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m
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MI
MO
[
1
]
s
y
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to
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m
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MI
MO
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m
[
2
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2252
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8776
IJ
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Vo
l.
8
,
No
.
1
,
A
p
r
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2
0
1
9
:
29
–
38
30
T
h
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M
O
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s
s
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alg
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ith
m
.
V
-
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[
3
]
is
u
s
ed
to
ab
r
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p
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v
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t
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ex
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s
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c
h
a
n
n
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l.
Gen
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all
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w
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x
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ea
r
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d
etec
to
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s
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ased
o
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au
s
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o
f
i
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ab
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f
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to
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T
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ith
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ter
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(
SI
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)
[
4
]
w
h
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u
lt
s
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d
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it
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a
n
ce
B
E
R
p
r
esen
tatio
n
.
2.
SYST
E
M
M
O
DE
L
S
I
n
MI
MO
s
ch
e
m
e
co
n
s
is
t
s
o
f
n
u
m
b
er
o
f
tr
an
s
m
itter
s
an
d
r
ec
eiv
er
s
an
d
w
e
as
s
u
m
e
ch
a
n
n
el
is
f
lat
f
ad
in
g
R
a
y
lei
g
h
ch
a
n
n
el.
T
h
e
s
ig
n
al
i
s
co
n
ta
m
i
n
ated
b
y
ze
r
o
m
ea
n
ad
d
itiv
e
w
h
i
te
Gau
s
s
ian
n
o
i
s
e
(
A
W
GN)
[5
-
6
]
.
T
h
e
ar
r
iv
in
g
s
i
g
n
al
b
e
a
b
le
to
d
escr
ib
e
as:
=
̇
+
(
1
)
No
w
=
[
1
,
,
2
3
,
,
]
(
2
)
An
d
th
e
c
h
an
n
el
m
atr
i
x
is
s
h
o
w
n
i
n
th
e
g
iv
e
n
eq
u
at
io
n
̇
=
[
ℎ
11
ℎ
12
⋯
ℎ
21
ℎ
2
2
…
⋮
ℎ
1
⋮
ℎ
2
⋱
…
ℎ
1
ℎ
2
⋮
ℎ
]
(
3
)
W
h
er
e,
̇
is
a
ch
an
n
el
i
m
p
u
l
s
e
r
esp
o
n
s
e,
tr
an
s
m
itted
s
i
g
n
al
=
[
1
,
2
]
(
4
)
An
d
n
o
is
e
=
[
1
,
2
]
(
5
)
3.
SI
M
UL
AT
I
O
N
S O
F
M
I
M
O
CH
ANNE
L
CAP
ACI
T
Y
I
n
m
u
ltip
le
i
n
p
u
t
a
n
d
m
u
l
tip
l
e
o
u
tp
u
t
s
y
s
te
m
h
a
v
i
n
g
M_
T
tr
an
s
m
it
a
n
te
n
n
a
s
an
d
N_
R
r
ec
eiv
in
g
an
ten
n
a
s
an
d
t
h
e
ch
a
n
n
e
l
tr
an
s
f
er
m
atr
ix
i
s
r
ep
r
esen
ted
as
H
w
i
th
d
i
m
en
s
io
n
M_
T
×N
_
R
.
T
h
e
o
u
tp
u
t
s
ig
n
a
l
ca
n
b
e
d
escr
ib
ed
as
in
eq
u
atio
n
(
1
)
.
W
e
p
r
esu
m
e
a
MI
MO
d
o
w
n
li
n
k
w
i
th
M_
T
tr
an
s
m
it
a
n
ten
n
a
s
at
t
h
e
b
a
s
e
tr
an
s
ce
i
v
er
s
tatio
n
a
n
d
N_
R
r
ec
eiv
e
an
te
n
n
as
at
th
e
m
o
b
ile
s
tatio
n
,
w
h
er
e
t
h
e
ch
a
n
n
el
i
s
r
ec
o
g
n
ized
to
th
e
r
ec
eiv
er
b
u
t
n
o
t
to
th
e
tr
an
s
m
itter
.
W
h
en
t
h
e
tr
a
n
s
m
it
ted
s
i
g
n
al
s
ar
e
i
n
d
ep
en
d
en
t
w
it
h
e
q
u
al
p
o
w
er
at
ea
c
h
an
ten
n
a,
t
h
e
er
g
o
d
ic
ch
a
n
n
el
c
ap
ac
it
y
t
ak
e
n
o
v
er
t
h
e
p
r
o
b
ab
i
lit
y
d
is
tr
ib
u
tio
n
o
f
G
is
g
iv
e
n
b
y
:
=
{
2
[
(
+
×
]
}
(
6)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
I
C
T
I
SS
N:
2252
-
8776
A
n
ew co
mp
lexity
r
ed
u
ctio
n
m
eth
o
d
s
o
f V
-
B
LAS
T MI
MO syst
em
in
a
co
mmu
n
ica
ti
o
n
ch
a
n
n
el
(
S
u
n
ita
P
a
n
d
a
)
31
W
h
er
e
G
is
a
n
×
tr
an
s
f
er
m
atr
ix
o
f
th
e
f
lat
-
f
ad
i
n
g
ch
a
n
n
e
l,
P
is
th
e
to
tal
tr
an
s
m
i
tted
p
o
w
er
,
an
d
N
is
t
h
e
v
ar
ia
n
ce
o
f
t
h
e
in
d
ep
en
d
en
t G
au
s
s
ia
n
n
o
i
s
e
at
ea
ch
r
ec
eiv
e
a
n
ten
n
a.
C
h
a
n
n
el
ca
p
ac
it
y
d
escr
ib
es
u
t
m
o
s
t
er
r
o
r
-
f
r
ee
d
ata
r
a
te
th
at
a
ch
an
n
el
ca
n
h
o
ld
.
I
n
F
ig
u
r
e
2
s
h
o
w
s
MI
MO
ch
a
n
n
e
l
ca
p
ac
it
y
f
o
r
A
W
GN
in
a
v
ar
iab
le
tr
an
s
m
it
tin
g
a
n
ten
n
a
k
ee
p
i
n
g
a
f
ix
ed
n
u
m
b
er
o
f
r
ec
eiv
i
n
g
an
ten
n
a
a
n
d
F
i
g
u
r
e
3
al
s
o
id
en
ti
f
ies
h
o
w
c
h
an
n
el
ca
p
ac
it
y
af
f
ec
t
s
i
n
v
ar
iab
le
n
u
m
b
er
o
f
tr
an
s
m
i
tti
n
g
a
n
d
r
ec
eiv
in
g
a
n
ten
n
a.
Fig
u
r
e
2
.
MI
MO
ch
an
n
el
ca
p
ac
it
y
(
v
ar
iab
le
tr
an
s
m
itti
n
g
an
te
n
n
a
k
ee
p
i
n
g
a
f
ix
ed
n
u
m
b
er
o
f
r
ec
eiv
in
g
a
n
ten
n
a)
Fig
u
r
e
3
.
MI
MO
ch
an
n
el
ca
p
ac
it
y
(
v
ar
iab
le
n
u
m
b
er
o
f
tr
an
s
m
it
tin
g
a
n
d
r
ec
eiv
in
g
a
n
ten
n
a)
4.
V
-
B
L
AST
P
RO
C
E
DUR
E
:
Gen
er
all
y
i
n
tr
an
s
m
itti
n
g
s
y
s
t
e
m
a
in
f
o
r
m
atio
n
i
s
d
ec
o
d
ed
a
n
d
ad
d
icted
to
a
n
u
m
b
er
o
f
s
u
b
-
s
ec
tio
n
s
ca
lled
as
la
y
er
s
.
