient tech
nique for hi
g
h
data rate wirele
ss
comm
unication sy
stem due
to its stron
g
anti-inte
rfere
n
ce
cap
abilit
y, high spe
c
t
r
um efficie
n
cy and rob
u
st
ness to freq
u
ency
sele
ctive fad
i
ng chan
nel
[1-2]. In the si
ngl
e
carri
er tran
sm
issi
on
syste
m
, the ada
ptive
equali
z
ation
is ap
plied to
e
liminate inte
r-symbol in
te
rf
eren
ce
(ISI), whi
c
h in
crea
ses the
difficul
t
y
of receiver d
e
sig
n
for the
compl
e
xity of the
equali
z
e
r
and the al
go
rithm structu
r
e. Ho
wever, t
he
ISI cause
d
by
multipath pro
pagatio
n ca
n
be effectivel
y redu
ce
d by inse
rting
cy
cli
c
prefix (CP)
in
the OFDM
system. Being
one of the most su
itabl
e tran
smissi
on tech
nolo
g
y
of broadb
a
n
d
comm
uni
cati
on, OFDM
h
a
s be
en ad
o
p
ted as a
st
a
ndard for digi
tal audio b
r
o
adcastin
g
(DAB),
Digital Vide
o Broad
ca
sting
-
Te
rre
strial
(DVB-T
)
,
wirel
e
ss LAN
(80
2
.11), wi
rele
ss WA
N (8
02.
16)
[3] and so
on sin
c
e the
1980
s. Furt
herm
o
re,
with the develo
p
ment of mo
dern
digital signal
pro
c
e
ssi
ng t
e
ch
nolo
g
y, OFDM
ha
s become a
n
efficient mod
u
lation sch
e
m
e for the f
ourth
-
gene
ration
(4
G) wi
rele
ss mobile commu
nicatio
n
s.
Cha
nnel
esti
mation is an
importa
nt issue for
OFDM
system. Sin
c
e the commu
nicatio
n
data di
strib
u
tes i
n
fre
que
n
c
y dom
ain
an
d time d
o
mai
n
, the
cha
n
n
e
l e
s
timation
is
carrie
d out
in
freque
ncy do
main
a
nd
tim
e
dom
ain as well.
Th
e
tim
e
-do
m
ain
-
ba
sed cha
nnel e
s
timation obt
ains
CIR by pro
c
e
ssi
ng the
time-domai
n data, t
hen tran
sform
s
it to cha
nnel freq
ue
ncy
response(CF
R
) utilizing
D
FT. Channel
estimation
in frequency domain
for OFDM system
s
i
s
often ca
rri
ed
out by usi
ng
pilots, which
are
som
e
kno
w
n
seq
uen
ce
s. As
sho
w
n i
n
Figu
re 1, th
ere
are
two
cl
assical
pilot p
a
ttern
s,
whi
c
h
a
r
e th
e bl
ock-t
y
pe patte
rn
b
y
inse
rting
pil
o
t tone
s into
all
of the su
bcarriers of O
F
DM sy
mbol
s a
nd the
com
b
-type pattern
by inse
rting
pilot tone
s i
n
to
each OF
DM
symbol
s. The
forme
r
on
e i
s
susce
p
ti
ble
to fast fadin
g
ch
ann
el, the later
one
i
s
robu
st to freq
uen
cy sele
cti
v
e fading env
ironm
ent.
The LS
-ba
s
e
d
algo
rithm,
as the
sim
p
l
e
st
chan
nel
estimation
m
e
thod in
freq
uen
cy, is
su
sceptible t
o
Ga
ussia
n
noise d
r
ama
t
ically [4-5].
While
the m
i
nimum m
e
a
n
-squa
re
error
(MMSE) e
s
ti
mator
sho
w
s
good p
e
rfo
r
m
ance [6], it
require
s
kno
w
l
edge of t
he chann
el
statist
i
cs
and the
signa
l-to-n
oise rati
o (SNR), whi
c
h inevit
ably i
n
crea
se
s co
mputational
complexity. Some
studie
s
tu
rne
d
to L
MMS
E [7] and
SVD [8] de
comp
ositio
n
to re
duce th
e computatio
nal
compl
e
xity, Zhou
W a
nd L
a
m WH
red
u
c
e
com
p
lexity by usi
ng the
fast Fo
urie
r t
r
an
sform
(F
F
T
)
operation [9], howeve
r
th
e com
putatio
nal co
mple
xit
y
remain
s hig
h
. As [10] sh
owe
d
, the DF
T-
based e
s
tima
tor improves
CIR availa
bly from the LS
estimato
r by limiting the nu
mber of
cha
n
nel
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 621
7 –
6223
6218
taps in time
domain. Th
e perfo
rma
n
c
e is im
proved by de
cidi
ng sig
n
ifica
n
t
chann
el ta
ps
adaptively wit
hout info
rmat
ion on th
e
ch
annel
statis
ti
cs i
n
[11]. Neverthele
s
s,
all the meth
o
d
s
above only d
eal with noi
se
outside of
L
taps, noise insid
e
of
L
taps is ign
o
re
d.
