TELK
OMNIKA
Indonesian
Journal
of
Electrical
Engineering
V
ol.
12,
No
.
9,
September
2014,
pp
.
6860
6867
DOI:
10.11591/telk
omnika.v12.i9.4678
6860
Pilot-aided
Joint
Channel
Estimation
f
or
OFDM
based
Cooperative
Multi-cell
Netw
orks
Y
uan
W
ang*
1
,
Zhongpei
Zhang
1
,
and
Yixian
Chen
2
1
Univ
ersity
of
Electronic
Science
and
T
echnology
of
China/
National
K
e
y
Labor
ator
y
of
Science
and
T
echnology
on
Comm
unications
1
No
.2006,
Xiyuan
A
v
e
,
W
est
Hi-T
ech
Zone
,
611731,
Chengdu,
China,
+86-028-83201114
2
Southw
est
Univ
ersity
f
or
Nationalities/
College
of
Electr
ical
and
Inf
or
mation
Engineer
ing
2
Y
ihuan
Lu
South
Sect.4,
610041,
Chengdu,
China,
+86-028-85522012
*Corresponding
author
,
e-mail:
w
ang.yuan@china.com.cn
Abstract
Multi-cell
joint
channel
estimation
(JCE)
is
the
basis
f
or
application
of
m
ulti-ce
ll
cooper
ativ
e
pro-
cessing.
F
or
w
eakness
of
the
e
xisting
algor
ithms
that
po
w
er
dela
y
profile
(PDP)
kno
wledge
of
all
m
ultiple
cells
need
be
kno
wn
or
pilot
sequence
sets
of
all
cells
m
ust
be
identical,
in
this
paper
,
a
pilot-aided
time
domain
JCE
algor
ithm
is
presented.
And
then,
b
y
using
Gener
aliz
ed
Akaik
e
Inf
or
mation
Cr
iter
ion
(GAIC)
to
estimate
PDPs
of
all
cells
f
or
reducing
the
signal
space
of
channel
estimation,
the
paper
fur
ther
optimiz
es
this
JCE
algor
ithm.
Sim
ulation
results
sho
w
that
the
proposed
algor
ithms
ha
v
e
good
mean
square
error
(MSE)
and
corresponding
space
frequency
b
loc
k
coded
(SFBC)
cooper
ativ
e
m
ulti-cell
tr
ansmission
system
has
the
good
bit
error
r
ate
(BER)
perf
or
mance
too
.
K
e
yw
or
ds:
Multi-cell
cooper
ation,
Pilot-aided,
Joint
channel
estimation,
GAIC
Cop
yright
c
2014
Institute
of
Ad
v
anced
Engineering
and
Science
.
All
rights
reser
v
ed.
1.
Intr
oduction
Recently
,
f
or
solving
the
se
v
ere
inter-cell
interf
erence
(ICI)
prob
lem
in
deplo
yment
of
Or-
thogonal
F
requ
ency
Division
Mu
ltiple
xing
(OFDM)
based
future
wireless
comm
unication
netw
or
ks
,
the
emerging
technologies
based
on
m
ulti-cell
cooper
ation
and
joint
process
are
receiving
more
attention
and
research.
Ne
v
er
theless
,
the
emplo
yments
of
these
technologies
are
highly
depen-
dent
on
the
whole
e
xact
channel
state
inf
or
mation
(CSI)
among
the
cooper
ativ
e
BSs
and
the
users
.
Theref
ore
the
optim
um
channel
estimation
is
the
base
of
future
wireless
comm
unication
netw
or
ks
.
In
cooper
ativ
e
cellular
systems
,
joint
channel
estimation
(JCE),
which
is
initially
applied
in
a
m
ulti-user
scheme
,
could
be
e
xtended
to
a
m
ulti-cell
en
vironment
and
obtain
better
perf
or
mance
as
depicted
in
pub
lications
[1–3].
Ho
w
e
v
er
,
m
ulti-cell
JCE
needs
the
po
w
er
dela
y
profiles
(PDP)
kno
wledge
of
m
ultiple
cells
kno
wn
b
y
receiv
er
or
pilot
sequence
sets
of
all
cells
being
identical
(in
this
paper
,
w
e
e
xploit
PDP
to
precisely
represent
m
ultipath
dela
ys
po
w
er
and
m
ultipath
tap
locations
[4],
the
belo
w
is
same).