T
h
e
la
y
er
s
ar
e
p
r
ec
is
e
p
ar
allel
tr
an
s
v
e
r
s
el
y
t
h
e
f
r
ee
d
o
m
a
n
d
th
e
c
y
cl
i
n
g
p
r
o
ce
s
s
is
d
is
co
n
n
ec
ted
b
ef
o
r
e
co
m
m
u
n
icatio
n
.
A
r
r
iv
i
n
g
s
i
g
n
al
at
ev
er
y
e
n
d
o
f
ta
k
e
d
eli
v
er
y
o
f
a
n
te
n
n
a
is
a
s
u
p
er
p
o
s
itio
n
o
f
N
f
ad
ed
s
y
m
b
o
l
s
w
it
h
A
W
GN.
P
ar
ticu
l
ar
l
y
in
B
L
A
ST
s
y
s
te
m
s
,
i.e
.
s
p
ac
e
an
d
ti
m
e,
id
en
ti
f
icatio
n
m
e
th
o
d
is
o
b
tain
ed
u
p
r
ig
h
t
f
o
r
e
v
er
y
r
ec
ei
v
e
d
v
ec
to
r
.
E
x
cl
u
s
i
v
el
y
b
ea
ti
n
g
o
f
s
i
m
p
li
f
icatio
n
,
s
u
p
p
o
s
e
th
at
th
e
i
n
itia
l
ch
ar
a
cter
is
to
b
e
id
en
tif
ied
.
T
h
e
id
en
ti
f
icatio
n
p
r
o
ce
d
u
r
e
m
ai
n
l
y
t
w
o
s
tep
s
,
i.e
.
,
n
o
s
i
n
ess
r
ep
r
ess
io
n
a
n
d
i
n
ter
f
er
en
ce
ca
n
ce
llatio
n
(
s
u
b
tr
ac
ti
o
n
)
.
T
h
e
co
n
tai
n
m
en
t
p
r
o
ce
s
s
n
u
ll
s
o
u
t
i
n
tr
u
s
io
n
b
y
an
al
y
tical
th
e
ar
r
iv
i
n
g
v
ec
t
o
r
o
n
to
th
e
u
n
ac
ce
p
tab
le
s
u
b
s
p
ac
e
o
f
th
e
s
u
b
s
p
ac
e
s
p
an
n
ed
w
it
h
th
e
in
q
u
is
it
iv
e
in
f
o
r
m
atio
n
.
Fo
llo
w
in
g
t
h
at,
th
e
u
s
u
a
l
f
i
n
d
i
n
g
o
f
th
e
p
r
i
m
ar
y
s
y
m
b
o
l
is
d
o
n
e.
I
n
ter
v
e
n
tio
n
ter
m
i
n
atio
n
is
n
o
th
i
n
g
b
u
t
id
en
t
i
f
ied
s
y
m
b
o
l
is
eli
m
i
n
ated
as
o
f
t
h
e
a
r
r
iv
in
g
v
ec
to
r
.
T
h
e
B
L
A
ST
d
is
co
v
er
y
m
e
th
o
d
co
m
b
i
n
es
b
o
th
li
n
ea
r
as
w
e
ll a
s
n
o
n
li
n
ea
r
alg
o
r
it
h
m
s
.
I
n
a
s
i
m
u
latio
n
u
s
in
g
m
atlab
R
2
0
0
9
s
i
m
b
o
l e
r
r
o
r
r
ate
o
f
V
–
B
L
A
ST
1
6
×
4
QA
M
ca
n
b
e
m
ea
s
u
r
ed
as
s
h
o
w
n
F
ig
u
r
e
4
.
Star
tin
g
w
it
h
g
en
er
atio
n
o
f
Q
A
M
s
i
g
n
al
a
n
d
th
en
ad
d
w
it
h
A
W
GN
an
d
f
in
all
y
d
ec
o
d
in
g
t
h
e
r
ec
eiv
ed
s
y
m
b
o
l
f
o
r
v
ar
io
u
s
v
al
u
es.
0
5
10
15
20
25
30
0
5
10
15
20
25
30
35
S
N
R
(
d
B
)
C
h
a
n
n
e
l
C
a
p
a
c
i
t
y
(
b
i
t
/
S
/
H
z
)
M
I
M
O
C
h
a
n
n
e
l
C
a
p
a
c
i
t
y
4
*
4
3
*
4
2
*
4
1
*
4
1
*
1
0
5
10
15
20
25
30
0
5
10
15
20
25
30
35
S
I
G
N
A
L
T
O
N
O
I
S
E
R
A
T
I
O
(
d
B
)
C
H
A
N
N
E
L
C
A
P
A
C
I
T
Y
(
b
i
t
/
S
/
H
z
)
M
I
M
O
C
H
A
N
N
E
L
C
A
P
A
C
I
T
Y
4
*
4
3
*
3
2
*
2
1
*
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8776
IJ
-
I
C
T
Vo
l.
8
,
No
.
1
,
A
p
r
il
2
0
1
9
:
29
–
38
32
Fig
u
r
e
4
.
SER
p
er
f
o
r
m
a
n
ce
s
o
f
V
-
B
L
AST
1
6
×
4
QA
M
5.
V
-
B
L
AST
D
E
T
E
C
T
I
O
N
M
E
T
H
O
DS:
B
L
A
ST
MI
MO
d
etec
tio
n
ca
n
b
e
clas
s
i
f
ied
i
n
t
w
o
ca
te
g
o
r
ies
i.e
:
1
)
L
i
n
ea
r
(
Z
F
an
d
MM
SE)
,
2
)
No
n
lin
ea
r
(
ML
a
n
d
VB
L
AST
)
P
er
f
o
r
m
a
n
ce
o
f
b
o
th
lin
er
n
o
n
lin
ea
r
d
etec
tio
n
s
c
h
e
m
e
ca
n
b
e
an
al
y
ze
d
th
r
o
u
g
h
an
i
n
d
ex
c
alled
as
b
it
er
r
o
r
r
ate
(
B
E
R
)
.
No
n
lin
ea
r
V
-
B
L
AST
d
e
tectio
n
al
g
o
r
ith
m
p
r
o
v
id
es
a
g
o
o
d
B
E
R
p
er
f
o
r
m
a
n
ce
co
m
p
ar
ed
to
lin
er
o
n
e.
5
.
1
.
Z
er
o
F
o
rc
ing
(
Z
F
)
I
t
is
o
n
e
o
f
th
e
m
o
s
t
s
u
itab
le
an
d
s
i
m
p
le
s
t
d
etec
tio
n
s
c
h
e
m
e
in
V
-
B
L
A
ST
MI
MO
s
y
s
te
m
.
Gen
er
all
y
ze
r
o
f
o
r
cin
g
i
s
n
o
th
i
n
g
b
u
t o
p
p
o
s
ite
f
ilter
w
h
ic
h
i
s
to
r
ec
o
m
p
e
n
s
e
t
h
e
ch
a
n
n
el
o
u
tp
u
t
f
u
n
ct
io
n
.
A
s
it
is
a
lin
ea
r
eq
u
alize
r
,
it
d
o
es
n
o
t
ta
k
e
t
h
e
n
o
is
e
b
u
t
w
i
ll
p
er
f
o
r
m
b
etter
in
h
i
g
h
s
i
g
n
al
to
n
o
is
e
r
atio
.
W
e
co
n
s
id
er
is
th
e
ze
r
o
f
o
r
cin
g
eq
u
alize
r
m
a
t
r
ix
th
e
n
it
m
u
s
t a
s
s
u
r
e
t
h
e
f
o
ll
o
w
i
n
g
cr
iter
ia
.
=
1
(7
)
No
w
,
=
(
H
)
−
1
(8
)
As
f
ar
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er
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o
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m
a
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ce
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al
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ate
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h
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g
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m
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lat
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er
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d
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ad
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er
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n
F
ig
u
r
e
6
s
h
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r
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ate
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er
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ce
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F
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ee
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Fig
u
r
e
5
.
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E
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p
er
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Z
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F
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d
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Fig
u
r
e
6
.
