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a
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K
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w
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s
:
B
it e
r
r
o
r
r
ate
Mu
ltip
ath
f
ad
in
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Ph
ase
co
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g
r
u
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cy
R
ak
e
r
ec
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T
im
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-
of
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T
h
is i
s
a
n
o
p
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a
c
c
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ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Nad
ir
Mo
h
am
ed
Ab
d
elaz
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Dep
ar
tm
en
t o
f
C
o
m
p
u
ter
E
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g
i
n
ee
r
in
g
a
n
d
Scien
ce
s
,
Ap
p
lied
C
o
lleg
e,
J
az
an
Un
iv
er
s
ity
Al
Ma
ar
ef
ah
R
d
,
J
az
an
,
J
izan
R
eg
io
n
,
J
izan
C
ity
,
Sau
d
i A
r
a
b
ia
E
m
ail:
alp
r
o
f
in
f
i
n
ity
@
g
m
ail.
co
m
,
n
a
b
d
elaz
iz@
jaza
n
u
.
ed
u
.
s
a
1.
I
NT
RO
D
UCT
I
O
N
Ultr
a
-
wid
eb
an
d
(
UW
B
)
tech
n
o
lo
g
y
h
as
em
er
g
ed
as
a
p
iv
o
tal
s
o
lu
tio
n
f
o
r
h
ig
h
-
d
ata
-
r
ate
co
m
m
u
n
icatio
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s
an
d
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n
tim
e
ter
-
ac
cu
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ate
in
d
o
o
r
lo
ca
lizati
o
n
an
d
r
a
d
ar
s
en
s
in
g
[
1
]
,
lev
er
ag
in
g
ca
r
r
ier
-
less
tr
an
s
m
is
s
io
n
with
ex
tr
em
ely
l
o
w
p
o
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s
p
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al
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s
ity
ac
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o
s
s
3
.
1
–
1
0
.
6
GHz
(
b
an
d
wid
t
h
≥
5
0
0
MH
z)
[
2
]
,
[
3
]
.
Acc
o
r
d
in
g
to
FC
C
r
eg
u
latio
n
s
,
a
s
ig
n
al
is
UW
B
if
it
s
-
10
d
B
f
r
ac
tio
n
al
b
an
d
wid
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;
=
2
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−
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≥
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.
20
(
1
)
o
r
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o
c
cu
p
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≥
5
0
0
MH
z
[
2
]
.
T
h
is
lar
g
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b
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n
ab
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p
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in
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els
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T
h
e
I
E
E
E
8
0
2
.
1
5
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4
z
-
2
0
2
0
am
en
d
m
en
t
[
4
]
f
u
r
th
e
r
en
h
an
ce
s
UW
B
p
h
y
s
ical
lay
er
f
o
r
s
ec
u
r
e
r
an
g
i
n
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
C
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p
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g
I
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N:
2088
-
8
7
0
8
Utiliz
in
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p
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s
e
co
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e
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cy
te
ch
n
iq
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e
i
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ec
ep
tio
n
p
erfo
r
ma
n
ce
…
(
N
a
d
ir
Mo
h
a
med
A
b
d
el
a
z
iz
)
1273
UW
B
s
ig
n
als
f
ac
e
s
ev
er
e
d
eg
r
ad
atio
n
d
u
e
to
th
r
ee
f
u
n
d
a
m
en
tal
lim
itatio
n
s
:
i)
d
en
s
e
m
u
ltip
ath
co
m
p
o
n
en
ts
ca
u
s
in
g
in
ter
-
s
y
m
b
o
l
in
ter
f
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n
ce
(
I
SI)
in
e
n
v
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m
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ts
lik
e
I
E
E
E
8
0
2
.
1
5
.
3
a
C
M4
ch
an
n
els
(
NL
OS,
4
-
1
0
m
)
[
5
]
;
ii)
n
ar
r
o
wb
an
d
in
ter
f
er
e
n
ce
(
NB
I
)
f
r
o
m
co
ex
is
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g
s
y
s
tem
s
s
u
ch
a
s
I
E
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8
0
2
.
1
1
a
at
5
GHz
,
an
d
f
u
tu
r
e
W
i
-
Fi 7
(
8
0
2
.
1
1
b
e
)
in
th
e
6
GHz
b
an
d
[
6
]
; a
n
d
iii)
lo
w
s
ig
n
al
-
to
-
n
o
is
e
r
atio
s
(
SNR
)
d
u
e
to
s
tr
in
g
en
t
tr
an
s
m
it
p
o
wer
lim
its
(
-
4
1
.
3
d
B
m
/MHz
)
[
7
]
.
T
r
ad
i
tio
n
al
en
er
g
y
-
b
ased
d
etec
tio
n
m
eth
o
d
s
,
i
n
clu
d
in
g
co
n
v
en
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al
R
ak
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r
ec
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r
s
with
m
ax
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r
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c
o
m
b
in
i
n
g
(
MRC
)
,
ex
h
ib
it
cr
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s
h
o
r
tco
m
in
g
s
:
tem
p
late
d
ep
en
d
e
n
cy
r
e
q
u
ir
in
g
p
r
ec
is
e
p
u
ls
e
tem
p
lates
v
u
ln
er
ab
le
to
d
is
to
r
tio
n
[
8
]
,
n
o
is
e
s
en
s
itiv
ity
with
en
er
g
y
d
etec
tio
n
d
eg
r
a
d
in
g
b
elo
w
0
d
B
SN
R
[
9
]
,
an
d
m
u
ltip
at
h
am
b
ig
u
ity
wh
er
e
d
elay
-
lo
ck
ed
lo
o
p
s
f
ail
to
d
is
tin
g
u
is
h
co
h
er
e
n
t p
ath
s
f
r
o
m
n
o
is
e
[
1
0
]
.
Ph
ase
co
n
g
r
u
en
c
y
(
PC
)
,
a
co
n
ce
p
t
p
io
n
ee
r
ed
in
im
a
g
e
p
r
o
ce
s
s
in
g
[
1
1
]
,
[
1
2
]
,
o
f
f
er
s
a
tr
an
s
f
o
r
m
ativ
e
p
ar
ad
ig
m
s
h
if
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b
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ex
p
lo
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g
p
h
ase
co
h
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ce
ac
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o
s
s
f
r
e
q
u
en
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r
ath
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th
an
s
ig
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m
ag
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d
e.
I
n
im
ag
e
p
r
o
ce
s
s
in
g
,
PC
d
etec
ts
f
ea
tu
r
es
(
ed
g
es,
co
r
n
er
s
)
wh
e
r
e
Fo
u
r
i
er
co
m
p
o
n
en
ts
ar
e
m
ax
im
ally
in
-
p
h
ase,
en
s
u
r
in
g
in
v
ar
ian
ce
t
o
co
n
tr
ast,
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m
i
n
atio
n
,
a
n
d
a
m
p
litu
d
e
f
lu
ctu
a
tio
n
s
[
1
3
]
.
T
h
is
p
r
o
p
er
ty
d
ir
e
ctly
m
ap
s
to
UW
B
s
ig
n
al
d
etec
tio
n
:
p
u
ls
e
e
d
g
es
c
o
r
r
esp
o
n
d
t
o
p
h
ase
-
alig
n
ed
ev
en
ts
ac
r
o
s
s
th
e
wid
e
UW
B
s
p
ec
tr
u
m
,
m
ak
in
g
PC
in
h
er
en
tly
r
o
b
u
s
t
to
th
e
am
p
l
itu
d
e
f
ad
i
n
g
th
at
cr
ip
p
les
e
n
e
r
g
y
-
b
ased
m
eth
o
d
s
[
1
4
]
.
Fig
u
r
e
1
illu
s
tr
ates
th
e
6
th
-
d
er
i
v
ativ
e
Gau
s
s
ian
p
u
ls
e
u
s
ed
th
r
o
u
g
h
o
u
t
th
is
s
tu
d
y
,
wh
ile
Fig
u
r
e
2
d
em
o
n
s
tr
ates
t
h
e
f
u
n
d
am
e
n
tal
PC
co
n
ce
p
t
—
Fo
u
r
ier
co
m
p
o
n
en
ts
ac
h
iev
in
g
m
ax
im
al
p
h
ase
alig
n
m
en
t
at
f
ea
tu
r
e
b
o
u
n
d
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ies
(
s
q
u
ar
e
wav
e
ed
g
es
in
Fig
u
r
e
2
(
a)
,
tr
ian
g
u
lar
wav
e
p
ea
k
s
in
Fig
u
r
e
2
(
b
)
.
Fig
u
r
e
1
.