I
n
gener
al,
the
signals
receiv
ed
from
diff
erent
BSs
or
diff
erent
users
will
not
ha
v
e
the
same
PDP
f
or
diff
erent
spatial
locations
of
these
BSs
or
users
[5]
and
while
the
PDP
kno
wledge
will
not
be
kno
wn
a
pr
ior
i
to
receiv
er
,
these
prob
lems
mak
e
the
pr
actical
v
alue
of
m
ulti-cell
JCE
reduced
se
v
erely
.
F
or
this
w
eakness
,
this
paper
presents
a
pilot-aided
time
domain
JCE
algor
ithm
f
or
cooper
ativ
e
m
ulti-cell
netw
or
k
and
der
iv
es
the
corresponding
Cr
amer-
Rao
bound
(CRB)
when
PDPs
of
m
ultiple
cells
are
not
same
and
unkno
wn.
Then,
b
y
using
Gener
aliz
ed
Akaik
e
Inf
or
mation
Cr
iter
ion
(GAIC)
to
estimate
PDPs
of
all
cells
f
or
reducing
the
signal
space
of
channel
estimation,
the
paper
fur
ther
optimiz
es
this
JCE
algor
ithm.
The
rest
of
the
paper
is
organiz
ed
as
f
ollo
ws
.
Section
2
introduces
a
cooper
ativ
e
m
ulti-cell
OFDM
system
model.
Section
3
presents
a
pilot-aided
time
domain
m
ulti-cell
JCE
algor
ithm
and
fur
ther
optimiz
es
it
b
y
e
xp
loiting
GAIC
.
Numer
ical
sim
ulations
are
presented
to
v
er
ify
perf
or
mance
of
the
proposed
algor
ithms
in
section
4
and
the
paper
will
be
concluded
in
last
Section
5.
Receiv
ed
December
25,
2013;
Re
vised
J
une
5,
2014;
Accepted
J
une
28,
2014
Evaluation Warning : The document was created with Spire.PDF for Python.
TELK
OMNIKA
ISSN:
2302-4046
6861
Notation:
In
this
paper
,
Bold
letters
represent
a
matr
ix
or
a
v
ector
;
d
x
e
denotes
the
nearest
integer
larger
than
or
equal
to
x
;
(
)
H
stands
f
or
the
conjugate
tr
anspose;
diag(
)
indicates
the
diagonal
matr
ix;
I
N
denotes
N
N
identity
matr
ix;
jj
jj
is
the
Euclidean
nor
m;
E
[
]
represents
e
xpectation.
2.
System
Model
C
e
l
l
1
C
e
l
l
2
U
se
r
u
B
S
1
B
S
2
C
e
l
l
3
B
S
3
O
t
h
e
r
U
s
e
r
s
B
a
c
k
h
a
u
l
Figure
1.
An
OFDM
based
m
ulti-cell
cooper
ation
scenar
io
with
frequency
reuse
1.
Consider
an
OFDM
system
oper
ating
with
a
bandwidth
of
B
w
=
1
=T
Hz
(
T
is
th
e
sampling
per
iod)
and
consisting
a
total
of
N
subcarr
iers
using
QPSK
modulation
o
v
er
frequency
selectiv
e
Ra
yleigh
f
ading
channels
.
A
cyclic
prefix
(CP)
of
length
L
C
P
is
inser
ted
bef
ore
each
symbol.
Comb-type
pilot
patter
n
is
e
xploited
to
perf
or
m
channel
estimation
i.e
.,
in
each
symbol,
N
p
tones
used
as
pilots
to
assist
channel
estimation
are
e
v
enly
distr
ib
uted
o
v
er
N
subcarr
iers
with
equal
po
w
er
.
Channel
impulse
response
(CIR)
has
L
m
ultipath
components
,
where
each
path
is
char-
acter
iz
ed
b
y
a
comple
x
gain
f
actor
h
l
(
t
)
and
a
corresponding
dela
y
l
(
t
)
:
h
(
t;
)
=
L
1
X
l
=0
h
l
(
t
)
(
l
(
t
)
T
)
(1)
In
pr
actice
,
PDP
of
channel
is
considered
to
be
constant
o
v
er
a
fr
ame
,
so
t
in
(1)
can
be
ignored
and
channel
frequency
response
(CFR)
v
ector
f
or
the
k
-th
subcarr
ier
of
the
n
-th
OFDM
symbol
can
be
e
xpressed
as
H
(
n;
k
)
=
L
1
X
l
=0
h
l
(
n
)
exp(
j
2
N
k
l
)
;
k
=
1
;
;
N
(2)
Since
JCE
does
not
need
to
distinguish
do
wnlink
or
uplink
of
system
[3],
an
application
scenar
io
of
cooper
ativ
e
Multi-cell
OFDM
system
do
wnlink
is
illustr
ated
as
an
e
xample
in
Figure
1.