V
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B
L
AST
Z
F d
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r
(
u
n
ch
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n
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n
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a
0
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10
15
10
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L
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T
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=
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21
22
23
24
25
26
27
28
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r
x
=
4
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
I
C
T
I
SS
N:
2252
-
8776
A
n
ew co
mp
lexity
r
ed
u
ctio
n
m
eth
o
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o
f V
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2
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M
ini
m
u
m
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ea
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re
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M
M
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ar
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m
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er
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et
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d
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ate
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m
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ain
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est
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ar
as
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li
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ea
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d
etec
to
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is
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ce
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ed
.
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f
is
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e
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MSE
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atr
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f
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er
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s
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alize
r
.
=
(
H
+
1
S
N
R
I
)
−
1
(9
)
5
.
3
.
Su
cc
ess
iv
e
inte
rf
er
ence
ca
ncella
t
io
n (
SI
C)
Gen
er
all
y
t
h
e
r
es
u
lt
o
f
th
e
p
r
ev
io
u
s
l
y
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ti
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ied
s
y
m
b
o
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u
s
ed
to
w
it
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r
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w
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ter
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ce
o
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cc
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s
s
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m
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ted
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u
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t
g
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is
e
to
a
m
et
h
o
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lled
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e
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io
n
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ir
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ted
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etec
tio
n
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o
d
e
an
d
al
s
o
it is
ca
lled
as S
u
cc
ess
iv
e
I
n
ter
f
er
en
ce
C
a
n
ce
lla
tio
n
(
SIC)
[
7
]
.
As
f
ar
as
lo
w
co
m
p
lex
it
y
is
co
n
ce
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n
ed
s
u
b
-
o
p
ti
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al
al
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o
r
ith
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f
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r
Z
F
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SIC,M
MSE
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SI
C
co
n
s
is
t
o
f
f
o
llo
w
in
g
s
tep
s
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a.
Or
d
er
in
g
:
Dec
id
e
t
h
e
m
o
s
t
f
a
v
o
u
r
ab
le
d
etec
tio
n
o
r
d
er
co
r
r
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n
d
s
to
to
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te
o
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t
th
e
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x
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tr
ea
m
w
it
h
m
i
n
i
m
u
m
er
r
o
r
d
is
cr
ep
an
c
y
.
b.
I
n
ter
f
er
en
ce
C
an
ce
l
latio
n
:
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p
r
o
x
im
a
tio
n
th
e
s
ig
n
al
f
r
o
m
th
e
tr
an
s
m
itter
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ta
k
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a
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in
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tic
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t
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ec
to
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c.
Sli
cin
g
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h
e
A
p
p
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m
ate
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d
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th
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s
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l
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d
in
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en
t
w
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n
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d.
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ter
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a
n
ce
llatio
n
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u
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tr
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iv
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s
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er
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o
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d
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ic
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lt
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s
e
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ld
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ll
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n
d
v
o
id
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m
t
h
e
i
n
w
ar
d
s
i
g
n
al
v
ec
to
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f
o
r
th
e
r
e
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ain
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an
s
m
itti
n
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g
n
al.
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n
a
s
i
m
u
latio
n
g
r
ap
h
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
7
w
h
ic
h
d
escr
ib
es
er
r
o
r
p
r
o
b
ab
ilit
y
o
f
V
-
B
L
AST
2
×
2
Z
F,
Z
F
-
O
SIC,M
MSE
A
N
D
M
MSE
-
O
SIC
Fig
u
r
e
7
.
E
r
r
o
r
p
r
o
b
ab
ilit
y
o
f
V
-
B
L
AST
2
×2
Z
F,
Z
F
-
OSI
C
,
MM
SE
an
d
MM
SE
-
OSI
C
5
.
4
.
M
AXI
M
U
M
L
I
K
E
L
I
H
O
O
D
(
M
L
)
:
I
t
is
o
n
e
o
f
t
h
e
eq
u
aliza
t
io
n
m
eth
o
d
u
s
ed
i
n
n
o
n
lin
ea
r
c
h
an
n
el.
Se
v
er
al
d
r
a
w
b
ac
k
s
w
h
ic
h
co
m
e
s
in
Z
F
a
n
d
MM
SE
a
n
d
also
SI
C
d
etec
tio
n
m
et
h
o
d
w
h
ic
h
ca
n
b
e
r
eso
lv
ed
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th
i
s
m
et
h
o
d
.
E
v
en
t
h
o
u
g
h
co
m
p
u
tatio
n
al
co
m
p
le
x
itie
s
m
o
r
e
t
h
a
n
t
h
e
p
r
ev
io
u
s
m
et
h
o
d
b
u
t
p
r
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tatio
n
o
f
t
h
is
d
etec
tio
n
tec
h
n
iq
u
e
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s
m
o
r
e
r
eliab
le
th
a
n
p
r
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io
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s
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n
e.
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h
is
tech
n
iq
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es
w
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r
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th
e
r
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le
o
f
m
a
x
i
m
u
m
li
k
eli
h
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o
d
[
8
]
b
et
w
ee
n
t
h
e
ar
r
iv
in
g
s
i
g
n
a
l
an
d
th
e
m
u
l
ti
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n
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el
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atr
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x
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w
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t
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th
e
T
x
s
ig
n
al
s
to
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ca
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t
th
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e
w
ith
lea
s
t
d
is
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ce
.
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h
e
ap
p
r
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x
i
m
ate
tr
a
n
s
m
itted
s
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g
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al
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ca
n
b
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s
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g
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L
d
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tio
n
m
et
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o
d
w
h
ic
h
is
i
n
th
e
f
o
llo
w
i
n
g
eq
u
atio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8776
IJ
-
I
C
T
Vo
l.
8
,
No
.
1
,
A
p
r
il
2
0
1
9
:
29
–
38
34
̂
=
[
|
−
|
]
2
̂
(
1
0
)
F
ca
n
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e
tak
e
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as
Fro
b
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i
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o
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m
.
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n
F
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g
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r
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8
s
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m
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o
n
B
E
R
g
r
ap
h
o
f
4
×4
MM
SE
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SI
C
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d
ML
d
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to
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an
d
F
ig
u
r
e
9
w
h
ic
h
d
escr
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h
o
w
V
-
B
L
A
ST
QR
d
ec
o
m
p
o
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it
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n
d
etec
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n
b
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er
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tr
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F d
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to
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.
Fig
u
r
e
8
.
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E
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p
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r
m
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s
o
f
V
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etec
tio
n
(
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Fig
u
r
e
9
.
B
E
R
p
er
f
o
r
m
a
n
ce
s
o
f
V
-
B
L
AST
QR
d
ec
o
m
p
o
s
itio
n
d
etec
tio
n
5
.
5
.
V
B
L
AST
-
S
T
B
C
:
VB
L
A
ST
-
ST
B
C
[
9
-
1
2
]
s
y
s
te
m
co
n
s
is
t
o
f
M
tr
a
n
s
m
it
a
n
d
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n
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n
as
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d
t
h
e
tr
an
s
m
itted
s
y
m
b
o
ls
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e
m
u
ltip
le
x
ed
in
to
(
X+
Y)
la
y
er
s
,
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e
h
i
g
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er
X
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e
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en
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e
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er
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i
n
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e
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h
e
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~
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e
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ted
as th
e
ST
B
C
la
y
er
s
,
i
n
w
h
ich
t
h
e
s
y
m
b
o
ls
ar
e
en
co
d
ed
w
ith
g
2
co
d
e
an
d
ar
e
tr
an
s
m
itted
b
y
2
C
a
n
te
n
n
as.
T
h
e
ch
an
n
el
ca
n
b
e
d
escr
ib
ed
as
∈
−
.