Figure 1. Pilot Sub-ca
rri
er
Arran
gem
ent: Block-type (a
) and Comb
-type (b)
In this pape
r, we propo
se a
novel QR-ba
s
ed [
12] algo
rithm to reduce the noise in
side of
L
taps.
In order
to avoid high com
put
ational co
m
p
lexity, we ch
oose the
LS estimato
r, the
n
redu
ce th
e n
o
ise
outsi
de
of
L
taps
by DFT e
s
timat
o
r, finally up
date CI
R by
pro
c
e
ssi
ng d
a
ta
matrix in tim
e
do
main
by QR de
co
mp
osition.
The
results of
co
mputer si
mul
a
tions sho
w
the
prop
osed alg
o
rithm a
c
hiev
es lo
wer BER and better
co
mmuni
cation
perfo
rman
ce.
2. Sy
stem Model
Figure 2. Baseban
d Model
of a Typical
OFDM Syste
m
Figure 2
sho
w
s a
typical b
l
ock
dia
g
ra
m of
OF
DM
system with pilot
sign
al a
ssi
st
ed. The
binary info
rm
ation data a
r
e gro
upe
d an
d mapp
ed in
t
o
multi-am
plitude-multi-p
h
a
s
e
signal
s. After
comb
-type
pi
lot insertion,
the mo
dula
t
ed data
X(k)
a
r
e
se
nt to an
IDFT
block
and
a
r
e
multiplexed into
x(n
)
.
)}
(
{
)
(
k
X
IDFT
n
x
,
1
0
,
)
2
exp(
)
(
1
1
0
N
n
N
nk
j
k
X
N
N
k
(1)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
QR-ba
s
ed
Ch
annel Estim
a
tion for Orth
og
onal Frequ
en
cy
Divi
sio
n
Multiplexi
ng… (Peilong Ji
ang
)
6219
Assu
ming th
e numb
e
r of
sub
c
a
rri
ers is
N
. In orde
r to avoid ISI and co
nsequ
e
n
t inter-
carrie
r inte
rfe
r
en
ce
(ICI), a
CP is
appe
nd
ed to
the O
F
DM
symbol.
Assu
ming th
e
length of
CP
Ng
is gre
a
ter tha
n
maximum time delay, then the ISI is removed.
1
,
,
1
,
0
),
(
1
,
,
1
,
),
(
)
(
N
n
n
x
N
N
n
n
N
x
n
x
g
g
g
g
(2)
After passin
g
throug
h a m
u
ltipath chan
nel
, one
re
ce
ived discrete-time domai
n
OFDM
sign
al
y
g
(n
)
is represented
by:
)
(
)
(
)
(
)
(
n
w
n
h
n
x
n
y
g
g
(3)
W
h
er
e
⨂
d
e
notes cy
clic
convolutio
n
op
eration,
w(n
)
is Additive White Gaussia
n
Noise
(AWG
N) and
h(n
)
is CI
R. It can be
rep
r
e
s
ente
d
by:
1
0
)
(
)
2
exp(
)
(
i
i
D
i
r
N
n
T
f
j
h
n
h
i
,
1
0
N
n
(4)
Whe
r
e
τ
is th
e total numb
e
r of tra
n
smit paths,
hi
i
s
the co
mplex i
m
pulse respo
n
se
of
the
i
th path, ƒ
Di
is the ith
path Doppler frequency
shift,
λ
is the delay sp
rea
d
index, and
r
i
is
the
i
th path delay time normalize
d
by sa
mpling time
. Removin
g
the CP in the re
ceiving
side:
1
0
),
(
)
(
N
n
N
n
y
n
y
g
g
(5)
Then
y(
n)
is
sent to DFT bl
ock for the fol
l
owin
g ope
rat
i
on:
)}
(
{
)
(
n
y
DFT
k
Y
1
0
,
)
2
exp(
)
(
1
1
0
N
n
N
nk
j
n
y
N
N
k
(6)
Assuming there i
s
no ISI, I is the ICI
caus
ed by
Doppler frequency
shift, the system
freque
ncy
-
do
main mod
e
l is rep
r
e
s
e
n
ted
by:
1
0
),
(
)
(
)
(
)
(
)
(
N
k
k
W
k
I
k
H
k
X
k
Y
(7)
Whe
r
e:
)
2
exp(
)
)
sin(
2
exp(
)
(
1
0
k
N
r
j
T
f
T
f
T
f
j
h
k
H
i
i
D
D
D
i
i
i
i
(8)
)
2
exp(
)
(
1
)
(
1
0
1
,
0
K
N
r
j
S
K
X
h
N
k
I
i
i
N
k
K
K
i
)]
(
2
exp[
1
)]
(
2
exp[
1
K
k
T
f
N
j
K
k
T
f
j
S
i
i
D
D
(9)
The pilot si
g
nal
Y(p)
is e
x
tracted from
receiving si
g
nals, an
d the
CFR
)
(
~
p
H
for pilot
sub
-
chan
nel
s by LS estimator is:
)
(
)
(
)
(
~
p
X
p
Y
p
H
(10)
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 621
7 –
6223
6220
W
h
er
e
p
i
s
th
e ind
e
x of
pil
o
t su
b-ch
ann
els. T
he
CF
R for
data
su
b-cha
nnel
s i
s
o
b
tained
by interpolati
on.