N
B
S
BSs
each
equipped
with
N
T
tr
ansmit
antennas
cooper
ativ
ely
tr
ansmit
to
U
users
distr
ib
uted
around
N
B
S
cells
.
Based
on
cooper
ation,
pilot
sets
of
m
ultiple
cells
are
kno
wn
b
y
e
v
er
y
user
and
e
xploited
to
estimate
corresponding
CSI,
while
all
BSs
could
share
these
inf
or
mation.
Theref
ore
joint
process
technique
can
be
used
to
fur
ther
impro
v
e
system
perf
or
mance
.
Without
loss
of
gener
ality
,
w
e
discuss
channel
estimation
f
or
case
of
only
one
user
,
be-
cause
,
from
signal
processing
point
of
vie
w
,
m
ultiple
antenna
wireless
channels
and
m
ulti-user
wireless
channels
ha
v
e
no
intr
insical
diff
erence
,
if
the
channels
are
assumed
to
be
independent
from
each
other
both
can
be
reduced
to
a
Multiple-Input
and
Single
Output
(MISO)
channel
model
[3].
So
the
system
diag
r
am
is
depicted
as
Figure
2.
Pilot-aided
JCE
f
or
cooper
ativ
e
m
ulti-cell
netw
or
ks
(Y
uan
W
ang)
Evaluation Warning : The document was created with Spire.PDF for Python.
6862
ISSN:
2302-4046
S
p
a
c
e
-
F
r
e
q
u
en
c
y
en
c
o
d
er
I
F
F
T
I
F
F
T
B
T
S
1
I
F
F
T
I
F
F
T
B
T
S
N
B
S
FFT
FFT
S
p
a
c
e
-
F
r
e
q
u
e
n
c
y
d
e
c
o
d
e
r
C
h
a
n
n
e
l
E
s
t
i
m
a
t
o
r
P
D
P
E
s
t
i
m
a
t
o
r
Figure
2.
Pilot-aided
time
domain
JCE
model
f
or
m
ulti-cell
cooper
ation
system.
3.
Pilot-aided
time
domain
joint
c
hannel
estimation
Because
of
the
diff
erence
on
location
f
or
m
ultiple
cells
,
the
PDPs
of
these
cells
are
not
same
[5].
So
,
set
channel
order
as
L
,
w
e
represent
the
condition
that
PDPs
of
diff
erent
cells
are
not
same
with
the
maxim
um
time
dela
y
set
n
(1)
L
;
;
(
N
B
S
)
L
o
.
Call
f
or
each
OFDM
symbol,
N
p
pilot
symbols
f
p
(
s
);
s
=
1
;
;
N
p
g
are
e
v
enly
inser
ted
into
the
N
subcarr
iers
at
positions
f
k
s
;
k
s
=
(
s
1)
D
f
;
D
f
=
N
=N
p
;
s
=
1
;
;
N
p
g
with
equal
po
w
er
E
p
=
j
p
(
s
)
j
2
and
equal
distance
D
f
betw
een
tw
o
adjacent
pilots
,
where
k
s
indicates
the
subcarr
ier
inde
x
of
pilot.
3.1.
Pilot-aided
time
domain
c
hannel
estimation
algorithm
Assuming
the
perf
ect
synchronization
in
m
ultiple
cells
,
the
receiv
ed
signal
v
ector
on
pilot
subcarr
iers
of
the
n
-th
OFDM
symbol
betw
een
the
j
-th
tr
ansmit
antenna
of
i
-th
BS
and
the
q
-th
receiv
e
antenna
of
user
u
can
be
e
xpressed
as:
Y
q
p;u
(
n
)
=
N
B
S
P
i
=1
N
T
P
j
=1
X
p;u;j
;i
(
n
)
H
q
p;u;j
;i
(
n
)
+
W
q
p;u
(
n
)
=
N
B
S
P
i
=1
N
T
P
j
=1
X
p;u;j
;i
(
n
)
F
p
h
q
u;j
;i
(
n
)
+
W
q
p;u
(
n
)
=
G
p;u
(
n
)
h
q
u
(
n
)
+
W
q
p;u
(
n
)
(3)
Where
,
Y
q
p;u
(
n
)
=
[
Y
q
p;u
(
n;
k
1
)
;
;
Y
q
p;u
(
n;
k
N
p
)]
T
is
the
frequency-domain
receiv
ed
v
ector
of
N
p
dimension.