W
h
er
e
ch
an
n
el
s
tate
co
ef
f
icie
n
t
ca
n
b
e
d
en
o
ted
as
ℎ
W
h
ich
is
a
co
m
p
le
x
g
ain
f
r
o
m
it
tr
a
n
s
m
it
ted
an
te
n
n
a
t
o
j
th
r
ec
eiv
e
an
te
n
n
a.
T
h
e
s
y
s
te
m
f
u
n
ctio
n
ca
n
b
e
r
ep
r
es
en
ted
as
=
̇
+
,
w
h
er
e
r
is
t
h
e
r
ec
eiv
ed
m
atr
i
x
,
an
d
n
is
th
e
A
W
GN
n
o
is
e
m
atr
ix
a
n
d
X
i
s
t
h
e
tr
a
n
s
m
itted
b
lo
ck
m
atr
i
x
.
T
h
e
tr
an
s
m
itted
p
o
w
er
o
f
ea
ch
s
y
m
b
o
l
i
n
X
is
d
ef
in
ed
as
[
|
|
2
]
=
W
h
er
e
is
th
e
to
tal
tr
an
s
m
i
tted
p
o
w
er
.
A
t t
h
e
r
ec
eiv
er
,
t
h
e
ch
a
n
n
e
l
m
atr
ix
̇
is
d
ec
o
m
p
o
s
ed
as
̇
=
b
y
ex
p
lo
it QR d
ec
o
m
p
o
s
itio
n
.
5
.
6
.
Q
-
R
deco
m
po
s
it
io
n
I
t is o
n
e
o
f
th
e
m
et
h
o
d
s
to
s
o
l
v
e
m
atr
ix
i
n
v
er
s
io
n
p
r
o
b
le
m
a
n
d
ca
n
b
e
ca
lc
u
lated
w
it
h
̇
=
[
]
∗
[
]
.
Fig
u
r
e
9
s
h
o
w
s
B
E
R
p
er
f
o
r
m
an
ce
o
f
V
-
B
L
AST
QR
d
ec
o
m
p
o
s
itio
n
d
etec
tio
n
.
C
o
m
p
le
x
it
y
is
s
u
e:
As
f
ar
as
co
m
p
u
tatio
n
al
co
m
p
le
x
it
y
i
s
c
o
n
ce
r
n
ed
th
e
ab
o
v
e
d
ec
o
d
er
s
m
en
tio
n
in
th
i
s
p
ap
er
w
it
h
H
is
h
ig
h
.
I
n
o
r
d
er
to
i
m
p
r
o
v
e
t
h
e
co
m
p
u
ta
tio
n
al
c
o
m
p
le
x
itie
s
w
e
h
av
e
to
m
o
d
if
y
it
an
d
s
e
t
a
m
i
n
i
m
u
m
co
m
p
lex
i
ties
w
i
th
Q
R
d
ec
o
m
p
o
s
itio
n
is
p
r
o
p
o
s
ed
.
T
h
e
d
im
e
n
s
io
n
s
4
N×
(
M
-
1
)
ar
e
u
s
ed
f
o
r
d
ep
ar
tu
r
e
s
y
m
b
o
ls
w
i
th
it
s
ch
a
n
n
el
m
atr
i
x
H
ca
n
b
e
r
ep
lace
d
w
it
h
N
×
M
.
T
h
e
co
m
p
le
x
it
y
r
ed
u
ctio
n
w
it
h
Q
R
d
ec
o
m
p
o
s
it
io
n
is
in
v
alid
f
o
r
th
e
d
i
m
en
s
io
n
N
<
M
-
1
.
6.
P
RO
P
O
SE
D
L
C
-
Q
R
A
L
G
O
RIT
H
M
Step
i.
Gen
er
all
y
d
ec
o
m
p
o
s
i
tio
n
o
f
with
̇
ca
n
b
e
p
er
f
o
r
m
ed
b
y
t
h
e
f
o
llo
w
i
n
g
m
atr
i
x
o
p
er
atio
n
i.e
̇
=
[
11
12
⋯
21
22
…
⋮
1
⋮
2
⋮
…
1
2
⋮
]
[
11
12
…
0
22
…
0
0
0
0
…
0
1
2
⋮
]
Step
ii.
I
f
≥
g
o
to
s
tep
-
iii el
s
e
s
tep
:
v
ii
0
1
2
3
4
5
6
7
8
9
10
10
-2
10
-1
10
0
S
N
R
(
d
B
)
BER
V
B
L
A
S
T
M
L
D
E
T
E
C
T
I
O
N
(
Q
P
S
K
M
O
D
U
L
A
T
I
O
N
)
4
*
4
,
M
M
S
E
-
S
I
C
4
*
4
,
M
L
0
2
4
6
8
10
12
14
16
18
20
10
-3
10
-2
10
-1
10
0
t
x
=
4
,
r
x
=
4
,
V
b
l
a
s
t
Q
R
D
e
c
o
m
p
o
s
i
t
i
o
n
o
f
d
e
t
e
c
t
i
o
n
S
N
R
(
d
B
)
BER
ZF
QR
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
I
C
T
I
SS
N:
2252
-
8776
A
n
ew co
mp
lexity
r
ed
u
ctio
n
m
eth
o
d
s
o
f V
-
B
LAS
T MI
MO syst
em
in
a
co
mmu
n
ica
ti
o
n
ch
a
n
n
el
(
S
u
n
ita
P
a
n
d
a
)
35
Step
iii.
A
p
p
r
o
x
i
m
ate
m
e
s
s
a
g
e
s
i
g
n
al
o
f
ST
B
C
lay
er
w
it
h
2
×
2
d
ec
o
d
er
Step
iv
.
V
-
B
L
AST
la
y
er
d
ep
en
d
s
o
n
th
e
in
itial a
p
p
r
o
x
i
m
a
te
m
e
s
s
a
g
e
s
ig
n
al
o
f
ST
B
C
Step
v
.
No
s
in
e
s
s
d
eletio
n
o
r
ca
n
ce
llat
i
o
n
Step
v
i.
ST
B
C
lev
el
w
i
th
ST
B
C
2
×
N
d
ec
o
d
er
Step
v
ii.
I
f
N
=
M−
1
g
o
to
Step
-
v
i
ii e
ls
e
s
tep
-
x
ii (
in
v
alid
)
Step
v
iii.
p
r
im
ar
y
ap
p
r
o
x
i
m
ated
m
ess
a
g
e
s
ig
n
al
o
f
ST
B
C
la
y
er
w
it
h
2
×
1
d
ec
o
d
er
Step
ix
.
V
-
B
L
AST
la
y
er
d
ep
en
d
s
o
n
th
e
in
itial a
p
p
r
o
x
i
m
a
ted
m
es
s
ag
e
s
ig
n
als o
f
ST
B
C
.
Step
x
.
I
n
tr
u
s
io
n
eli
m
i
n
atio
n
.
Step
x
i.
ST
B
C
w
ith
ST
B
C
(
2
−
2
)
d
ec
o
d
e
r
Step
x
ii.
Sto
p
.
7.
CO
M
P
UT
AT
I
O
NAL
CO
M
P
L
E
XIT
I
E
S
O
F
P
RO
P
O
SE
D
Q
R
DE
CO
M
P
O
S
I
T
I
O
N
W
I
T
H
CO
NVEN
T
I
O
NA
L
D
E
CO
D
E
R
T
h
e
d
im
e
n
s
io
n
2
(
−
1
)
×
2
o
f
t
h
e
c
h
an
n
el
tr
an
s
f
er
f
u
n
ct
io
n
H
ca
n
b
e
d
eter
m
i
n
ed
t
h
r
o
u
g
h
co
m
p
le
x
it
y
o
f
tr
ad
itio
n
a
l d
ec
o
d
er
s
s
u
ch
a
s
ze
r
o
f
o
r
ce
,
m
in
i
m
u
m
m
ea
n
s
q
u
ar
e
a
n
d
co
n
v
e
n
ti
o
n
al
QR
d
ec
o
d
er
.
a.