3. QR-b
ase
d Chan
nel Esti
mation
Figure 3 gives a block dia
g
ra
m of DF
T-based e
s
tima
tor. Since the
estimated CI
R from
LS has mo
st of its power
con
c
e
n
trate
d
on the first
L
samples,
the DFT-ba
sed e
s
timati
on
redu
ce
s the n
o
ise p
o
wer th
at exists outsi
de of the CIR part.
The CF
R
)
(
~
k
H
LS
obtained fro
m
L
S
-ba
s
ed e
s
ti
mator is
sent
to IDFT:
T
N
LS
LS
h
h
h
n
w
n
h
k
H
IDFT
n
h
]
,
,
,
,
[
)}
(
~
)
(
)
(
~
{
)
(
~
1
1
0
(11)
A
ssu
ming
L
i
s
less than
Ng
, the CIR in tradition
al app
roa
c
h is:
L
n
k
H
IDFT
n
h
LS
0
)},
(
~
{
)
(
(12)
Figure 3. Block
Diag
ram o
f
the DFT-b
a
sed Ch
ann
el Estimation
By using Equ
a
tion (11
)
an
d Equation (1
2), CIR
can b
e
divided into
two part
s
:
otherwise
n
w
L
n
n
w
n
h
n
h
LS
),
(
~
0
),
(
~
)
(
)
(
~
(13)
By ignori
ng t
he n
o
ise o
u
tside of
L
ta
ps,
the
DFT
-
ba
sed e
s
timato
r
diminish the
effect of
noise:
otherwise
L
n
n
w
n
h
n
h
DFT
,
0
0
),
(
~
)
(
)
(
~
(14)
Then
)
(
~
n
h
DFT
is tran
sforme
d to freq
uen
cy domai
n:
)}
(
~
{
)
(
~
n
h
DFT
k
H
DFT
DFT
(15)
As sh
own in
Equation
(12
)
, noise in
sid
e
of
L
taps
still exists in
DF
T-ba
se
d met
hod. We
prop
ose a no
vel time-dom
ain algo
rithm
base
d
on Q
R
de
comp
osi
t
ion to further red
u
ce noise.
The e
s
timate
d tran
smitter
data
e
X
~
ca
n be recove
red by
simply divi
din
g
the re
ceive
d
sign
al by
the cha
nnel resp
on
se:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
QR-ba
s
ed
Ch
annel Estim
a
tion for Orth
og
onal Frequ
en
cy
Divi
sio
n
Multiplexi
ng… (Peilong Ji
ang
)
6221
1
0
,
)
(
~
)
(
~
N
k
k
H
k
Y
X
DFT
e
(16)
From Equ
a
tio
n
(3), the tim
e
-do
m
ain receiving sign
als
y(
n)
without
CP is denot
ed as:
w
h
A
y
(17)
x
~
trans
formed from
e
X
~
by DFT is se
nt back chann
el estim
a
tion blo
ck to
form A:
1
2
1
1
0
1
1
0
]
[
L
N
N
N
L
N
L
N
N
L
N
x
x
x
x
x
x
x
x
x
x
A
(18)
The sol
u
tion
of Equation (17) is:
2
2
min
arg
~
y
h
A
h
(19)
It is
as
s
u
med that A=Q
O
R
，
whe
r
e
Q i
s
a
orthog
onal
m
a
trix, R i
s
a
n
uppe
r tria
ngu
lar
matrix.
O
R
A
Q
T
(20)
y(n
)
is
pr
oc
ess
e
d
b
y
Q
T
:
O
y
y
Q
n
T
(21)
Con
s
id
erin
g Equation (18), (19), (2
0), (2
1):
n
new
y
h
R
~
(22)
No
w, we g
e
t new
CIR
new
h
~
, then sent it ba
ck to Equation
(12)-Equatio
n
(15
)
to dimini
sh
the noise
wh
ich exits insi
de of
L
taps again. We give the block diag
ram of
the QR-ba
s
ed
cha
nnel e
s
ti
mation in Fig
u
re 4.