X
p;u;j
;i
(
n
)
=
diag
f
p
u;j
;i
(
n;
1)
;
;
p
u;j
;i
(
n;
N
p
)
g
indicates
the
pilot
matr
ix
of
di-
mension
N
p
N
p
with
element
p
u;j
;i
(
n;
k
)
representing
the
k
-th
pilot
symbol
of
n
-th
OFDM
symbol
betw
een
the
j
-th
tr
ansmit
antenna
of
i
-th
base
station
and
the
user
u
.
H
q
u;j
;i
(
n
)
=
[
H
q
u;j
;i
(
n;
0)
;
;
H
q
u;j
;i
(
n;
N
p
1)]
T
denotes
the
CFR
v
ector
betw
een
the
j
-th
tr
ansmit
antenna
of
i
-th
BS
and
the
q
-th
receiv
e
anten
na
of
user
u
.
While
h
q
u;j
;i
(
n
)
=
[
h
q
u;j
;i
(
n;
0)
;
;
h
q
u;j
;i
(
n;
N
1)]
T
is
the
corresponding
CIR
v
ector
.
F
p
is
the
N
p
N
dimension
submatr
ix
der
iv
ed
from
the
N
-point
FFT
matr
ix
whose
(
s;
l
)
-th
element
is
denoted
b
y
[
F
p
]
s:l
=
e
xp
(
j
2
k
s
l
=
N
)
,
s
=
1
;
;
N
p
;
l
=
1
;
;
N
.
So
the
cor
responding
equiv
alent
matr
ix
f
or
the
total
pilots
of
m
ultiple
cells
can
be
e
x-
pressed
as
G
p;u
(
n
)
=
[
X
p;u;
1
;
1
(
n
)
F
p
;
;
X
p;u;N
T
;
1
(
n
)
F
p
;
;
X
p;u;
1
;N
B
S
(
n
)
F
p
;
;
X
p;u;N
T
;N
B
S
(
n
)
F
p
]
with
dimension
of
N
p
N
B
S
N
T
N
.
While
the
equiv
alent
CIR
matr
ix
can
be
sho
wn
as
h
q
u
(
n
)
=
[
h
q
u;
1
;
1
T
(
n
)
;
;
h
q
u;N
T
;
1
T
(
n
)
;
;
h
q
u;
1
;N
B
S
T
(
n
)
;
;
h
q
u;N
T
;N
B
S
T
(
n
)]
T
of
N
B
S
N
T
N
1
dimension
.
W
q
p;u
(
n
)
is
a
noise
v
ector
of
dimension
N
p
1
,
whose
entr
ies
are
TELK
OMNIKA
V
ol.
12,
No
.
9,
September
2014
:
6860
6867
Evaluation Warning : The document was created with Spire.PDF for Python.
TELK
OMNIKA
ISSN:
2302-4046
6863
assumed
to
be
i.i.d.
and
comple
x
Gaussian
distr
ib
uted
with
z
ero-mean
and
equal
v
ar
iance
2
w
.
Since
PDPs
remain
constant
o
v
er
a
fr
ame
,
n
of
(3)
can
be
ignored.
Thereb
y
igno
r
ing
the
inde
x
of
u
and
q
,
(3)
can
be
re
wr
itten
as
Y
p
=
G
p
h
+
W
p
(4)
Ob
viously
,
G
p
is
an
ill-conditioned
matr
ix.
According
to
least
squared
(LS)
cr
iter
ia,
there
is
no
cer
tain
solution
of
(4).
F
or
tunately
,
CIR
is
alw
a
ys
m
uch
shor
ter
than
OFDM
symbol
length,
i.
e
.,
max
f
(
i
)
L
g
N
;
i
=
1
;
;
N
B
S
.