Six
th
-
d
er
iv
ativ
e
Ga
u
s
s
ian
m
o
n
o
cy
cle
u
s
ed
as UWB
p
u
ls
e
wav
ef
o
r
m
,
e
x
h
ib
itin
g
ze
r
o
DC
co
m
p
o
n
en
t a
n
d
co
m
p
lian
ce
with
FC
C
s
p
ec
tr
al
m
ask
r
eq
u
ir
em
en
ts
(
a)
(
b
)
Fig
u
r
e
2
.
Ph
ase
co
n
g
r
u
en
cy
c
o
n
ce
p
t: (
a)
f
ir
s
t six
Fo
u
r
ier
c
o
m
p
o
n
e
n
ts
o
f
a
s
q
u
ar
e
wav
e
s
h
o
win
g
p
h
ase
alig
n
m
en
t a
t e
d
g
e
tr
an
s
itio
n
s
;
(
b
)
f
ir
s
t six
Fo
u
r
ier
co
m
p
o
n
en
ts
o
f
a
tr
ian
g
u
la
r
wav
e
s
h
o
win
g
p
h
ase
alig
n
m
e
n
t
at
p
ea
k
lo
ca
tio
n
s
.
Ma
x
im
al
p
h
ase
co
h
er
en
ce
id
e
n
tifie
s
f
ea
tu
r
e
b
o
u
n
d
ar
ies r
eg
a
r
d
less
o
f
am
p
litu
d
e
T
h
e
r
esear
ch
g
ap
ad
d
r
ess
ed
in
th
is
p
ap
e
r
is
th
r
ee
f
o
ld
:
i
)
e
x
is
tin
g
PC
f
o
r
m
u
latio
n
s
[
1
1
]
,
[
1
5
]
in
c
u
r
h
ig
h
c
o
m
p
u
tatio
n
al
co
s
ts
u
n
s
u
itab
le
f
o
r
r
ea
l
-
tim
e
UW
B
p
r
o
ce
s
s
in
g
;
ii)
n
o
co
m
p
r
eh
e
n
s
iv
e
f
r
am
ewo
r
k
lin
k
s
PC
-
d
r
iv
en
m
u
ltip
ath
d
is
cr
im
i
n
atio
n
to
R
ak
e
co
m
b
in
in
g
o
p
t
im
izatio
n
;
an
d
iii)
th
e
co
m
p
ar
ativ
e
ef
f
icac
y
o
f
PC
u
n
d
er
d
if
f
er
en
t
UW
B
m
o
d
u
latio
n
s
ch
em
es
(
DS
-
UW
B
v
s
.
T
H
-
UW
B
)
an
d
NB
I
co
n
d
itio
n
s
r
em
ain
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
16
,
No
.
3
,
J
u
n
e
20
26
:
1
2
7
2
-
1
2
8
5
1274
u
n
ex
p
l
o
r
ed
.
Fu
r
th
e
r
m
o
r
e,
r
ec
e
n
t
ad
v
a
n
ce
s
in
m
o
n
o
g
e
n
ic
d
i
f
f
er
en
tial
PC
[
1
6
]
,
[
1
7
]
a
n
d
iter
ativ
e
PC
f
o
r
cr
ac
k
d
etec
tio
n
[
1
8
]
h
av
e
n
o
t
b
ee
n
tr
an
s
lated
to
UW
B
R
ak
e
o
p
tim
izatio
n
.
Ho
wev
er
;
th
is
p
ap
er
o
p
tim
izes
UW
B
r
ec
ep
tio
n
i
n
m
u
ltip
ath
c
h
an
n
e
ls
b
y
in
teg
r
atin
g
PC
with
a
s
elec
tiv
e
R
ak
e
(
S
-
R
ak
e)
r
ec
eiv
er
in
tr
o
d
u
cin
g
f
iv
e
n
o
v
el
co
n
tr
ib
u
tio
n
s
s
tated
as f
o
llo
ws:
a.
PC
-
g
u
id
ed
S
-
R
ak
e
ar
ch
itectu
r
e
th
at
u
s
es
p
h
ase
co
h
er
e
n
ce
m
etr
ics
to
id
en
tify
an
d
p
r
io
r
itize
m
u
ltip
ath
co
m
p
o
n
en
ts
f
o
r
c
o
m
b
in
i
n
g
,
eli
m
in
atin
g
tem
p
late
d
e
p
en
d
e
n
cy
an
d
m
itig
atin
g
m
u
ltip
ath
am
b
ig
u
ity
.
b.
Ma
th
em
atica
l
f
o
r
m
u
latio
n
o
f
iter
ativ
e
PC
f
o
r
UW
B
wit
h
ex
p
licit
s
u
b
-
b
a
n
d
d
ec
o
m
p
o
s
itio
n
,
Hilb
er
t
tr
an
s
f
o
r
m
-
b
ased
p
h
ase
ex
tr
a
ctio
n
,
an
d
PC
m
etr
ic
ca
lcu
latio
n
f
o
r
r
ea
l
-
tim
e
m
u
ltip
ath
co
m
p
o
n
en
t
id
en
tific
atio
n
.
c.
C
o
m
p
r
eh
en
s
iv
e
p
er
f
o
r
m
a
n
ce
v
alid
atio
n
u
n
d
er
I
E
E
E
8
0
2
.
1
5
.
3
a
C
M4
ch
an
n
els
with
NB
I
(
I
E
E
E
8
0
2
.
1
1
a
at
SIR
=
-
3
0
d
B
to
0
d
B
)
,
d
em
o
n
s
tr
atin
g
4
d
B
SNR
g
ain
at
B
E
R
=1
0
⁻⁴
v
er
s
u
s
co
n
v
en
tio
n
al
R
ak
e.
d.
C
o
m
p
ar
ativ
e
an
aly
s
is
o
f
DS
-
UW
B
an
d
T
H
-
UW
B
with
PC
en
h
an
ce
m
e
n
t,
r
e
v
ea
lin
g
DS
-
UW
B
's
3
×
B
E
R
ad
v
an
tag
e
u
n
d
e
r
ex
tr
em
e
in
ter
f
er
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ce
d
u
e
to
c
h
ip
-
s
y
n
c
h
r
o
n
o
u
s
p
h
ase
co
h
er
e
n
ce
.
e.
T
OA
esti
m
atio
n
im
p
r
o
v
em
e
n
t
o
f
6
2
%
(
R
MSE
r
ed
u
ctio
n
f
r
o
m
1
.
8
n
s
t
o
0
.
6
8
n
s
)
th
r
o
u
g
h
PC
-
b
ased
p
u
ls
e
ed
g
e
d
etec
tio
n
.
T
h
e
p
ap
e
r
is
o
r
g
a
n
i
ze
d
as
f
o
llo
ws:
Se
cti
o
n
2
p
r
ese
n
ts
t
h
e
m
et
h
o
d
o
l
o
g
y
i
n
cl
u
d
i
n
g
;
s
y
s
t
em
m
o
d
e
l
d
e
m
o
n
s
tr
ati
n
g
DS
-
UW
B
an
d
T
H
-
UW
B
tr
a
n
s
c
ei
v
e
r
s
c
h
em
es
wit
h
PC
in
te
g
r
at
io
n
,
d
et
ails
t
h
e
UW
B
p
r
o
p
a
g
a
ti
o
n
ch
an
n
el
m
o
d
e
l
(
I
E
E
E
8
0
2
.
1
5
.
3
a
C
M
4
)
,
d
esc
r
i
b
es
t
h
e
P
C
-
o
p
t
im
i
ze
d
S
-
R
a
k
e
r
e
ce
iv
e
r
a
r
c
h
i
tec
tu
r
e
a
n
d
alg
o
r
it
h
m
.
S
ec
t
io
n
3
p
r
ese
n
ts
s
im
u
la
ti
o
n
r
es
u
l
ts
a
n
d
a
n
al
y
s
i
s
.
Se
cti
o
n
4
p
r
es
en
ts
t
h
e
d
is
c
u
s
s
io
n
w
h
ic
h
co
v
er
s
k
e
y
f
i
n
d
in
g
s
,
i
m
p
lic
ati
o
n
s
a
n
d
lim
itat
io
n
s
o
f
t
h
e
s
tu
d
y
,
c
o
m
p
a
r
is
o
n
wit
h
p
r
i
o
r
w
o
r
k
s
a
n
d
l
ite
r
at
u
r
e
,
r
el
ev
a
n
ce
o
f
t
h
e
s
t
u
d
y
t
o
n
ew/
c
u
r
r
e
n
t
r
ea
l
-
w
o
r
l
d
t
ec
h
n
o
l
o
g
ies
.
S
ec
t
io
n
5
p
r
es
en
ts
co
n
cl
u
s
i
o
n
o
f
t
h
e
r
e
s
ea
r
c
h
s
tu
d
y
.
2.
M
E
T
H
O
D
2
.
1
.