Figure 4. Block
Diag
ram o
f
the QR-b
ased Ch
ann
el Estimation
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TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 621
7 –
6223
6222
4. Simulation Resul
t
s
In this se
ction
,
we investiga
t
e the BER perform
an
ce o
f
the propo
se
d cha
nnel e
s
t
i
matio
n
algorith
m
on
multipath Rayleigh fadin
g
a
nd Doppl
er
sprea
d
chan
ne
l. The pa
ram
e
ters of chan
nel
is sh
own in Table 1.
Table 1. Para
meters of Ra
yleigh Ch
ann
el
Ra
y
l
eigh Cha
nne
l
Path Numbe
r
Average Po
w
e
r(
dB)
Dela
y
(
µs)
1 0
0
2 -1.0857
1
3 -2.1715
2
4 -3.2572
3
5 -4.3429
4
The modul
ation & demodulation method of p
ilot symbols and data symbol
s is QDPSK.
The ba
sic
system param
eters fo
r the si
mulation
s are
summa
rized
in Table 2.
Table 2: Simulation Enviro
nment
Parameter Value
Carrier f
r
eque
ncy
2(GHz)
FFT size
1024
Length of CP
8
Pilot subcarrier spacing
18
Modulation orde
r
QDPSK
Here
we
assume that
the
gu
ard
inte
rvals a
r
e l
ong
er tha
n
the
m
a
ximum d
e
la
y spread
of the cha
n
n
e
l. The prop
ose
d
algo
rith
m,
LS-ba
s
ed
method an
d DFT
-
ba
se
d
algorithm
a
r
e
simulate
d an
d comp
ared i
n
Figure 5.
Figure 5. BER Perfo
r
man
c
e in Differen
t
Chann
el
The differe
nt Dop
p
ler F
r
eq
uen
cy Shift are u
s
ed in the
simulation. F
i
gure
5(a
)
sh
ows the
perfo
rman
ce
whe
n
the m
a
ximum Dop
p
ler frequ
en
cy is 132
Hz, the DFT
-
ba
sed e
s
timator is
0.9dB bette
r than LS
-lin
ear
estimato
r and
abo
ut
2dB from
th
e propo
se
d
method. Fi
g.5(b
)
depi
cts the S
E
R sim
u
latio
n
s for th
e m
a
ximum Dop
p
ler frequ
en
cy is 264
Hz. In the Figu
re,
the
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TELKOM
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ISSN:
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046
QR-ba
s
ed
Ch
annel Estim
a
tion for Orth
og
onal Frequ
en
cy
Divi
sio
n
Multiplexi
ng… (Peilong Ji
ang
)
6223
perfo
rman
ce
of pro
posed
a
ppro
a
ch is 2.
5dB bette
r th
an DFT-ba
se
d estim
a
tor
which i
s
simila
r to
the LS-lin
ear estimato
r. A comp
re
hen
si
ve analysi
s
o
f
Figure
5 sh
ows that whil
e not in Fig
u
r
e
5(a
)
, the BE
R
still exists in Fig
u
re
5
(
b)
when S
N
R>1
0dB, th
at mean
s
a
bigge
r
Dop
p
ler
Freq
uen
cy S
h
ift led to po
ore
r
pe
rforma
nce. Ab
ove a
ll, the QR-ba
s
ed
algo
rithm
ren
o
vating
CIR
from
DFT
e
s
timator obt
ains lo
wer
BER an
d i
m
prove
s
OF
DM
com
m
u
n
icatio
n
syst
em
perfo
rman
ce.
5. Conclusio
n
To overcome
the short
c
o
m
ing that DF
T estimator i
gnores n
o
ise
outside of
L
taps, we
pre
s
ent and a
nalyze a
n
o
vel
QR-b
ased algorith
m
to u
pdate
CIR f
r
o
m
DFT
e
s
timator a
nd
red
u
c
e
noise in
side
of
L
taps. Th
e simul
a
tion
sho
w
s that th
e BER
pe
rformance is
2-2
.
5dB better t
han
conve
n
tional
DFT
-
ba
sed
method
and
LS-line
a
r alg
o
rithm,
h
e
n
c
e,
the OFDM
commu
nication
system i
s
imp
r
oved.
Ackn
o
w
l
e
dg
ements
This work
was
su
ppo
rted
by Natural
Scien
c
e
Fou
ndation
of
Hunan
proje
c
t Rin
g
-
resonato
r
-sp
e
ctro
scopi
c-b
a
se
d dete
c
tion mechani
sm and meth
ods of ga
s
pollution, pro
j
ect
numbe
r 14
JJ2013 a
nd Na
tural Scie
nce
Foundatio
n of Xinjiang p
r
oje
c
t Dete
ction theory an
d
method
s of gas poll
u
tion, proje
c
t num
b
e
r 201
321
1A
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