Z
F
by
m
ea
ns
o
f
Cha
nn
el
̇
:
T
o
co
m
p
u
te
t
h
e
Z
F e
q
u
al
izer
Y
f
r
o
m
eq
u
atio
n
(
7
)
is
co
n
s
is
t
s
o
f
f
o
llo
w
i
n
g
Step
s
.
Step
i.
8
(
−
1
)
2
×
m
u
lt
ip
licatio
n
s
a
n
d
4
(
−
1
)
2
×
(
2
−
1
)
ad
d
itio
n
s
r
eq
u
ir
ed
f
o
r
m
u
ltip
l
y
w
it
h
.
So
to
tal
ar
ith
m
etic
o
p
er
atio
n
s
r
eq
u
ir
ed
is
4
(
−
1
)
2
×
(
4
−
1
)
Step
ii.
I
n
th
i
s
s
tep
Ga
u
s
s
ian
el
i
m
in
a
tio
n
m
a
tr
ix
i
n
v
er
s
io
n
o
f
.
T
h
er
ef
o
r
e
th
e
n
u
m
b
er
o
f
m
u
lt
if
ac
eted
ca
lcu
latio
n
in
t
h
is
m
o
v
e
i
s
2
3
(
−
1
)
3
.
Step
iii.
E
x
ec
u
te
(
)
−
1
w
i
th
.
I
t n
ee
d
s
2
3
(
−
1
)
2
×
m
u
ltip
licati
o
n
s
a
n
d
2
3
(
−
1
)
2
−
4
(
−
1
)
Step
iv
.
A
d
d
itio
n
s
.
T
h
er
ef
o
r
e
to
tal
ar
ith
m
e
tic
ca
lcu
latio
n
s
in
t
h
i
s
s
te
p
is
2
4
(
−
1
)
3
−
4
(
−
1
)
.
Step
v
.
C
alcu
late
eq
u
alize
r
m
atr
i
x
Y
m
u
ltip
l
y
in
g
w
i
th
r
ec
ei
v
ed
v
ec
to
r
.
T
h
er
ef
o
r
e
th
e
to
tal
n
u
m
b
er
o
f
ar
ith
m
etic
o
p
er
atio
n
s
i
n
t
h
e
Z
F
-
VB
L
A
ST
s
y
s
te
m
is
2
3
(
−
1
)
3
+
2
2
(
−
1
)
2
×
(
8
−
1
)
+
2
(
−
1
)
(
2
−
1
)
.
b.
M
M
SE
w
it
h Cha
nn
el
H
T
o
ca
lcu
late
th
e
MM
SE
eq
u
ali
ze
r
f
ilter
m
atr
i
x
Y
f
r
o
m
eq
u
ati
o
n
(
8
)
is
co
n
s
is
t
s
o
f
f
o
llo
w
i
n
g
Step
s
.
Step
i.
8
(
−
1
)
2
×
mul
tip
licatio
n
s
a
n
d
4
(
−
1
)
2
×
(
2
−
1
)
ad
d
itio
n
s
r
eq
u
ir
ed
f
o
r
m
u
ltip
l
y
w
it
h
.
So
to
tal
ar
ith
m
atic
o
p
er
atio
n
s
r
eq
u
ir
ed
is
4
(
−
1
)
2
×
(
4
−
1
)
.
Step
ii.
p
er
f
o
r
m
s
ad
d
itio
n
o
f
w
it
h
1
S
N
R
I
.
T
h
er
ef
o
r
e
th
e
to
tal
ar
ith
m
et
i
c
ca
lcu
latio
n
s
i
n
th
i
s
s
tep
is
2
(
−
1
)
.
Step
iii.
I
n
th
i
s
s
tep
Ga
u
s
s
ian
eli
m
i
n
atio
n
m
atr
i
x
in
v
er
s
io
n
o
f
(
+
2
)
.
T
h
er
ef
o
r
e
ar
i
th
m
eti
c
ca
lcu
latio
n
s
i
n
th
i
s
s
tep
is
8
(
−
1
)
3
.
Step
iv
.
E
x
ec
u
te
(
+
2
)
−
1
w
i
th
.
Step
v
.
C
alcu
late
eq
u
al
izer
m
atr
ix
Y
m
u
ltip
l
y
in
g
w
i
th
r
ec
eiv
ed
v
ec
to
r
.
T
h
er
ef
o
r
e
to
tal
n
u
m
b
er
o
f
ar
ith
m
eti
c
o
p
er
atio
n
s
in
MM
SE
-
VB
L
A
S
T
s
y
s
te
m
i
s
2
3
(
−
1
)
3
+
2
2
(
−
1
)
2
×
(
8
−
1
)
+
2
2
(
−
1
)
.
c.
T
ra
ditio
na
l Q
R
deco
m
po
s
it
i
o
n by
m
ea
n
s
o
f
H
Step
i.
No
w
QR
d
ec
o
m
p
o
s
itio
n
w
it
h
H
ca
n
b
e
p
er
f
o
r
m
ed
w
it
h
r
ec
eiv
ed
s
ig
n
al
v
ec
to
r
.
B
ec
au
s
e
t
h
e
asp
ec
t
o
f
th
e
ch
a
n
n
e
l
tr
an
s
f
er
f
u
n
ctio
n
i
s
2
(
−
1
)
×
2
.
T
h
er
ef
o
r
e
to
tal
ar
ith
m
etic
o
p
er
atio
n
s
o
f
th
is
m
et
h
o
d
is
8
(
−
1
)
2
+
8
3
(
1
−
)
(
−
1
)
2
.
T
h
u
s
to
tal
n
u
m
b
er
o
f
ar
ith
m
etic
ca
lc
u
latio
n
s
i
n
QR
d
ec
o
m
p
o
s
itio
n
i
s
8
(
−
1
)
2
+
8
3
(
1
−
)
(
−
1
)
2
+
2
(
−
1
)
(
4
−
1
)
.
Step
ii.
I
t
d
ec
o
d
es
d
ep
a
r
tu
r
e
s
y
m
b
o
l
s
w
it
h
to
w
ar
d
s
t
h
e
b
ac
k
r
ep
lace
m
en
t
w
it
h
ca
n
ce
l
latio
n
a
n
d
it
n
ee
d
s
(
2
M
−
3
)
×
(
M
−
1
)
m
u
lt
ip
licat
io
n
s
,
(M
−
2
)
×(
2
M
−
3
)
ad
d
itio
n
s
,
2
(
M
−
1
)
−
1
s
u
b
tr
ac
tio
n
s
an
d
2
(
M
−
1
)
d
iv
is
io
n
s
.
T
h
er
ef
o
r
e
th
e
o
v
er
all
m
u
l
tif
ac
e
ted
s
u
m
s
ca
lc
u
l
atio
n
s
o
f
s
tr
ai
g
h
t
QR
d
ec
o
m
p
o
s
itio
n
is
8
(
−
1
)
3
+
8
3
(
1
−
)
(
−
1
)
2
+
(
2
−
3
)
2
+
2
(
−
1
)
(
4
+
1
)
−
1
.
d.
L
o
w
co
m
ple
x
it
ies
Q
R
w
it
h H
Step
i.
A
p
p
l
y
Q
R
d
ec
o
m
p
o
s
i
tio
n
[
1
3
-
14
]
to
th
e
ch
an
n
el
H
an
d
m
u
l
tip
licatio
n
o
f
w
i
th
.
No
w
×
is
th
e
d
i
m
en
s
io
n
o
f
th
e
ch
a
n
n
el
tr
an
s
f
er
f
u
n
ct
io
n
H
th
er
ef
o
r
e
ar
ith
m
etic
ca
lcu
la
tio
n
is
2
3
3
.
A
f
t
er
m
u
ltip
licatio
n
o
f
w
it
h
it
r
eq
u
ir
e
×
m
u
ltip
licatio
n
s
a
n
d
(
−
1
)
×
ad
d
itio
n
s
’
.