Dire
ct
-
s
equence
U
WB
(
DS
-
UWB
)
wit
h p
ha
s
e
co
ng
ruenc
y
T
h
e
d
ir
ec
t
-
s
eq
u
en
ce
UW
B
s
ch
em
e
em
p
lo
y
s
p
s
eu
d
o
-
r
an
d
o
m
n
o
is
e
(
PN)
s
eq
u
e
n
ce
s
to
s
p
r
ea
d
d
ata
b
its
ac
r
o
s
s
m
u
ltip
le
ch
ip
s
,
w
h
er
e
th
e
u
ltra
-
s
h
o
r
t
p
u
ls
e
wa
v
ef
o
r
m
ac
ts
as
th
e
f
u
n
d
am
e
n
tal
"c
h
ip
"
[
1
9
]
.
T
h
e
tr
an
s
m
itted
s
ig
n
al
f
o
r
th
e
k
-
th
u
s
er
is
:
(
)
(
)
=
√
∑
(
)
∑
⋅
(
)
⋅
(
−
−
)
−
1
=
0
∞
=
−
∞
(
2
)
w
h
er
e
is
en
er
g
y
p
er
b
it,
(
)
is
th
e
UW
B
p
u
ls
e
m
o
n
o
cy
cle
(
6
th
-
d
er
i
v
ativ
e
Gau
s
s
ian
)
,
(
)
is
th
e
PN
s
eq
u
en
ce
f
o
r
u
s
er
,
is
f
r
am
e
d
u
r
atio
n
,
is
ch
ip
d
u
r
atio
n
wi
th
=
.
,
(
)
ar
e
B
PS
K
-
m
o
d
u
lated
d
ata
s
y
m
b
o
ls
,
an
d
is
th
e
n
u
m
b
er
o
f
c
h
ip
s
p
er
b
it.
Fig
u
r
e
3
illu
s
tr
ates th
e
DS
-
UW
B
tr
an
s
m
it
ter
ar
ch
itectu
r
e.
Fig
u
r
e
3
.
DS
-
UW
B
tr
an
s
m
itte
r
ar
ch
itectu
r
e
s
h
o
win
g
PN seq
u
en
ce
s
p
r
ea
d
i
n
g
,
p
u
ls
e
g
en
er
at
io
n
,
an
d
B
PS
K
m
o
d
u
latio
n
s
tag
es
T
r
ad
itio
n
al
DS
-
UW
B
r
ec
eiv
e
r
s
u
s
e
co
r
r
elatio
n
-
b
ased
d
etec
tio
n
,
wh
ich
d
e
g
r
ad
es
u
n
d
er
m
u
ltip
ath
f
ad
in
g
a
n
d
in
ter
f
er
en
ce
.
T
h
is
p
ap
er
in
teg
r
ates PC
-
b
ased
p
r
o
ce
s
s
in
g
at
th
e
r
ec
eiv
er
th
r
o
u
g
h
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Utiliz
in
g
p
h
a
s
e
co
n
g
r
u
e
n
cy
te
ch
n
iq
u
e
i
n
r
ec
ep
tio
n
p
erfo
r
ma
n
ce
…
(
N
a
d
ir
Mo
h
a
med
A
b
d
el
a
z
iz
)
1275
Step
1
.
An
aly
tic
s
ig
n
al
c
o
n
v
e
r
s
io
n
:
C
o
n
v
er
t
r
ea
l
-
v
alu
e
d
r
e
ce
iv
ed
s
ig
n
al
r
(
t
)
t
o
an
aly
tic
f
o
r
m
u
s
in
g
Hilb
er
t
tr
an
s
f
o
r
m
:
(
)
=
(
)
+
.
ℋ
{
(
)
}
(
3
)
Step
2
.
Su
b
-
b
an
d
d
e
co
m
p
o
s
it
io
n
:
Dec
o
m
p
o
s
e
s
(
t
)
in
to
N=
8
s
u
b
-
b
a
n
d
s
u
s
in
g
s
h
o
r
t
-
tim
e
Fo
u
r
ier
tr
a
n
s
f
o
r
m
(
STFT
)
with
Gab
o
r
f
ilter
b
a
n
k
co
v
er
in
g
3
.
1
–
1
0
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GHz
,
ac
h
iev
in
g
tr
a
d
e
-
o
f
f
b
etwe
en
tim
e
r
eso
lu
tio
n
(
0
.
5
n
s
)
an
d
p
h
ase
esti
m
atio
n
ac
cu
r
ac
y
.
Fo
r
ea
ch
s
u
b
-
b
an
d
n
,
ex
tr
ac
t
in
s
tan
tan
eo
u
s
p
h
ase
(
)
an
d
am
p
l
itu
d
e
(
)
.
Step
3
.
Ph
ase
d
ev
iatio
n
ca
lc
u
latio
n
:
C
o
m
p
u
te
p
h
ase
d
ev
iatio
n
f
r
o
m
m
ea
n
:
∆
∅
(
)
=
c
os
(
∅
(
)
−
∅
̅
(
)
)
−
|
s
in
(
∅
(
)
−
∅
̅
(
)
)
|
(
4
)
wh
er
e
∅
̅
(
)
is
th
e
m
ea
n
p
h
ase
ac
r
o
s
s
s
u
b
-
b
an
d
s
.
Step
4
.
PC
m
etr
ic
co
m
p
u
tatio
n
:
C
alcu
late
p
h
ase
co
n
g
r
u
en
cy
at
ea
ch
tim
e
in
s
tan
t:
(
)
=
∑
(
)
.
∆
∅
(
)
∑
(
)
+
(
5
)
wh
er
e
p
r
e
ve
n
ts
divis
io
n
b
y z
e
r
o.
Step
5
.
Pu
ls
e
d
etec
ti
o
n
an
d
T
OA
esti
m
atio
n
:
I
d
en
tif
y
PC
p
ea
k
s
ex
ce
e
d
in
g
th
r
esh
o
ld
γ
=
0
.
7
as
p
u
ls
e
ed
g
e
lo
ca
tio
n
s
:
T
OA
⇐
a
r
g
ma
x
(
(
)
)
(
6
)
Step
6
.
Mu
ltip
ath
co
m
p
o
n
e
n
t
id
en
tific
atio
n
:
R
an
k
m
u
ltip
a
th
co
m
p
o
n
en
ts
b
y
PC
m
ag
n
itu
d
e;
s
elec
t
to
p
M
co
m
p
o
n
en
ts
f
o
r
S
-
R
ak
e
c
o
m
b
i
n
in
g
.
2
.
2
.
T
im
e
-
ho
pp
ing
UWB
(
T
H
-
UWB
)
wit
h
ph
a
s
e
co
ng
ru
en
cy
TH
-
UW
B
em
p
lo
y
s
p
u
ls
e
-
p
o
s
itio
n
m
o
d
u
latio
n
(
PP
M)
with
tim
e
-
h
o
p
p
in
g
co
d
es
f
o
r
m
u
ltip
le
ac
ce
s
s
.
T
h
e
tr
an
s
m
itted
s
ig
n
al
f
o
r
th
e
k
-
th
u
s
er
is
:
(
)
(
)
=
∑
(
−
−
(
)
−
(
)
)
∞
=
−
∞
(
7
)
w
h
er
e
is
th
e
PP
M
tim
e
s
h
if
t
,
(
)
is
th
e
T
H
co
d
e,
is
ch
ip
d
u
r
atio
n
,
an
d
(
)
ar
e
d
ata
s
y
m
b
o
ls
.
Fig
u
r
e
4
illu
s
tr
ates
th
e
tim
e
an
d
f
r
e
q
u
en
c
y
d
o
m
ain
c
h
ar
ac
ter
is
tics
o
f
th
e
g
en
er
at
ed
s
ig
n
als,
clea
r
ly
d
em
o
n
s
tr
atin
g
h
o
w
th
e
co
m
b
in
atio
n
o
f
tim
e
-
h
o
p
p
in
g
co
d
e
s
an
d
PP
M
tim
e
s
h
if
ts
alter
s
th
e
u
n
if
o
r
m
p
u
ls
e
in
ter
v
als
in
to
a
p
s
eu
d
o
-
r
an
d
o
m
s
eq
u
en
ce
.
Fig
u
r
es
4
(
a
)
a
n
d
4
(
b
)
s
h
o
w
u
n
m
o
d
u
lated
an
d
m
o
d
u
lated
T
H
-
UW
B
p
u
ls
e
tr
ain
s
,
r
esp
ec
tiv
ely
.
(
a)
(
b
)
Fig
u
r
e
4
.