Lettin
g
L
b
=
d
N
p
=
(
N
T
N
B
S
)
e
and
consider
ing
max
f
(
i
)
L
g
L
b
,
(4)
can
be
rearr
anged
as
Y
p
=
G
0
p
h
+
W
p
(5)
where
G
0
p
=
[
X
p;
1
;
1
F
p;L
b
;
;
X
p;N
T
;
1
F
p;L
b
;
;
X
p;
1
;N
B
S
F
p;L
b
;
;
X
p;N
T
;N
B
S
F
p;L
b
]
is
a
equiv
a-
lent
matr
ix
with
dim
ension
of
N
p
N
B
S
N
T
L
b
,
F
p;L
b
stands
f
or
the
matr
ix
F
p
retaining
the
first
L
b
columns
.
Because
h
j
;i
is
modified
as
an
L
b
-dimensional
v
ector
,
the
equiv
alent
CIR
matr
ix
can
be
sho
wn
as
h
=
[
h
1
;
1
T
;
;
h
N
T
;
1
T
;
;
h
1
;N
B
S
T
;
;
h
N
T
;N
B
S
T
]
T
with
dimension
of
N
B
S
N
T
L
b
1
.
So
w
e
can
obtain
the
corresponding
LS
estimator
f
or
h
:
^
h
=
(
G
0
p
H
G
0
p
)
1
G
0
p
H
Y
p
(6)
F
rom
(6),
the
MSE
of
single
tap
of
h
with
m
ulti-cell
JCE
can
be
giv
en
b
y
M
S
E
LS
=
1
N
B
S
N
T
L
C
P
E
[
jj
^
h
h
jj
2
]
=
2
w
N
B
S
N
T
L
C
P
tr
[(
G
0
p
H
G
0
p
)
1
]
(7)
3.2.
Pilots
Design
According
to
[6],
if
(
G
0
p
H
G
0
p
)
1
=
I
N
B
S
N
T
L
b
=
(
N
p
E
p
)
can
be
satisfied,
(6)
will
be
sim-
plified
as
^
h
=
I
N
B
S
N
T
L
b
G
0
p
H
Y
p
=
(
N
p
E
p
)
with
computational
comple
xity
being
g
reatly
reduced;
While
minim
um
MSE
v
alue
2
w
=
(
N
p
E
p
)
will
be
obtain.
W
e
e
xploit
Chu
sequence
to
design
pilots
which
has
perf
ect
or
thogonality
as
[7]
to
meet
this
condition.
First,
w
e
arbitr
ar
ily
choose
a
length
of
N
p
Chu
sequence
[8]
f
c
(
s
);
s
=
1
;
;
N
p
g
as
the
basis
p
ilot
sequence
f
or
fur
ther
design.
The
s
-th
element
of
a
length
of
N
p
Chu
sequence
is
e
x-
pressed
as:
c
(
s
)
=
e
j
(
r
(
s
1)
2
)
=N
p
;
f
or
ev
en
N
p
e
j
(
r
(
s
1)
s
)
=N
p
;
f
or
odd
N
p
;
s
=
1
;
;
N
p
(8)
in
which
r
and
N
p
are
relativ
ely
pr
ime
.
Then,
let
=
L
b
,
the
pilot
v
alue
p
j
;i
(
s
)
sent
from
the
j
-th
tr
ansmit
antenna
of
i
-th
BS
can
be
descr
ibed
as:
p
j
;i
(
s
)
=
A
c
(
s
)
e
j
2
s
((
i
1)
N
T
+(
j
1))
N
p
(9)
where
A
=
p
E
p
is
the
amplitude
of
pilot
symbol.
i
=
1
;
;
N
B
S
indicates
the
inde
x
of
cell
or
BS
,
j
=
1
;
;
N
T
denotes
the
inde
x
of
tr
ansmit
antenna,
s
=
1
;
;
N
p
represents
t
he
inde
x
of
pilot
symbol.
Due
to
the
perf
ect
per
iodic
autocorrelation
proper
ty
of
the
polyphase
Chu
sequ-ence
,
the
pilot
sequences
designed
as
(9)
will
be
or
thogonal
to
each
other
and
leads
to
the
condition
of
(
G
0
p
H
G
0
p
)
1
=
I
N
B
S
N
T
L
b
=
(
N
p
E
p
)
being
satisfied.
Then
the
minim
um
MSE
of
channel
estimator
will
be
ob
tained.
Cr
amer-Rao
Bound
(CRB)
reflects
a
lo
w
er
bound
on
the
error
v
ar
iance
f
or
an
unbiased
estimator
.