T
h
u
s
,
to
tal
ca
lcu
latio
n
s
i
n
th
i
s
s
tep
i
s
is
2
3
3
+
.
(
2
−
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8776
IJ
-
I
C
T
Vo
l.
8
,
No
.
1
,
A
p
r
il
2
0
1
9
:
29
–
38
36
Step
ii.
I
n
th
is
f
ir
s
t
ap
p
r
o
x
i
m
atio
n
s
ig
n
a
ls
o
f
th
e
ST
B
C
la
y
er
w
ith
2
×
2
r
ec
eiv
er
.
I
t
r
eq
u
ir
es
6
m
u
ltip
licatio
n
s
,
3
ad
d
itio
n
s
an
d
1
s
u
b
tr
ac
tio
n
.
T
h
er
ef
o
r
e
ar
it
h
m
e
tic
ca
lcu
latio
n
s
in
t
h
i
s
s
te
p
is
1
0
.
Step
iii.
I
n
lo
w
co
m
p
le
x
it
y
Q
R
d
ec
o
m
p
o
s
itio
n
d
ata
s
y
m
b
o
ls
o
f
V
-
B
L
AST
la
y
er
o
f
in
i
tial
ap
p
r
o
x
i
m
atio
n
s
y
g
n
a
l
co
n
tai
n
s
(
−
1
)
(
−
2
)
ad
d
itio
n
s
2
(
−
2
)
s
u
b
tr
ac
tio
n
s
(
+
1
)
(
−
2
)
m
u
ltip
licatio
n
s
an
d
2
(
−
2
)
d
iv
is
io
n
s
.
T
h
u
s
th
e
ar
it
h
m
etic
ca
lcu
l
atio
n
s
i
n
th
is
s
ta
g
e
i
s
2
(
−
2
)
(
+
2
)
Step
iv
.
I
n
th
i
s
is
f
o
r
in
ter
f
er
e
n
ce
ca
n
ce
llatio
n
.
T
h
u
s
t
h
e
n
u
m
b
er
n
u
m
b
er
o
f
ca
lcu
latio
n
i
n
t
h
is
s
tep
is
4
(
−
2
)
.
Step
v
.
T
h
u
s
n
u
m
b
er
o
f
co
m
p
le
x
ar
it
h
m
etic
o
p
er
atio
n
s
in
th
i
s
s
tep
2
(
4
−
1
)
.
Ulti
m
a
tel
y
,
th
e
to
tal
s
u
m
s
o
f
LC
-
Q
R
is
2
−
3
3
+
(
+
2
)
(
2
−
1
)
+
2
(
2
−
4
)
+
4
(
−
1
)
+
10
T
ab
le
1
s
h
o
w
s
co
m
p
ar
i
s
o
n
s
o
f
d
if
f
er
en
t
d
ec
o
d
er
s
i
n
w
h
ic
h
p
r
o
p
o
s
ed
L
C
-
Q
R
d
ec
o
d
er
p
r
o
v
id
es
le
s
s
ar
ith
m
etic
o
p
er
atio
n
s
th
a
n
o
th
er
m
e
n
tio
n
ed
d
ec
o
d
er
s
T
ab
le
1
.
C
o
m
p
ar
is
o
n
o
f
Dif
f
er
en
t D
ec
o
d
er
s
D
e
c
o
d
e
r
s
T
o
t
a
l
c
o
mp
l
e
x
a
r
i
t
h
m
a
t
i
c
o
p
e
r
a
t
i
o
n
s
ZF
w
i
t
h
H
8
(
−
1
)
3
+
4
(
−
1
)
2
×
(
8
−
1
)
+
2
(
−
1
)
(
2
−
1
)
M
M
S
E
w
i
t
h
H
2
3
(
−
1
)
3
+
2
2
(
−
1
)
2
×
(
8
−
1
)
+
(
4
−
4
)
QR
w
i
t
h
H
8
(
−
1
)
3
+
8
3
(
1
−
)
(
−
1
)
2
+
(
2
−
3
)
2
+
2
(
−
1
)
(
4
+
1
)
−
1
L
o
w
c
o
mp
l
e
x
i
t
y
-
Q
R
w
i
t
h
H
2
−
3
3
+
(
+
2
)
(
2
−
1
)
+
2
(
2
−
4
)
+
4
(
−
1
)
+
1
8.
E
RRO
R
P
RO
B
AB
I
L
I
T
Y
I
N
V
-
B
L
AST
SYS
T
E
M
WI
T
H
L
O
W
CO
M
P
L
E
XI
T
I
E
S
Q
R
DE
CO
M
P
O
SI
T
I
O
N
T
h
e
ar
r
iv
in
g
s
i
g
n
al
in
MI
M
O
[
1
5
-
17
]
co
m
m
u
n
icatio
n
s
y
s
te
m
b
e
ab
le
to
b
e
d
escr
ib
ed
s
in
ce
=
+
T
h
e
ch
an
n
el
o
r
d
er
is
N
×M
a
n
d
n
is
n
o
t
h
in
g
b
u
t
A
W
GN
h
av
in
g
N
×
2
m
atr
ices
w
it
h
v
a
r
ian
ce
2
.
T
h
e
co
v
ar
ian
ce
m
atr
i
x
o
f
x
i
s
[
∗
]
=
2
.
T
h
e
s
ig
n
al
to
n
o
i
s
e
r
atio
(
SNR
)
ca
n
b
e
d
en
o
ted
as
=
2
2
I
n
a
s
i
m
u
la
ti
o
n
u
s
i
n
g
m
a
tlab
s
h
o
w
n
in
Fig
u
r
e
1
0
w
h
ic
h
d
escr
ib
es
er
r
o
r
p
r
o
b
a
b
ilit
y
o
f
4
×4
V
-
B
L
A
ST
Z
F,M
M
SE
an
d
QR
d
ec
o
m
p
o
s
i
tio
n
d
etec
tio
n
.
C
o
m
p
ar
is
io
n
g
r
ap
h
s
h
o
w
s
QR
d
ec
o
m
p
o
s
i
tio
n
m
eth
o
d
p
r
o
v
id
es b
etter
p
er
f
o
r
m
an
ce
t
h
an
tr
ad
ito
n
al
Z
F a
n
d
MM
SE
co
u
n
ter
p
ar
t.
A
s
f
ar
as
lo
w
co
m
p
lex
i
t
y
QR
m
et
h
o
d
is
co
n
ce
r
n
ed
it p
r
o
v
id
es b
etter
r
esu
lt t
h
an
tr
ad
itio
n
al
QR
,
M
MSE
,
Z
F a
n
d
Z
F
-
I
S
w
h
ic
h
is
s
h
o
w
n
i
n
F
ig
u
r
e
1
1
.
Fig
u
r
e
10.
E
r
r
o
r
p
r
o
b
ab
ilit
y
o
f
4
×4
V
-
B
L
A
ST
Z
F,
MM
SE
an
d
QR
d
ec
o
m
p
o
s
itio
n
d
etec
tio
n
Fig
u
r
e
11.
E
r
r
o
r
p
r
o
b
ab
ilit
y
o
f
p
r
o
p
o
s
ed
4
×4
V
-
B
L
A
ST
9.
P
RO
P
O
SE
D
V
-
B
L
AS
T
WI
T
H
VARIAB
L
E
I
T
E
RA
T
I
O
NS
B
E
R
p
er
f
o
r
m
a
n
ce
s
o
f
V
-
B
L
AST
v
ar
iab
le
it
er
atio
n
m
et
h
o
d
ca
n
b
e
s
h
o
w
n
in
F
i
g
u
r
e
1
2
.
T
ab
le
2
s
h
o
w
s
iter
atio
n
s
Vs
SN
R
.