T
im
e
an
d
f
r
eq
u
en
cy
d
o
m
ain
r
e
p
r
esen
tatio
n
s
o
f
T
H
-
UW
B
s
ig
n
als:
(
a)
Un
m
o
d
u
lat
ed
T
H
-
UW
B
p
u
ls
e
tr
ain
s
h
o
win
g
p
e
r
io
d
ic
p
u
ls
e
tr
an
s
m
is
s
io
n
with
o
u
t d
ata
m
o
d
u
latio
n
an
d
(
b
)
.
M
o
d
u
lated
T
H
-
UW
B
p
u
ls
e
tr
ain
with
PP
M
en
co
d
in
g
s
h
o
win
g
p
u
ls
e
p
o
s
itio
n
s
h
if
ts
r
ep
r
esen
ti
n
g
b
in
a
r
y
d
ata
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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:
2
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8
8
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I
n
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lec
&
C
o
m
p
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n
g
,
Vo
l.
16
,
No
.
3
,
J
u
n
e
20
26
:
1
2
7
2
-
1
2
8
5
1276
Pre
v
io
u
s
wo
r
k
o
n
o
p
tim
u
m
co
m
b
in
in
g
f
o
r
T
H
-
I
R
[
2
0
]
s
h
o
w
ed
;
PC
in
teg
r
atio
n
f
o
r
T
H
-
U
W
B
f
o
llo
w
s
id
en
tical
s
tep
s
1
-
6
as
DS
-
UW
B
,
with
th
e
k
ey
d
if
f
er
en
ce
t
h
a
t
T
H
-
UW
B
's
ir
r
eg
u
lar
p
u
ls
e
ti
m
in
g
af
f
ec
ts
p
h
ase
co
h
er
en
ce
.
T
h
e
s
p
ar
s
e,
n
o
n
-
u
n
if
o
r
m
p
u
ls
e
s
p
ac
in
g
in
T
H
-
UW
B
d
ilu
te
s
p
h
ase
alig
n
m
en
t
ac
r
o
s
s
s
u
b
-
b
an
d
s
,
r
esu
ltin
g
in
wea
k
er
PC
r
esp
o
n
s
es c
o
m
p
ar
ed
to
DS
-
UW
B
's c
h
ip
-
s
y
n
ch
r
o
n
o
u
s
s
tr
u
ctu
r
e.
2
.
3
.
Co
m
pa
riso
n o
f
DS
-
UW
B
a
nd
T
H
-
UW
B
wit
h P
C
en
ha
ncem
ent
T
ab
le
1
s
u
m
m
ar
izes th
e
s
tr
u
ct
u
r
al
d
if
f
e
r
en
ce
s
an
d
PC
im
p
lic
atio
n
s
f
o
r
b
o
th
m
o
d
u
latio
n
s
ch
em
es.
T
ab
le
1
.
Stru
ctu
r
al
c
o
m
p
a
r
is
o
n
o
f
DS
-
UW
B
an
d
T
H
-
UW
B
with
PC
im
p
licatio
n
s
F
e
a
t
u
r
e
DS
-
U
W
B
(
B
P
M
)
TH
-
U
W
B
(
P
P
M
)
P
C
i
m
p
l
i
c
a
t
i
o
n
P
u
l
s
e
t
i
mi
n
g
C
h
i
p
-
s
y
n
c
h
r
o
n
o
u
s,
r
e
g
u
l
a
r
Ti
me
-
h
o
p
p
e
d
,
i
r
r
e
g
u
l
a
r
DS
-
U
W
B
:
e
n
h
a
n
c
e
d
p
h
a
s
e
c
o
h
e
r
e
n
c
e
;
TH
-
U
W
B
:
d
i
l
u
t
e
d
p
h
a
s
e
a
l
i
g
n
me
n
t
M
u
l
t
i
p
l
e
a
c
c
e
ss
P
N
seq
u
e
n
c
e
c
o
d
i
n
g
Ti
me
-
h
o
p
p
i
n
g
c
o
d
e
s
DS
-
U
W
B
:
p
r
e
d
i
c
t
a
b
l
e
p
h
a
se
p
a
t
t
e
r
n
s
;
TH
-
U
W
B
:
r
a
n
d
o
m
p
h
a
se
v
a
r
i
a
t
i
o
n
s
M
o
d
u
l
a
t
i
o
n
Bi
-
P
h
a
se
(
B
P
S
K
)
P
u
l
s
e
-
P
o
si
t
i
o
n
DS
-
U
W
B
:
p
h
a
se
t
r
a
n
si
t
i
o
n
s a
t
c
h
i
p
b
o
u
n
d
a
r
i
e
s
;
TH
-
U
W
B
:
p
o
si
t
i
o
n
s
h
i
f
t
s
a
f
f
e
c
t
p
h
a
s
e
a
l
i
g
n
me
n
t
S
p
e
c
t
r
a
l
c
h
a
r
a
c
t
e
r
i
s
t
i
c
s
C
o
n
t
i
n
u
o
u
s s
p
e
c
t
r
u
m
C
o
m
b
-
l
i
n
e
s
p
e
c
t
r
u
m
DS
-
U
W
B
:
b
r
o
a
d
e
r
p
h
a
s
e
c
o
h
e
r
e
n
c
e
;
TH
-
U
W
B
:
i
n
t
e
r
m
i
t
t
e
n
t
p
h
a
s
e
a
l
i
g
n
me
n
t
P
C
d
e
t
e
c
t
i
o
n
c
a
p
a
b
i
l
i
t
y
H
i
g
h
(
r
e
g
u
l
a
r
f
e
a
t
u
r
e
s)
M
o
d
e
r
a
t
e
(
sp
a
r
se
f
e
a
t
u
r
e
s)
DS
-
U
W
B
:
3
×
l
o
w
e
r
B
ER
u
n
d
e
r
N
B
I
(
d
e
m
o
n
s
t
r
a
t
e
d
i
n
S
e
c
t
i
o
n
5
)
2
.
4
.
UWB
pro
pa
g
a
t
io
n c
ha
n
nel m
o
del
T
h
e
I
E
E
E
8
0
2
.
1
5
.
3
a
ch
a
n
n
el
m
o
d
el,
b
ased
o
n
t
h
e
m
o
d
if
ied
Saleh
-
Vale
n
zu
ela
(
S
-
V)
ap
p
r
o
ac
h
,
ac
cu
r
ately
ca
p
tu
r
es UWB
m
u
l
tip
ath
ch
ar
ac
ter
is
tics
[
5
]
T
h
e
c
h
an
n
el
im
p
u
ls
e
r
esp
o
n
s
e
is
:
ℎ
(
)
=
∑
∑
,
⋅
(
−
−
,
)
−
1
=
0
−
1
=
0
(
8
)
wh
er
e;
.
r
ep
r
esen
ts
th
e
m
u
lti
p
ath
g
ain
co
e
f
f
icien
ts
,
r
ep
r
esen
ts
th
e
d
elay
s
o
f
th
e
th
clu
s
ter
,
,
r
ep
r
esen
ts
th
e
d
elay
s
o
f
th
e
-
th
m
u
ltip
ath
co
m
p
o
n
e
n
t
“r
ay
”
with
in
th
e
-
th
clu
s
ter
ar
r
iv
al
tim
e
(
)
.
Sh
ad
o
win
g
ef
f
ec
t
o
f
th
e
t
o
tal
m
u
ltip
ath
en
er
g
y
is
lo
g
-
n
o
r
m
al
d
is
tr
ib
u
ted
an
d
is
r
e
p
r
esen
ted
b
y
t
h
e
ter
m
,
an
d
r
ef
er
s
to
th
e
th
r
ea
lizatio
n
.
Mo
r
eo
v
er
,
clu
s
ter
ar
r
iv
als
f
o
llo
w
Po
is
s
o
n
d
is
tr
ib
u
ted
with
“Cl
u
s
ter
ar
r
iv
al
r
ate”
(
):
(
\
−
1
)
=
⋅
(
−
⋅
(
−
−
1
)
)
(
9
)
wh
ile
R
ay
ar
r
iv
als with
in
clu
s
ter
s
also
f
o
llo
w
Po
is
s
o
n
d
is
tr
ib
u
tio
n
with
“Ray
ar
r
iv
al
r
ate”
(
)
,
an
d
>>
:
(
,
\
(
−
1
)
,
)
=
⋅
(
−
⋅
(
,
−
(
−
1
)
,
)
(
1
0
)
T
h
is
s
tu
d
y
em
p
lo
y
s
th
e
m
o
d
if
ied
Saleh
-
Vale
n
zu
ela
ch
a
n
n
el
m
o
d
el
(
C
M4
)
ch
an
n
el
p
ar
am
eter
s
(
NL
OS,
4
-
1
0
m
r
an
g
e,
ex
tr
e
m
e
m
u
ltip
ath
)
with
Λ=0
.
0
6
6
7
n
s
⁻¹,
λ
=2
.