The
CRB
f
or
an
arbitr
ar
y
estimator
^
h
j
;i
of
h
with
signal
model
as
(5)
is
giv
en
Pilot-aided
JCE
f
or
cooper
ativ
e
m
ulti-cell
netw
or
ks
(Y
uan
W
ang)
Evaluation Warning : The document was created with Spire.PDF for Python.
6864
ISSN:
2302-4046
b
y
[9]:
C
R
B
(
^
h
j
;i
)
=
(
L
2
w
)
=
(
N
p
E
p
)
(10)
While
MSE
of
^
h
j
;i
is
defined
as:
M
S
E
=
E
[
jj
h
j
;i
^
h
j
;i
jj
2
]
C
R
B
(
^
h
j
;i
)
(11)
3.3.
Optim
um
algorithm
In
broadband
wireless
comm
unications
,
m
ultipath
channel
is
sparse
in
gener
al.
The
chan-
nel
estimation
accur
acy
can
be
impro
v
ed
b
y
once
kno
wing
the
PDP
kno
wledge
of
channel.
In
[10],
GAIC
cr
iter
ion
is
applied
to
MIMO
sparse
channel
estimation
prob
lem
to
estimate
PDP
in
an
iter
a-
tiv
e
manner
and
obtain
better
perf
or
mance
.
W
e
e
xtend
this
algor
ithm
to
cooper
ativ
e
m
ultiple
cells
scheme
.
Because
the
PDPs
of
diff
erent
cells
are
not
same
and
the
PDPs
of
diff
erent
tr
ansmit
antennas
in
a
cell
are
identical,
f
or
each
cell
only
the
PDP
of
channel
estimator
betw
een
the
first
tr
ansmit
antenna
and
user
,
i.e
.
^
h
1
;i
;
i
=
1
;
;
N
B
S
,
needs
to
estimate
.
Then,
f
or
estimator
^
h
1
;i
,
the
GAIC
cost
function
f
or
a
test
channel
order
l
has
the
f
or
m:
GAI
C
1
;i
(
l
)
=
L
b
=
2
ln(
^
2
1
;i
;
l
)
+
ln(ln(
L
b
))(
l
+
1)
(12)
is
a
user
specified
par
ameter
,
^
2
1
;i
;
l
denotes
the
estima
tion
of
noise
v
ar
iance
f
or
channel
order
l
and
is
giv
en
b
y
^
2
1
;i
;
l
=
(
^
h
1
;i
^
h
1
;i
;
l
)
H
F
H
p
;
L
b
X
H
p
;1
;i
X
p
;1
;i
F
p
;
L
b
(
^
h
1
;i
^
h
1
;i
;
l
)
=L
b
=
(
^
h
1
;i
^
h
1
;i
;
l
)
H
N
p
I
L
b
(
^
h
1
;i
^
h
1
;i
;
l
)
=L
b
(13)
where
^
h
1
;i
;
l
is
the
channel
estimator
f
or
channel
order
l
and
padded
with
L
b
l
z
eros
.
X
p
;1
;i
F
p
;
L
b
is
the
submatr
ix
from
G
0
p
of
(5)
with
N
p
L
b
dimension.
The
GAIC
test
is
e
x
ecuted
as
f
ollo
wing
steps:
Algorithm
1
Optimization
f
or
JCE
with
GAIC
test
1:
Initially
set
P
=
L
C
P
;
2:
Calculate
the
cost
function
GAI
C
1
;i
(
L
)
f
or
L
=
1
;
;
P
;
3:
Obtain
the
GAIC
estimator
as
^
L
=
arg
min
L
f
GAI
C
1
;i
(
L
)
g
;
4:
Remo
v
e
the
eff
ect
of
the
ne
wly
estimated
tap
b
y
setting
^
h
1
;i
(
^
L
)
=
0
;
5:
Set
P
=
^
L
1
and
repeat
1-3
to
estimate
the
ne
xt
significant
tap
positions;
6:
If
^
L
6
=
1
go
to
step
4.
Then
the
set
f
^
L
g
giv
es
the
positions
of
significant
channel
taps
and
it
could
be
utiliz
ed
to
impro
v
e
perf
or
mance
of
the
estimator
as
^
h
0
j
;i
(
l
)
=
^
h
j
;i
(
l
)
;
l
2
f
^
L
g
0
;
l
=
2
f
^
L
g
;
j
=
1
;
;
N
T
;
i
=
1
;
;
N
B
S
(14)
In
addition,
this
algor
ithm
m
ust
be
satisfied
with
L
b
>
L
C
P
>
max
f
(
i
)
L
g
;
i
=
1
;
;
N
B
S
.