As
n
u
m
b
er
o
f
iter
atio
n
in
cr
ea
s
es
,
p
ar
ticu
lar
l
y
7
th
iter
atio
n
y
ield
s
lo
w
SN
R
co
r
r
esp
o
n
d
in
g
l
y
s
ig
n
i
f
ica
n
tl
y
i
m
p
r
o
v
e
m
en
t
o
f
B
E
R
as
s
h
o
w
n
in
F
i
g
u
r
e
1
2
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
ca
n
b
e
ap
p
lied
to
4
×4
MI
M
O
–
QP
S
K
s
ch
e
m
e.
B
eg
in
w
it
h
th
e
f
ir
s
t
iter
atio
n
p
r
o
ce
d
u
r
e
m
a
k
e
s
u
r
e
if
th
e
es
ti
m
ated
SNR
g
i
v
es
to
t
h
e
ac
ce
p
ted
B
E
R
o
r
n
o
t.
I
f
y
e
s
t
h
e
r
est
o
f
th
e
s
y
m
b
o
l
s
ar
e
lin
ea
r
l
y
d
et
ec
ted
o
r
else
,
th
e
0
2
4
6
8
10
12
14
16
18
20
0
.
2
4
0
.
2
5
0
.
2
6
0
.
2
7
0
.
2
8
0
.
2
9
0
.
3
0
.
3
1
0
.
3
2
0
.
3
3
E
b
/
N
o
i
n
d
B
e
r
r
o
r
p
r
o
b
a
b
i
l
i
t
y
T
x
=
4
,
R
x
=
4
,
B
P
S
K
m
o
d
u
l
a
t
i
o
n
ZF
M
M
S
E
QR
0
5
10
15
20
25
30
0
0
.
0
2
0
.
0
4
0
.
0
6
0
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0
8
0
.
1
0
.
1
2
E
b
/
N
o
i
n
d
B
e
r
r
o
r
p
r
o
b
a
b
i
l
i
t
y
T
x
=
4
,
R
x
=
4
,
Q
P
S
K
m
o
d
u
l
a
t
i
o
n
Z
F
+
I
S
ZF
M
M
S
E
QR
L
C
-
Q
R
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
I
C
T
I
SS
N:
2252
-
8776
A
n
ew co
mp
lexity
r
ed
u
ctio
n
m
eth
o
d
s
o
f V
-
B
LAS
T MI
MO syst
em
in
a
co
mmu
n
ica
ti
o
n
ch
a
n
n
el
(
S
u
n
ita
P
a
n
d
a
)
37
iter
atio
n
s
ca
r
r
y
o
n
a
w
ai
tin
g
r
ea
ch
in
g
t
h
e
B
E
R
r
eq
u
ir
e
m
e
n
t
.
B
u
t
th
e
o
n
l
y
d
r
a
w
b
ac
k
is
t
h
a
t
f
o
r
lo
w
v
alu
e
s
o
f
SNR
it
i
n
cr
ea
s
es
t
h
e
co
m
p
u
t
atio
n
al
co
m
p
lex
it
y
.
W
e
m
a
y
u
s
e
also
an
o
t
h
er
m
et
h
o
d
to
d
ir
ec
tl
y
f
i
n
d
o
u
t
t
h
e
n
u
m
b
er
o
f
iter
atio
n
s
,
f
r
o
m
t
h
e
SNR
v
alu
e.
Step
i.
I
n
itializi
n
g
(
o
r
d
er
in
g
)
Step
ii.
Nu
m
b
er
o
f
iter
at
io
n
s
Ki=1
Step
iii.
Nu
lli
n
g
,
s
lici
n
g
an
d
ca
n
ce
lla
ti
o
n
Step
iv
.
I
f
o
u
r
tar
g
eted
B
E
R
is
ac
h
iev
e
d
o
r
=
g
o
to
s
tep
-
v
el
s
e
=
−
1
g
o
to
s
t
ep
-
iii
Step
v
.
Sto
p
iter
atio
n
s
an
d
MM
SE
f
o
r
r
est.
Dire
ct
m
et
ho
d:
Step
i.
Step
:i I
n
itializ
in
g
(
o
r
d
er
in
g
)
Step
ii.
Step
:ii Nu
l
lin
g
,
s
l
icin
g
a
n
d
ca
n
ce
llatio
n
Step
iii.
Step
:iii
Get
SN
R
v
a
lu
e
f
r
o
m
e
s
ti
m
ato
r
Step
iv
.
Step
:iv
No
o
f
iter
atio
n
s
=
m
in
(
2
,
m
a
x
(
(
3
4
(
19
−
)
)
)
Step
v
.
Step
:v
MM
SE
li
n
ea
r
d
etec
tio
n
f
o
r
r
est.
Step
v
i.
Step
:v
i s
to
p
T
ab
le
3
s
h
o
w
s
p
er
f
o
r
m
a
n
ce
o
f
co
m
p
lex
it
y
r
atio
u
s
i
n
g
d
if
f
er
e
n
t
al
g
o
r
ith
m
i
n
w
h
ic
h
t
h
e
d
ir
ec
t
m
et
h
o
d
g
iv
e
s
5
8
% c
o
m
p
lex
i
t
y
r
atio
as
co
m
p
ar
ed
w
ith
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I
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N
:
2252
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8776
IJ
-
I
C
T
Vo
l.
8
,
No
.
1
,
A
p
r
il
2
0
1
9
:
29
–
38
38
RE
F
E
R
E
NC
E
S
[1
]
W
.
Ya
n
,
S
.
S
u
n
,
a
n
d
Z.
L
e
i,
“
A
lo
w
c
o
m
p
lex
it
y
V
BLA
S
T
OFDM
d
e
tec
ti
o
n
a
lg
o
ri
th
m
f
o
r
w
irele
ss
LA
N
s
y
ste
m
s,”
IEE
E
Co
mm
u
n
ica
t
io
n
s L
e
tt
e
rs
,
v
o
l.
8
,
n
o
.
6
,
p
p
.
3
7
4
–
3
7
6
,
Ju
n
.
2
0
0
4
.
[2
]
Z.
L
u
o
,
S
.
L
iu
,
M
.
Zh
a
o
,
a
n
d
Y
.
L
iu
,
“
A
No
v
e
l
F
a
st
Re
c
u
rsiv
e
M
M
S
E
-
S
IC
D
e
tec
ti
o
n
A
lg
o
rit
h
m
f
o
r
V
-
BLA
S
T
S
y
st
e
m
s,”
IEE
ET
ra
n
sa
c
ti
o
n
s
o
n
W
ire
les
s Co
mm
u
n
ica
ti
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n
s
,
v
o
l.
6
,
n
o
.
6
,
p
p
.
2
0
2
2
–
2
0
2
5
,
J
u
n
.
2
0
0
7
.
[3
]
He
n
u
c
h
u
l
L
e
,
By
e
o
n
g
si
Lee
,
a
n
d
In
k
y
u
L
e
e
,
“
Itera
ti
v
e
d
e
tec
ti
o
n
a
n
d
d
e
c
o
d
in
g
w
it
h
a
n
im
p
ro
v
e
d
V
-
BL
A
S
T
f
o
r
M
IM
O
-
OFDM
sy
ste
m
s,”
IEE
E
J
o
u
rn
a
l
o
n
S
e
lec
ted
Are
a
s
in
Co
mm
u
n
ica
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n
s
,
v
o
l.
2
4
,
n
o
.
3
,
p
p
.
5
0
4
–
5
1
3
,
M
a
r.
2
0
0
6
.
[4
]
T
.
Ki
m
a
n
d
S
.
C.
P
a
rk
,
“
Re
d
u
c
e
d
c
o
m
p
lex
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e
tec
ti
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f
o
r
V
-
BL
A
S
T
s
y
ste
m
s
f
ro
m
it
e
ra
ti
o
n
c
a
n
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e
ll
in
g
,
”
in
Pro
c
.