1
n
s
⁻¹,
an
d
R
MS
d
elay
s
p
r
ea
d
≈
2
5
n
s
.
Mo
r
eo
v
er
,
PC
u
tili
za
tio
n
in
th
e
s
tu
d
y
en
h
a
n
ce
s
r
ec
ep
tio
n
in
S
-
V
ch
an
n
els th
r
o
u
g
h
:
a.
Mu
ltip
ath
d
is
cr
im
in
atio
n
:
(
)
p
ea
k
s
id
en
tify
co
h
e
r
en
t
MPC
s
with
alig
n
ed
p
h
ases
ac
r
o
s
s
s
u
b
-
b
a
n
d
s
,
en
ab
lin
g
d
etec
tio
n
o
f
wea
k
p
at
h
s
b
u
r
ied
in
n
o
is
e
(
th
r
esh
o
ld
-
f
r
ee
o
p
er
atio
n
)
.
b.
T
OA
esti
m
atio
n
:
PC
p
ea
k
s
s
er
v
e
as
p
r
ec
is
e
tim
in
g
m
ar
k
er
s
f
o
r
p
u
ls
e
ed
g
es,
o
u
tp
er
f
o
r
m
in
g
en
e
r
g
y
d
etec
tio
n
in
lo
w
SNR
(
<0
d
B
)
.
c.
R
ak
e
f
in
g
er
s
elec
tio
n
:
MPC
s
with
m
ax
im
al
PC
ar
e
p
r
io
r
itized
f
o
r
S
-
R
ak
e
co
m
b
in
in
g
,
m
itig
atin
g
m
u
ltip
ath
am
b
ig
u
ity
wh
e
r
e
co
n
v
en
tio
n
al
d
elay
-
lo
ck
e
d
lo
o
p
s
f
ail.
d.
NB
I
m
itig
atio
n
:
I
E
E
E
8
0
2
.
1
1
a
in
ter
f
er
e
n
ce
at
5
GHz
d
is
r
u
p
t
s
p
h
ase
co
h
er
en
ce
o
n
ly
i
n
a
f
f
e
cted
s
u
b
-
b
an
d
s
,
leav
in
g
PC
p
ea
k
s
in
tact
in
o
th
er
s
.
2
.
5
.
PC
-
o
ptim
ized
s
elec
t
iv
e
Ra
k
e
re
ce
iv
er
2
.
5
.
1
.
L
im
it
a
t
io
ns
o
f
c
o
nv
ent
io
na
l R
a
k
e
re
ce
iv
er
s
C
o
n
v
en
tio
n
al
R
ak
e
r
ec
eiv
er
s
u
s
u
ally
f
ac
e
f
u
n
d
am
e
n
tal
lim
itatio
n
s
in
UW
B
s
y
s
tem
s
s
u
ch
as:
a.
E
n
er
g
y
-
b
ased
d
etec
tio
n
:
MRC
p
r
io
r
itizes
h
ig
h
-
SNR
p
ath
s
b
u
t
f
ails
u
n
d
er
r
ap
id
am
p
litu
d
e
f
ad
in
g
a
n
d
NB
I
,
ca
u
s
in
g
er
r
o
r
f
lo
o
r
s
d
ep
e
n
d
en
t
o
n
SIR
[
9
]
.
b.
T
em
p
late
d
ep
e
n
d
en
c
y
:
Ma
tc
h
ed
f
ilter
in
g
r
eq
u
ir
es
p
r
ec
is
e
p
u
ls
e
tem
p
lates
v
u
l
n
er
ab
le
to
d
is
to
r
tio
n
i
n
NL
OS c
h
an
n
els
[
8
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Utiliz
in
g
p
h
a
s
e
co
n
g
r
u
e
n
cy
te
ch
n
iq
u
e
i
n
r
ec
ep
tio
n
p
erfo
r
ma
n
ce
…
(
N
a
d
ir
Mo
h
a
med
A
b
d
el
a
z
iz
)
1277
c.
Mu
ltip
ath
am
b
ig
u
ity
:
Dela
y
-
l
o
ck
ed
lo
o
p
s
s
tr
u
g
g
le
to
d
is
tin
g
u
is
h
co
h
e
r
en
t
p
ath
s
f
r
o
m
n
o
is
e
in
d
en
s
e
m
u
ltip
ath
clu
s
ter
s
[
1
0
]
.
Fig
u
r
e
5
s
h
o
ws
th
e
All
-
R
ak
e
r
ec
eiv
er
s
tr
u
ctu
r
e
co
m
b
in
in
g
all
L
m
u
ltip
ath
c
o
m
p
o
n
en
ts
,
wh
ich
is
im
p
r
ac
tical
f
o
r
UW
B
d
u
e
to
ex
ce
s
s
iv
e
co
m
p
lex
ity
.
W
h
ile
Fig
u
r
e
6
p
r
esen
ts
th
e
Selectiv
e
-
R
ak
e
(
S
-
R
ak
e)
s
tr
u
ctu
r
e
co
m
b
in
in
g
o
n
ly
th
e
M
b
est
co
m
p
o
n
e
n
ts
(
M
<
L
)
,
wh
er
e
f
in
g
er
s
elec
tio
n
cr
itically
im
p
ac
ts
p
er
f
o
r
m
an
ce
.
E
v
en
ad
ap
tiv
e
R
ak
e
alg
o
r
ith
m
s
[
2
1
]
s
tr
u
g
g
le
in
h
ig
h
ly
d
en
s
e
m
u
lti
p
ath
.
Fig
u
r
e
5
.
All
-
R
ak
e
r
ec
eiv
e
r
ar
ch
itectu
r
e
co
m
b
i
n
in
g
all
L
m
u
ltip
ath
co
m
p
o
n
en
ts
.
I
m
p
r
ac
tic
al
f
o
r
UW
B
d
u
e
to
co
m
p
lex
ity
(
L
ca
n
e
x
ce
ed
1
0
0
in
C
M4
ch
an
n
els)
Fig
u
r
e
6
.
Selectiv
e
-
R
ak
e
r
ec
ei
v
er
ar
ch
itectu
r
e
co
m
b
in
in
g
M
b
est m
u
ltip
ath
co
m
p
o
n
en
ts
(
M
=
4,
8,
1
2
8
i
n
th
is
s
tu
d
y
)
,
Fin
g
er
s
elec
tio
n
alg
o
r
it
h
m
d
eter
m
in
es wh
ic
h
p
ath
s
ar
e
co
m
b
in
e
d
2
.
5
.
2
.
PC
-
O
ptim
ized
S
-
Ra
k
e
a
rc
hite
ct
ure
T
h
is
p
ap
er
in
teg
r
ates PC
p
r
o
ce
s
s
in
g
in
to
an
S
-
R
ak
e
r
ec
eiv
er
as sh
o
wn
in
Fig
u
r
e
7
.
Fig
u
r
e
7
.
PC
-
o
p
tim
ized
S
-
R
ak
e
r
ec
eiv
er
ar
c
h
itectu
r
e
s
h
o
win
g
s
ig
n
al
f
lo
w
f
r
o
m
R
F f
r
o
n
t
-
e
n
d
th
r
o
u
g
h
PC
p
r
o
ce
s
s
in
g
b
lo
c
k
,
p
ea
k
d
etec
ti
o
n
,
f
in
g
er
s
elec
tio
n
,
d
elay
ad
j
u
s
tm
en
t,
an
d
MRC
co
m
b
in
in
g
.
T
h
e
PC
b
lo
ck
co
m
p
u
tes p
h
ase
c
o
h
er
en
ce
m
e
tr
ics g
u
id
in
g
all
s
u
b
s
eq
u
en
t stag
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
16
,
No
.
3
,
J
u
n
e
20
26
:
1
2
7
2
-
1
2
8
5
1278
W
h
er
e
th
e
PC
-
S
-
R
ak
e
ar
ch
itectu
r
e
co
n
s
is
ts
o
f
th
e
f
o
llo
win
g
p
ar
ts
:
a.
R
F f
r
o
n
t
-
en
d
:
An
ten
n
a,
L
NA,
an
d
d
o
w
n
-
co
n
v
er
s
io
n
s
tag
es.
b.
P
C
p
r
o
c
es
s
i
n
g
b
l
o
c
k
:
H
il
b
e
r
t
t
r
a
n
s
f
o
r
m
,
s
u
b
-
b
a
n
d
d
e
c
o
m
p
o
s
i
ti
o
n
,
p
h
a
s
e
e
x
t
r
a
c
ti
o
n
,
a
n
d
(
)
c
o
m
p
u
t
a
t
i
o
n
.
c.
Peak
d
etec
tio
n
an
d
T
OA
esti
m
atio
n
:
I
d
en
tifie
s
p
u
ls
e
ed
g
es a
n
d
m
u
ltip
ath
co
m
p
o
n
en
t
d
elay
s
.
d.