TELK
OMNIKA
V
ol.
12,
No
.
9,
September
2014
:
6860
6867
Evaluation Warning : The document was created with Spire.PDF for Python.
TELK
OMNIKA
ISSN:
2302-4046
6865
4.
Numberical
Sim
ulation
results
Sim
ulations
w
ere
carr
ied
out
to
demonstr
ate
MSE
and
bit
error
r
ate
(BER)
perf
or
mance
of
the
proposed
algor
ithms
and
the
MSE
is
defined
as
(11).
An
OFDM
system
is
sim
ulated
with
f
ollo
wing
par
ameters:
center
frequency
f
c
=
2
:
2
GH
z
,
bandwidth
B
w
=
5
M
H
z
,
n
umber
of
o
v
er
all
subcarr
iers
N
=
512
,
CP
length
L
C
P
=
24
.
Each
OFDM
fr
ame
consists
of
N
=
50
OFDM
symbols
.
Comb-type
pilot
patter
n
is
emplo
y
ed
in
syst
em
with
n
umber
of
pilot
subcarr
iers
N
p
=
128
and
pilot
inter
v
al
D
f
=
4
.
The
mobile
speed
is
30km/h.
Assuming
that
the
cells
n
umber
N
B
S
=
2
in
sim
ulation
model,
one
BS
per
cell
and
each
BS
equipped
with
N
T
tr
ansmit
antennas
,
each
user
has
receiv
e
antennas
N
R
=
2
.
The
system
e
xploits
SFBC
and
QPSK
modulation.
Multipath
Ra
yleigh
f
ading
channels
are
considered
as
3GPP-TR-25.996
SCM
Case
II
channel
model
[11],
with
order
L
=
6
.
The
time
dela
y
po
w
ers
in
PDPs
of
m
ultiple
cells
is
assumed
to
be
e
xponential
with
pdf
(
t
)
/
exp(
t
)
.
While
the
m
ultipath
tap
locations
in
PDPs
of
m
ultiple
cells
contain
diff
erent
and
are
unif
or
mly
distr
ib
uted
o
v
er
[0
;
2510]
ns
.
F
or
the
con
v
enience
of
compar
ison,
let
L
b
=
32
d
N
p
=
(
N
T
N
B
S
)
e
,
E
p
=
1
and
define
Eb/N0
as
(
N
T
E
p
)
=
2
w
.
P
ar
ameter
is
chosen
as
2.5.
Figure
3
sho
ws
the
MSE
perf
or
mance
of
the
proposed
pilot-aided
m
ulti-cell
JCE
algo-
r
ithm
(denoted
as
P
A-MC-JCE)
and
its
optim
um
algor
ithm
with
GAIC
(denoted
as
GAIC-MC-JCE)
compares
with
the
corresponding
CRB
.
F
rom
the
figure
,
w
e
obser
v
e
that
the
MSE
of
m
ulti-cell
JCE
(indicated
as
MC-JCE)
with
PDPs
kno
wledge
kno
wn
accur
ately
coincides
with
the
cur
v
e
of
CRB
and
it
means
the
estimator
is
unbiased.
At
the
same
time
,
because
of
using
L
b
length
to
replace
the
accur
ate
PDPs
kno
wledge
,
the
MSE
perf
or
mance
of
P
A-MC-JCE
losses
about
7.5
dB
compared
with
CRB
.
Ho
w
e
v
er
,
due
to
optimization
of
GAIC
,
the
MSE
cur
v
e
of
GAIC-MC-JCE
is
close
to
CRB
with
Eb/N0
increasing.
0
5
1
0
1
5
2
0
1
0
-4
1
0
-3
1
0
-2
1
0
-1
1
0
0
Eb
/
N
0
(d
B)
M
S
E
P
A
-MC
-JC
E
G
A
I
C
-MC
-JC
E
PD
Ps
kn
o
w
n
MC
-JC
E
C
R
B
Figure
3.
MSE
perf
or
mance
compar
ison
f
or
v
ar
ious
m
ulti-cell
JCE
algor
ithms
.
Figure
4
and
Figure
5
illuminate
the
BER
perf
or
mance
compar
ison
f
or
v
ar
ious
m
ulti-cell
JCE
algor
ithms
with
tr
ansmit
antenna
of
one
or
tw
o
,
respectiv
ely
.