2
3
rd
In
ter
n
a
ti
o
n
a
l
T
e
c
h
n
ica
l
C
o
n
fer
e
n
c
e
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n
Circ
u
i
ts/S
y
ste
ms
,
Co
mp
u
ter
s
a
n
d
C
o
mm
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n
ic
a
ti
o
n
s
,
S
h
im
o
n
o
se
k
i,
2
0
0
8
,
p
p
.
4
9
7
–
5
0
0
.
[5
]
S
a
n
d
h
u
S
,
P
a
u
lraj
A
(2
0
0
0
)
S
p
a
c
e
-
T
i
m
e
Blo
c
k
Co
d
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s: A
Ca
p
a
c
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y
P
e
rsp
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ti
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e
.
IEE
E
Co
mm
u
n
L
e
tt
4
(1
2
):3
8
4
–
3
8
6
.
[6
]
S
.
M
.
A
la
m
o
u
t
i,
“
A
si
m
p
le
tra
n
sm
it
d
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rsit
y
tec
h
n
iq
u
e
f
o
r
wire
les
s
c
o
m
m
u
n
ica
ti
o
n
s,”
I
EE
E
J
.
S
e
lec
t.
Are
a
s
Co
mm
.
,
V
o
l
.
1
6
,
No
.
8
,
Oc
to
b
e
r
1
9
9
8
.
[7
]
G
.
J.
F
o
sc
h
in
i,
“
L
a
y
e
re
d
sp
a
c
e
-
ti
m
e
a
r
c
h
it
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c
tu
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o
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w
ir
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les
s
c
o
m
m
u
n
ica
ti
o
n
in
a
fa
d
in
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e
n
v
iro
n
m
e
n
t
w
h
e
n
u
sin
g
m
u
lt
i
-
e
le
m
e
n
a
n
ten
n
a
s”
,
Bell
L
a
b
s T
e
c
h
n
ica
l
J
o
u
r
n
a
l
,
1
9
9
6
.
[8
]
W
in
d
p
a
ss
in
g
e
r,
C.
,
&
F
isc
h
e
r,
R.
F
.
(2
0
0
3
,
M
a
rc
h
).
L
o
w
-
c
o
m
p
lex
it
y
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e
a
r
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m
a
x
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m
u
m
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p
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o
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g
f
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r
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IM
O
s
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s
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s
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e
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d
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ti
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.
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n
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n
fo
rm
a
t
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h
e
o
ry
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o
rk
sh
o
p
,
2
0
0
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.
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o
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e
e
d
in
g
s.
2
0
0
3
IEE
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(p
p
.
3
4
5
-
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4
8
)
.
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E
.
[9
]
M
a
o
T
,
M
o
tan
i
M
(2
0
0
5
)
S
T
B
C
-
VB
L
AS
T
fo
r
M
IM
O
W
ire
les
s
Co
mm
u
n
ica
ti
o
n
S
y
ste
ms
.
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ro
c
IEE
E
ICC
(ICC
2
0
0
5
)
4
:2
2
6
6
–
2
2
7
0
.
[1
0
]
T
a
ro
k
h
V
,
Ja
f
a
rk
h
a
n
i
H,
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ld
e
rb
a
n
k
A
R
(1
9
9
9
)
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p
a
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e
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i
m
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c
k
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d
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s
f
ro
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Orth
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l
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sig
n
s.
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E
T
ra
n
s
In
f
T
h
e
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ry
4
5
(5
):
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4
5
6
–
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6
7
.
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1
]
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a
n
g
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ia
X
G
(2
0
0
3
)
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p
p
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r
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u
n
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tes
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m
p
lex
Ort
h
o
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a
l
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p
a
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c
k
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s.
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E
T
r
a
n
s
I
n
f
T
h
e
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ry
4
9
(1
0
):2
7
8
8
–
2
7
9
6
.
[1
2
]
o
n
g
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ria
-
G
a
n
d
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ra
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a
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rn
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d
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z
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,
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rtez
J,
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z
d
re
s
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h
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,
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a
rra
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ich
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l
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(2
0
0
7
)
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i
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a
r
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e
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Ge
n
e
ra
ti
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n
fro
m
H
y
b
rid
S
T
BC
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VB
L
AS
T
Arc
h
it
e
c
tu
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s.
In
:
P
ro
c
e
e
d
i
n
g
s
o
f
4
th
In
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
En
g
i
n
e
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(ICEE
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2
0
0
7
)
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4
2
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1
4
5
.
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3
]
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o
ro
k
h
o
v
A
,
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o
re
D
A
,
P
a
u
lraj
A
J
(2
0
0
3
)
Re
c
e
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e
A
n
ten
n
a
S
e
lec
ti
o
n
f
o
r
M
IM
O
S
p
a
ti
a
l
M
u
lt
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p
le
x
in
g
:
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h
e
o
r
y
a
n
d
M
e
c
h
a
n
i
sm
s.
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E
T
ra
n
s
S
ig
n
a
l
Pro
c
e
ss
5
1
(1
1
):2
7
9
6
–
2
8
0
7
.
[1
4
]
Bo
h
n
k
e
,
R.
,
W
u
b
b
e
n
,
D.,
Ku
h
n
,
V
.
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&
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m
m
e
y
e
r,
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D.
(2
0
0
3
,
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c
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m
b
e
r).
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e
d
u
c
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d
c
o
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p
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M
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d
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tec
ti
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f
o
r
B
LA
S
T
a
rc
h
it
e
c
tu
re
s.
In
Glo
b
a
l
T
e
lec
o
mm
u
n
ica
ti
o
n
s
Co
n
fer
e
n
c
e
,
2
0
0
3
.
GLOBE
COM
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3
.
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E
(Vo
l.
4
,
p
p
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2
2
5
8
-
2
2
6
2
).
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[1
5
]
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n
u
c
h
u
l
L
e
,
By
e
o
n
g
si
Lee
,
a
n
d
In
k
y
u
L
e
e
,
“
Itera
ti
v
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d
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tec
ti
o
n
a
n
d
d
e
c
o
d
in
g
w
it
h
a
n
im
p
ro
v
e
d
V
-
BL
A
S
T
f
o
r
M
IM
O
-
OFDM
sy
ste
m
s,”
IEE
E
J
o
u
rn
a
l
o
n
S
e
lec
ted
Are
a
s
in
Co
mm
u
n
ica
ti
o
n
s
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v
o
l.
2
4
,
n
o
.
3
,
p
p
.
5
0
4
–
5
1
3
,
M
a
r.
2
0
0
6
.
[1
6
]
Zh
e
n
g
L
,
T
se
DN
C
(2
0
0
3
)
Div
e
rsity
a
n
d
M
u
lt
i
p
lex
in
g
:
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F
u
n
d
a
m
e
n
tal
T
ra
d
e
o
ff
in
M
u
lt
ip
le
A
n
ten
n
a
Ch
a
n
n
e
ls.
IEE
E
T
ra
n
s In
f
T
h
e
o
ry
4
9
(5
):
1
0
7
3
–
1
0
9
6
[1
7
]
S
a
n
d
e
e
p
G
,
Ra
v
i
-
T
e
ja
C,
Ka
l
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a
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a
-
Krish
n
a
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G
,
Re
d
y
V
U
(2
0
0
7
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o
w
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mp
lex
it
y
De
c
o
d
e
rs
fo
r
Co
mb
in
e
d
S
p
a
c
e
T
ime
Bl
o
c
k
Co
d
i
n
g
a
n
d
V
-
BL
A
S
T
.
In
:
P
r
o
c
e
e
d
in
g
s
o
f
IEE
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W
irele
ss
Co
m
m
u
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s
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n
d
Ne
tw
o
rk
in
g
Co
n
f
e
re
n
c
e
(W
CNC 2
0
0
7
)
5
8
2
-
5
8
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.