Fin
g
er
s
elec
tio
n
lo
g
ic:
R
an
k
s
MPC
s
b
y
PC
m
ag
n
itu
d
e,
s
elec
ts
to
p
M
f
o
r
c
o
m
b
in
in
g
.
e.
Dela
y
ad
ju
s
tm
en
t c
ir
cu
its
:
Fin
e
-
tu
n
es d
elay
s
b
ased
o
n
PC
-
g
u
id
ed
T
OA
esti
m
ates.
f.
MRC
co
m
b
in
er
:
Ma
x
im
al
r
atio
co
m
b
i
n
in
g
o
f
s
elec
ted
p
ath
s
.
2
.
5
.
3
.
PC
-
S
-
Ra
ke
a
lg
o
rit
hm
T
h
e
alg
o
r
ith
m
in
tr
o
d
u
ce
d
in
th
is
s
tu
d
y
f
o
r
PC
-
Selectiv
e
R
a
k
e
is
b
ased
o
n
PC
-
Gu
id
ed
S
-
R
ak
e
f
in
g
er
s
elec
tio
n
an
d
co
m
b
in
in
g
t
h
r
o
u
g
h
th
e
f
o
llo
win
g
c
r
iter
ia
an
d
s
tep
s
:
Input:
Received signal
r(t)
r
(
t
), number of Rake fingers
MM
, PC threshold
γ=0.7
γ
=0.7
Output:
Detected bits{
b
^
i
}, TOA estimates
{
τ
^
m
}
Step 1: Preprocessing
1.1 Compute analytic signal:
s
(
t
)=
r
(
t
)+
j
H{
r
(
t
)}
1.2 Decompose into N=8 sub
-
bands using Gabor filter bank:
s
n
(
t
)
=STFT
n
{
s
(
t
)}, n = 1,...,N
1.3 For each sub
-
band
n
:
1.3.1 Extract instantaneous phase:
ϕ
n
(
t
)=arg(
s
n
(
t
))
1.3.2 Extract instantaneous amplitude:
A
n
(
t
)=
∣
s
n
(
t
)
∣
Step 2:
PC
m
e
tr
i
c
co
m
p
u
t
at
i
o
n
:
M
o
no
g
e
n
i
c
d
i
f
fe
r
e
n
t
ia
l
P
C
m
e
th
o
d
s
[1
6
]
,
[
1
7
]
ha
v
e
d
e
m
o
ns
t
r
a
t
ed
robust e
dge de
tecti
on, mo
t
ivating
the UW
B pul
se
‑
e
dg
e
P
C
f
o
r
mu
l
a
t
i
on
:
2.1 Compute mean phase across sub
-
bands:
ϕ
ˉ
(
t
)= 1
/
N
∑
n
=1
N
ϕn
(
t
)
2.2 For each sub
-
band
n
:
Δ
ϕn
(
t
)=cos(
ϕn
(
t
)−
ϕ
ˉ
(
t
))−
∣
sin(
ϕn
(
t
)−
ϕ
ˉ
(
t
))
∣
2.3 Compute PC(t):
(
)
=
∑
(
)
.
∆
∅
(
)
∑
(
)
+
Step 3: Peak
d
etection and TOA
e
stimation
3.1 Identify local maxima of PC(t) exceeding threshold
γ
3.2 For each peak at time
t
p
:
τ
^
TOA
,
p
=
t
p
3.3 Sort peaks by PC magnitude descending
Step 4: Finger
s
election
4.1 Select top M peaks as Rake finger delays: {
τ
^
1
,
τ
^
2
, ...,
τ
^
M
}
4.2 For each selected path m:
Extract channel coefficient estimate:
h
^
m
=correlation
at
τ
^
m
Step 5: Delay
a
djustment
5.1 Fine
-
tune delays using PC peak centroid:
τ
^
mad
j
= ∫
t
⋅
PC
(
t
)
dt
/ ∫
PC
(
t
)
dt
;
over peak window
Step 6: MRC
c
ombining
6.1 Align received signal with adjusted delays
6.2 Combine:
y
(
t
)=∑
m
=1
M
h
^
m
∗
⋅
r
(
t
−
τ
^
mad
j
)
6.3 Detect bits:
b^
i
=
sign
(Re{
y
(
iT
b
)})
Return:
{
b
^
i
},
{
τ
^
m
}
2
.
5
.
4
.
Co
m
pu
t
a
t
i
o
na
l
co
m
plex
it
y
a
na
ly
s
is
T
h
e
P
C
-
S
-
R
a
k
e
p
r
o
p
o
s
ed
i
n
t
h
i
s
s
t
u
d
y
p
a
p
e
r
in
t
r
o
d
u
c
e
s
a
d
d
i
t
io
n
a
l
co
m
p
u
t
a
t
io
n
a
l
co
m
p
le
x
i
ty
c
o
m
p
a
r
ed
t
o
co
n
v
e
n
t
io
n
a
l
R
a
k
e
,
s
u
ch
c
o
m
p
l
ex
i
t
y
i
s
s
h
o
w
n
i
n
T
a
b
l
e
2
.
F
o
r
t
y
p
i
c
a
l
p
a
r
a
m
e
t
er
s
(N
s
=
1
0
0
0
s
a
m
p
l
e
s
/
f
r
a
m
e
,
M=
8
)
,
P
C
-
S
-
R
a
k
e
r
eq
u
i
r
e
s
~
2
.
3
×
m
o
r
e
o
p
er
a
t
i
o
n
s
t
h
a
n
co
n
v
e
n
t
io
n
a
l
R
a
k
e
.
H
o
w
e
v
er
,
h
y
b
r
id
P
C
-
en
e
r
g
y
d
e
t
e
c
t
io
n
c
a
n
r
ed
u
c
e
t
h
i
s
o
v
e
r
h
e
a
d
b
y
4
0
%
w
i
th
<0
.
5
d
B
SN
R
p
e
n
a
l
ty
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Utiliz
in
g
p
h
a
s
e
co
n
g
r
u
e
n
cy
te
ch
n
iq
u
e
i
n
r
ec
ep
tio
n
p
erfo
r
ma
n
ce
…
(
N
a
d
ir
Mo
h
a
med
A
b
d
el
a
z
iz
)
1279
T
ab
le
2
.
C
o
m
p
u
tatio
n
al
co
m
p
l
ex
ity
co
m
p
a
r
is
o
n
b
etwe
en
PC
-
S
-
R
ak
e
an
d
co
n
v
en
tio
n
al
R
ak
e
C
o
m
p
o
n
e
n
t
O
p
e
r
a
t
i
o
n
C
o
u
n
t
C
o
m
p
l
e
x
i
t
y
O
r
d
e
r
H
i
l
b
e
r
t
t
r
a
n
sf
o
r
m
O
(
N
s
l
o
g
N
s
)
p
e
r
f
r
a
me
O
(
N
s
l
o
g
N
s
)
S
u
b
-
b
a
n
d
d
e
c
o
m
p
o
s
i
t
i
o
n
(
8
b
a
n
d
s)
8
×
O
(
N
s
l
o
g
N
s
)
O
(8
N
s
l
o
g
N
s
)
P
h
a
se
e
x
t
r
a
c
t
i
o
n
8
×
N
s
O
(8
N
s
)
P
C
me
t
r
i
c
c
o
m
p
u
t
a
t
i
o
n
8
×
N
s
m
u
l
t
i
p
l
i
c
a
t
i
o
n
s
O
(8
N
s
)
P
e
a
k
d
e
t
e
c
t
i
o
n
O
(
N
s
)
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(
N
s
)
T
o
t
a
l
PC
o
v
e
r
h
e
a
d
~
O
(
1
0
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s
l
o
g
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s
)
M
o
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e
r
a
t
e
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o
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e
n
t
i
o
n
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l
R
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k
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M
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o
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e
r
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SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
AND
ANA
L
YS
I
S
Simu
latio
n
s
wer
e
co
n
d
u
cted
i
n
MA
T
L
AB
/Si
m
u
lin
k
u
s
in
g
t
h
e
I
E
E
E
8
0
2
.
1
5
.
3
a
C
M4
ch
an
n
el
m
o
d
el
with
th
e
f
o
llo
win
g
p
ar
am
eter
s
s
h
o
wn
in
T
ab
le
3
.
T
ab
le
3
.
Simu
latio
n
p
ar
am
eter
s
co
n
d
u
cted
i
n
th
e
s
tu
d
y
P
a
r
a
me
t
e
r
V
a
l
u
e
U
W
B
P
u
l
se
6
t
h
-
d
e
r
i
v
a
t
i
v
e
G
a
u
ss
i
a
n
(
c
e
n
t
e
r
f
r
e
q
u
e
n
c
y
6
.