In
Figure
4,
with
BS
each
equipped
with
one
tr
ansmit
antenna
the
BER
of
MC-JCE
with
PDPs
kno
wledge
kno
wn
has
slight
perf
or
mance
loss
as
compared
to
case
of
perf
ect
channel
kno
wledge
.
And
f
or
P
A-MC-JCE,
the
loss
is
about
2
dB
.
While
f
or
GAIC-MC-JCE
the
BER
cur
v
e
is
close
to
the
BER
of
MC-JCE
with
PDPs
kno
wn
g
r
adually
.
In
Figure
5,
with
BS
each
equipped
with
tw
o
antennas
the
BER
perf
or
mance
of
both
P
A-MC-JCE
and
GAIC-MC-JCE
get
r
apid
and
significant
impro
v
ement
and
the
cur
v
es
ha
v
e
been
Pilot-aided
JCE
f
or
cooper
ativ
e
m
ulti-cell
netw
or
ks
(Y
uan
W
ang)
Evaluation Warning : The document was created with Spire.PDF for Python.
6866
ISSN:
2302-4046
close
to
10
4
at
lo
w
Eb/N0
(less
than
12dB).
But
with
Eb/N0
increasing,
due
to
the
e
xistence
of
Doppler
frequen
cy
shift,
the
BER
cur
v
es
of
both
algor
ithms
encounter
error
floors
at
about
20dB
of
Eb/N0.
0
5
1
0
1
5
2
0
1
0
-5
1
0
-4
1
0
-3
1
0
-2
1
0
-1
Eb
/
N
0
(d
B)
B
E
R
P
A
-MC
-JC
E
G
A
I
C
-MC
-JC
E
PD
Ps
kn
o
w
n
MC
-JC
E
p
e
rf
e
ct
ch
a
n
n
e
l
kn
o
w
n
Figure
4.
BER
perf
or
mance
compar
ison
f
or
v
ar
ious
m
ulti-cell
JCE
algor
ithms
with
N
T
=
1
.
0
5
1
0
1
5
2
0
1
0
-5
1
0
-4
1
0
-3
1
0
-2
1
0
-1
Eb
/
N
0
(d
B)
B
E
R
P
A
-MC
-JC
E
G
A
I
C
-MC
-C
E
PD
Ps
kn
o
w
n
MC
-JC
E
p
e
rf
e
ct
ch
a
n
n
e
l
kn
o
w
n
Figure
5.
BER
perf
or
mance
compar
ison
f
or
v
ar
ious
m
ulti-cell
JCE
algor
ithms
with
N
T
=
2
.
5.
Conc
lusion
Based
on
m
ulti-cell
cooper
ation
OFDM
systems
,
this
paper
firstly
presents
a
pilot-aided
time
domain
JCE
algor
ithm
when
PDPs
of
m
ultiple
cells
are
not
same
and
unkno
wn
b
y
receiv
er
.
Then,
b
y
e
xploiting
GAIC
,
the
paper
fur
ther
optimiz
es
the
algor
ithm.
F
rom
sim
ulation
results
w
e
obser
v
e
that,
compared
with
the
corresponding
CRB
,
the
MSE
perf
or
mance
of
proposed
m
ulti-cell
JCE
algor
ithms
has
a
cer
tain
loss
.
This
perf
or
mance
gap
pro
vides
a
possibility
to
optimiz
e
the
m
ulti-cell
JCE
algor
ithms
and
it
is
a
fur
ther
need
to
study
.
TELK
OMNIKA
V
ol.
12,
No
.
9,
September
2014
:
6860
6867
Evaluation Warning : The document was created with Spire.PDF for Python.
TELK
OMNIKA
ISSN:
2302-4046
6867
Ac
kno
wledg
ement
The
authors
g
r
atefully
ac
kno
wledge
the
helpful
comments
and
suggestions
of
the
re
vie
w-
ers
,
which
ha
v
e
impro
v
ed
the
presentation.This
w
or
k
is
par
tially
suppor
ted
b
y
F
oundation
f
or
the
National
Science
and
T
echnology
Major
Project
(No
.
2012ZX03001027-003),
National
Natur
al
Science
F
oundation
of
China
(No
.
61101092),
Fundamental
Research
Funds
f
or
the
Centr
al
Uni-
v
ersities
(No
.
ZYGX2010J010),
science
f
oundation
of
Sichuan
pro
vince
(No
.
2010FZ0082).
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Evaluation Warning : The document was created with Spire.PDF for Python.