8
5
G
H
z
)
B
a
n
d
w
i
d
t
h
3
.
1
–
1
0
.
6
G
H
z
M
o
d
u
l
a
t
i
o
n
s
c
h
e
mes
DS
-
U
W
B
(
B
P
S
K
)
,
TH
-
U
W
B
(
P
P
M
)
C
h
a
n
n
e
l
m
o
d
e
l
I
EEE
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0
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.
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5
.
3
a
C
M
4
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S
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m)
A
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r
i
a
b
l
e
S
N
R
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0
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B
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N
B
I
I
EEE
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0
2
.
1
1
a
a
t
5
G
H
z
,
S
I
R
=
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0
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B
,
0
d
B
R
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e
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v
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t
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e
s
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o
n
v
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t
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o
n
a
l
R
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k
e
,
P
C
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S
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R
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k
e
R
a
k
e
f
i
n
g
e
r
s
4
,
8
,
1
6
,
3
2
,
6
4
,
1
2
8
P
C
s
u
b
-
b
a
n
d
s
8
(
G
a
b
o
r
f
i
l
t
e
r
b
a
n
k
)
P
C
t
h
r
e
s
h
o
l
d
γ
0
.
7
M
o
n
t
e
C
a
r
l
o
r
u
n
s
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0
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h
a
n
n
e
l
r
e
a
l
i
z
a
t
i
o
n
s
B
i
t
s
p
e
r
r
u
n
10⁵
C
o
n
f
i
d
e
n
c
e
l
e
v
e
l
9
5
%
(
e
r
r
o
r
b
a
r
s s
h
o
w
n
i
n
f
i
g
u
r
e
s)
3
.
1
.
B
E
R
perf
o
rm
a
nce
un
der
inte
rf
er
ence
Fig
u
r
e
8
co
m
p
ar
es
B
E
R
p
er
f
o
r
m
an
ce
u
n
d
er
h
ig
h
in
ter
f
e
r
e
n
ce
(
SIR=0
d
B
)
b
etwe
en
co
n
v
en
tio
n
al
R
ak
e
an
d
PC
-
S
-
R
ak
e
with
1
2
8
f
in
g
er
s
.
As
s
h
o
wn
in
Fig
u
r
e
8
,
th
e
k
e
y
o
b
s
er
v
atio
n
s
n
o
tic
ed
ca
n
b
e
c
o
n
clu
d
ed
in
:
i
)
PC
-
S
-
R
ak
e
ac
h
iev
es
4
d
B
SNR
g
ain
at
B
E
R
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0
⁻⁴,
i
i
)
th
e
r
e
is
4
0
%
B
E
R
r
ed
u
ctio
n
co
m
p
ar
ed
to
co
n
v
en
tio
n
al
R
ak
e
ac
r
o
s
s
all
SNR
,
an
d
iii
)
th
e
e
r
r
o
r
f
lo
o
r
h
as
b
ee
n
elim
in
ated
in
P
C
-
S
-
R
ak
e
wh
er
e
at
B
E
R
=
1
0
⁻³
m
ain
tain
ed
at
SIR
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0
d
B
v
s
.
co
n
v
en
tio
n
al
R
ak
e
f
ail
u
r
e.
Fig
u
r
e
8
.
B
E
R
v
s
.
SNR
f
o
r
PC
-
S
-
R
ak
e
(
1
2
8
f
in
g
er
s
)
v
s
.
co
n
v
en
tio
n
al
R
ak
e
u
n
d
er
I
E
E
E
8
0
2
.
1
1
a
i
n
ter
f
er
en
ce
(
SIR
=
0
d
B
)
in
C
M4
ch
an
n
el.
PC
-
S
-
R
ak
e
ac
h
iev
es 4
d
B
SNR
g
ain
at
B
E
R
=1
0
⁻⁴
an
d
m
ain
tai
n
s
B
E
R
=1
0
⁻³
at
SNR
=
0
d
B
wh
er
e
co
n
v
en
tio
n
al
R
ak
e
f
ails
.
E
r
r
o
r
b
a
r
s
in
d
icate
9
5
% c
o
n
f
id
en
ce
in
ter
v
als o
v
er
5
0
ch
a
n
n
el
r
ea
lizatio
n
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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:
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8
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8
7
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I
n
t J E
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&
C
o
m
p
E
n
g
,
Vo
l.
16
,
No
.
3
,
J
u
n
e
20
26
:
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2
7
2
-
1
2
8
5
1280
3
.
2
.
M
o
du
la
t
io
n
s
chem
e
co
m
pa
riso
n
Fig
u
r
e
9
co
m
p
a
r
es
DS
-
UW
B
an
d
T
H
-
UW
B
wi
th
PC
-
S
-
R
ak
e
u
n
d
er
e
x
tr
em
e
in
ter
f
e
r
en
ce
(
SIR
=
-
3
0
d
B
)
.
As s
h
o
wn
in
Fig
u
r
e
9
; D
S
-
UW
B
ac
h
iev
es 3
×
lo
wer
B
E
R
th
an
T
H
-
UW
B
at
all
SN
R
,
also
DS
-
U
W
B
's
ch
ip
-
s
y
n
ch
r
o
n
o
u
s
s
tr
u
ctu
r
e
c
r
ea
tes
r
ec
u
r
r
in
g
p
h
ase
-
alig
n
m
en
t
ev
en
ts
,
a
n
d
we
ca
n
n
o
tice
th
at
T
H
-
UW
B
's
ir
r
eg
u
lar
p
u
ls
e
tim
in
g
d
ilu
tes
p
h
ase
co
h
e
r
en
ce
wh
ich
is
c
lear
ly
lim
itin
g
PC
g
ain
s
,
f
in
ally
it
i
s
s
h
o
wn
in
Fig
u
r
e
9
th
at
at
B
E
R
=1
0
⁻³; D
S
-
UW
B
r
eq
u
ir
es 3
d
B
less
SN
R
th
an
T
H
-
UW
B
.
3
.
3
.
I
m
pa
c
t
o
f
Ra
k
e
f
ing
er
c
o
nfig
ura
t
io
n
Fig
u
r
e
1
0
s
h
o
ws cle
ar
ly
B
E
R
im
p
r
o
v
em
e
n
t w
ith
in
cr
ea
s
in
g
R
ak
e
f
in
g
er
s
in
PC
-
S
-
R
ak
e.
Fig
u
r
e
9
.
B
E
R
v
s
.
SNR
f
o
r
DS
-
UW
B
(
B
PS
K)
an
d
TH
-
UW
B
(
P
PM)
with
PC
-
S
-
R
ak
e
(
1
2
8
f
in
g
er
s
)
u
n
d
er
I
E
E
E
8
0
2
.
1
1
a
in
ter
f
er
en
ce
(
SIR
=
-
3
0
d
B
)
in
C
M4
ch
an
n
el.
DS
-
UW
B
ac
h
iev
es ~3
×
lo
wer
B
E
R
th
an
T
H
-
UW
B
d
u
e
to
ch
ip
-
s
y
n
ch
r
o
n
o
u
s
s
tr
u
ctu
r
e
en
h
an
cin
g
p
h
ase
co
h
er
en
ce
Fig
u
r
e
1
0
.
B
E
R
v
s
.
SNR
f
o
r
P
C
-
S
-
R
a
k
e
w
it
h
v
a
r
y
i
n
g
n
u
m
b
e
r
o
f
f
i
n
g
e
r
s
(
4
,
8,
1
6
,
32,
6
4
,
1
2
8
)
in
C
M
4
ch
an
n
el
(
S
I
R
=
0
d
B
)
.
I
n
c
r
e
asi
n
g
f
i
n
g
e
r
s
f
r
o
m
4
t
o
1
2
8
r
e
d
u
ce
s
B
E
R
b
y
>
4
0
%
at
SNR
=
5
d
B
.
1
2
8
-
f
i
n
g
er
co
n
f
i
g
u
r
a
ti
o
n
a
p
p
r
o
ac
h
es
t
h
e
o
r
et
ica
l
in
f
i
n
i
te
-
f
in
g
e
r
s
p
e
r
f
o
r
m
a
n
c
e
3
.
4
.
T
im
e
-
of
-
a
rr
iv
a
l
(
T
O
A)
estim
a
t
io
n a
cc
ura
cy
Fig
u
r
e
1
1
d
em
o
n
s
tr
ates T
OA
esti
m
atio
n
im
p
r
o
v
em
e
n
t w
ith
PC
-
S
-
R
ak
e.
Fig
u
r
e
1
1
.
T
OA
esti
m
atio
n
er
r
o
r
d
is
tr
ib
u
tio
n
f
o
r
PC
-
S
-
R
ak
e
v
s
.
en
er
g
y
-
b
ased
d
etec
tio
n
in
C
M4
ch
an
n
el
(
SNR
=5
d
B
)
.
PC
ac
h
iev
es 6
2
% R
MSE
r
ed
u
ctio
n
(
1
.
8
n
s
→
0
.
6
8
n
s
)
an
d
elim
in
ates la
r
g
e
er
r
o
r
s
(
>3
n
s
)
p
r
esen
t in
en
er
g
y
-
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ased
m
eth
o
d
s
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I
n
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&
C
o
m
p
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n
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SS
N:
2088
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Utiliz
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h
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s
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te
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iq
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e
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tio
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ma
n
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(
N
a
d
ir
Mo
h
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el
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Co
m
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ra
t
iv
e
re
ce
iv
er
a
rc
hite
ct
ure
perf
o
rm
a
nce
Fig
u
r
e
1
2
b
en
ch
m
ar
k
s
d
if
f
er
e
n
t U
W
B
r
ec
eiv
er
ar
ch
itectu
r
es.
Fig
u
r
e
1
2
.
B
E
R
v
s
.
SNR
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m
p
ar
is
o
n
o
f
f
o
u
r
r
ec
eiv
e
r
ar
ch
it
ec
tu
r
es in
C
M4
ch
an
n
el
(
SIR=0
d
B
)
:
i)
E
n
er
g
y
d
etec
tio
n
(
B
E
R
f
lo
o
r
at
1
0
⁻²)
; ii)
Ma
tch
e
d
f
ilter
(
4
8
% d
eg
r
ad
atio
n
in
m
u
ltip
ath
)
;
iii)
C
o
n
v
en
tio
n
al
R
ak
e
1
2
8
f
i
n
g
er
s
)
(
f
ails
at
SIR=0
d
B
)
; iv
)
PC
-
S
-
R
ak
e
(
1
2
8
f
in
g
e
r
s
)
(
o
p
tim
al
p
er
f
o
r
m
a
n
ce
,
4
d
B
g
ain
at
B
E
R
=1
0
⁻⁴)
3
.
6
.
Co
m
pa
ra
t
iv
e
re
ce
iv
er
a
rc
hite
ct
ure
perf
o
rm
a
nce
T
ab
le
4
p
r
o
v
id
es q
u
an
titativ
e
co
m
p
ar
is
o
n
o
f
PC
-
S
-
R
ak
e
v
s
.
co
n
v
en
tio
n
al
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ak
e.
T
ab
le
4
.
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a
n
titativ
e
p
er
f
o
r
m
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ce
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m
p
a
r
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o
n
: PC
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S
-
R
ak
e
v
s
.
co
n
v
e
n
tio
n
al
R
ak
e
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C
M4
C
h
an
n
el,
SIR=0
d
B
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e
t
r
i
c
C
o
n
v
e
n
t
i
o
n
a
l
R
a
k
e
PC
-
S
-
R
a
k
e
I
mp
r
o
v
e
m
e
n
t
S
N
R
a
t
B
ER
=
1
0
⁻
⁴
1
4
d
B
1
0
d
B
4
d
B
g
a
i
n
B
ER
a
t
S
N
R
=
5
d
B
4
.
2
×
1
0
⁻
²
1
.
8
×
1
0
⁻
²
5
7
%
r
e
d
u
c
t
i
o
n
TO
A
R
M
S
E
1
.
8
n
s
0
.
6
8
n
s
6
2
%
r
e
d
u
c
t
i
o
n
W
e
a
k
p
a
t
h
d
e
t
e
c
t
i
o
n
(
>
-
1
5
d
B
)
3
8
%
9
2
%
1
4
2
%
i
mpr
o
v
e
m
e
n
t
N
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I
su
p
p
r
e
ssi
o
n
(
S
I
R
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B
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1
2
d
B
2
8
d
B
1
3
3
%
i
mpr
o
v
e
m
e
n
t
M
u
l
t
i
p
a
t
h
a
m
b
i
g
u
i
t
y
e
r
r
o
r
s
4
5
%
8%
8
2
%
r
e
d
u
c
t
i
o
n
C
o
m
p
u
t
a
t
i
o
n
a
l
o
v
e
r
h
e
a
d
B
a
se
l
i
n
e
+
1
3
0
%
Tr
a
d
e
-
o
f
f
a
c
c
e
p
t
e
d
4.
DIS
CU
SS
I
O
N
4
.
1
.
K
ey
f
ind
ing
s
a
nd
im
pli
ca
t
io
ns
T
h
e
s
im
u
latio
n
r
esu
lts
v
alid
ate
p
h
ase
-
co
n
g
r
u
e
n
cy
'
s
(
PC
'
s
)
ef
f
ec
tiv
en
ess
in
o
v
er
co
m
i
n
g
f
u
n
d
am
en
tal
UW
B
ch
allen
g
es wh
ich
ca
n
b
e
co
n
clu
d
e
d
in
th
e
f
o
llo
win
g
p
o
in
ts
:
a.
Mu
ltip
ath
r
o
b
u
s
tn
ess
:
PC
id
en
tifie
s
p
h
ase
-
alig
n
ed
MPC
s
with
9
2
%
ac
cu
r
ac
y
in
th
e
p
r
o
p
o
s
ed
S
-
V
m
u
ltip
ath
d
en
s
e
C
M4
ch
an
n
el
s
,
in
clu
d
in
g
wea
k
p
ath
s
b
u
r
ie
d
b
elo
w
n
o
is
e
f
lo
o
r
(
1
4
2
%
im
p
r
o
v
em
e
n
t
o
v
er
co
n
v
en
tio
n
al
m
eth
o
d
s
)
.
T
h
is
th
r
esh
o
ld
-
f
r
ee
o
p
er
atio
n
en
ab
les
r
eliab
le
d
etec
tio
n
in
NL
OS
en
v
ir
o
n
m
e
n
ts
wh
er
e
en
er
g
y
-
b
ased
m
eth
o
d
s
f
ail.
b.
NB
I
i
m
m
u
n
ity
:
PC
m
ain
tain
s
2
8
d
B
in
ter
f
er
en
ce
s
u
p
p
r
es
s
io
n
b
y
ex
p
lo
itin
g
p
h
ase
co
n
s
is
ten
cy
—
NB
I
d
is
r
u
p
ts
p
h
ase
co
h
e
r
en
ce
o
n
ly
in
af
f
ec
ted
s
u
b
-
b
an
d
s
,
leav
in
g
PC
p
ea
k
s
in
tact
in
o
th
er
s
.
T
h
is
ex
p
lain
s
th
e
1
3
3
% im
p
r
o
v
em
e
n
t in
NB
I
s
u
p
p
r
ess
io
n
an
d
er
r
o
r
f
lo
o
r
elim
i
n
atio
n
(
B
E
R
=1
0
⁻³
m
ain
tain
ed
at
SIR
=
0
d
B
)
.
c.
L
o
w
-
SNR
o
p
er
atio
n
:
PC
ac
h
iev
es
B
E
R
=1
0
⁻³
at
S
NR
=0
d
B
th
r
o
u
g
h
n
o
is
e
-
d
is
cr
im
in
an
t
p
h
ase
m
etr
ics.
R
an
d
o
m
n
o
is
e
p
h
ases
y
ield
n
eg
lig
ib
le
PC
co
n
tr
ib
u
tio
n
s
,
en
ab
lin
g
o
p
er
atio
n
b
elo
w
th
e
0
d
B
SNR
th
r
esh
o
ld
wh
er
e
en
er
g
y
d
etec
t
io
n
co
llap
s
es.
d.
Mo
d
u
latio
n
d
e
p
en
d
e
n
ce
:
DS
-
UW
B
's
3
×
B
E
R
ad
v
an
tag
e
o
v
er
T
H
-
UW
B
u
n
d
er
NB
I
(
SIR
=
-
3
0
d
B
)
s
tem
s
f
r
o
m
s
tr
u
ctu
r
al
p
h
ase
co
h
e
r
en
ce
.
DS
-
UW
B
'
s
ch
ip
-
s
y
n
ch
r
o
n
o
u
s
PN
s
eq
u
en
ce
cr
ea
tes
r
eg
u
lar
p
h
ase
-
alig
n
m
en
t
ev
e
n
ts
at
ch
ip
b
o
u
n
d
ar
ies,
p
r
o
v
i
d
in
g
th
e
PC
alg
o
r
ith
m
with
f
r
eq
u
en
t,
s
tab
le
f
ea
tu
r
es
f
o
r
s
y
n
ch
r
o
n
izatio
n
.
T
H
-
UW
B
's a
p
er
io
d
ic
p
u
ls
e
tim
in
g
d
ilu
tes p
h
ase
co
h
er
en
ce
,
lim
itin
g
PC
g
ain
s
.
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