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e
DO
A
.
•
Step
5
: O
n
ea
c
h
in
ter
v
al
w
e
c
h
o
o
s
e
s
u
b
ar
r
a
y
g
i
v
en
a
m
a
x
i
m
u
m
o
f
s
o
u
r
ce
s
,
a
n
d
t
h
en
w
e
ca
lcu
late
th
e
m
ea
n
o
f
an
g
les to
o
b
ta
in
f
i
n
al
an
g
le
s
o
u
r
ce
s
.
Step
6
:
c
o
m
p
u
tin
g
th
e
f
in
al
DOA
,
af
ter
s
o
r
tin
g
an
d
ca
l
cu
late
th
e
av
e
r
ag
e
f
r
o
m
ea
ch
in
ter
v
a
l
an
d
s
ele
cte
d
s
u
b
a
r
r
ay
p
r
es
en
tin
g
th
e
m
ax
im
u
m
p
ea
k
s
5.
RE
SU
L
T
S O
F
SI
M
UL
AT
I
O
N
I
n
t
h
is
s
ec
tio
n
,
s
o
m
e
n
u
m
er
i
ca
l
r
esu
l
ts
ar
e
p
r
ese
n
ted
to
an
al
y
z
e
an
d
co
m
p
ar
e
th
e
est
i
m
atio
n
o
f
b
eh
av
io
r
o
f
t
h
e
n
e
w
p
r
o
p
o
s
ed
alg
o
r
ith
m
.
A
U
n
i
f
o
r
m
L
in
e
ar
A
r
r
a
y
(
U
L
A
)
w
i
th
12
in
te
r
s
en
s
o
r
s
p
ac
in
g
o
f
h
al
f
-
le
n
g
t
h
w
av
e
len
g
t
h
is
e
m
p
lo
y
ed
.
A
s
s
u
m
e
t
h
at
t
h
er
e
ar
e
t
w
o
clo
s
el
y
s
p
ac
ed
u
n
co
r
r
elate
d
n
ar
r
o
w
b
an
d
s
ig
n
al
s
o
u
r
ce
s
w
it
h
th
e
s
a
m
e
w
a
v
ele
n
g
t
h
λ
.
Si
m
u
latio
n
r
esu
lt
w
er
e
o
b
tain
ed
b
ased
o
n
1
0
0
s
n
ap
s
h
o
t
an
d
1
0
0
Mo
n
te
C
ar
lo
s
i
m
u
latio
n
r
u
n
s
.
T
h
e
m
et
h
o
d
p
r
o
p
o
s
ed
in
th
is
p
ap
er
is
d
en
o
ted
SS
-
MU
SIC
(
s
p
atial
s
a
m
p
li
n
g
MU
SIC)
.
Fig
u
r
e
3
s
h
o
w
s
an
ar
r
a
y
o
f
1
2
s
en
s
o
r
s
an
d
th
r
ee
s
u
b
n
et
w
o
r
k
s
(
L
=3
)
w
it
h
an
S
NR
=7
d
B
.
T
h
e
f
i
g
u
r
e
3
illu
s
tr
ates
th
e
d
etec
tio
n
r
i
g
h
t
r
ate
v
er
s
u
s
th
e
an
g
le
d
if
f
er
en
ce
o
f
o
u
r
p
r
o
p
o
s
ed
alg
o
r
ith
m
an
d
t
h
e
s
ta
n
d
ar
d
MU
SIC
alo
n
e
.
W
e
ca
n
s
ee
t
h
at
f
o
r
lo
w
an
g
u
lar
s
ep
ar
ati
o
n
δθ
s
ta
n
d
ar
d
MU
SIC
ca
n
n
o
t
d
etec
t
th
e
b
o
th
s
o
u
r
ce
s
,
w
h
ile
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
d
etec
t
s
lo
w
d
e
g
r
ee
an
g
u
lar
s
ep
ar
atio
n
.
I
n
t
h
is
s
ce
n
ar
io
,
Sta
n
d
ar
d
MU
SIC
d
etec
ts
an
a
n
g
u
lar
s
e
p
ar
atio
n
o
f
2
.
5
0
,
w
h
e
n
o
u
r
m
eth
o
d
SS
-
MU
SI
C
(
co
m
b
i
n
in
g
MU
SIC
a
n
d
s
p
atial
s
a
m
p
li
n
g
)
d
ete
cts
th
e
an
g
u
la
r
s
ep
ar
atio
n
at
0
.
5
0
.
T
h
u
s
,
t
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
ca
n
i
m
p
r
o
v
e
t
h
e
a
n
g
u
lar
r
eso
lu
tio
n
.
I
n
Fi
g
u
r
e
4
w
e
p
lo
t
d
etec
tio
n
p
r
o
b
ab
ilit
y
r
ate
v
er
s
u
s
SN
R
f
o
r
δθ
=
2
0
.
W
e
ca
n
s
ee
a
co
n
s
id
er
ab
le
i
m
p
r
o
v
e
m
en
t
o
f
d
etec
tio
n
p
r
o
b
ab
ilit
y
f
o
r
lo
w
SN
R
w
h
e
n
o
u
r
alg
o
r
ith
m
i
s
u
s
ed
co
m
p
ar
ed
w
i
th
MU
SIC
s
tan
d
ar
d
.
Fo
r
ex
a
m
p
le,
at
S
N
R
=1
0
,
th
e
p
r
o
b
ab
ilit
y
d
etec
ti
o
n
f
o
r
MU
SIC
s
tan
d
ar
d
is
les
s
th
a
n
1
0
%,
o
n
th
e
o
th
er
s
id
e,
it’
s
m
o
r
e
th
a
n
6
5
%
w
h
en
w
e
u
s
e
S
S
-
MU
SI
C
.
I
n
f
i
g
u
r
e
5
,
w
e
i
llu
s
tr
ate
th
e
m
ea
n
s
q
u
ar
e
er
r
o
r
(
MSE
)
f
o
r
d
ir
ec
tio
n
s
o
f
ar
r
iv
als
w
h
e
n
δ
θ
=
6
0
,
i
t
in
d
icate
s
t
h
at
S
S
-
MU
SI
C
f
o
ll
o
w
s
t
h
e
s
a
m
e
p
r
in
cip
le
a
s
M
USI
C
.
Me
a
n
w
h
ile,
it
i
n
d
icate
s
t
h
at
t
h
e
esti
m
atio
n
an
g
le
i
s
b
etter
f
o
r
w
ea
k
S
NR
,
in
th
e
o
th
er
h
a
n
d
,
f
o
r
h
i
g
h
e
r
SNR
t
h
e
n
e
w
m
et
h
o
d
d
o
es
n
’
t
g
i
v
e
a
n
y
b
etter
i
m
p
r
o
v
e
m
en
t.
F
ig
u
r
e
3
.
An
g
u
lar
r
eso
lu
tio
n
v
er
s
u
s
d
etec
tio
n
r
ate
Fig
u
r
e
4
.
SNR
v
er
s
u
s
d
etec
tio
n
r
ate
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
4
,
A
u
g
u
s
t
2
0
1
7
:
2
1
0
9
–
2
1
1
5
2114
Fig
u
r
e
5
.
SNR
v
er
s
u
s
R
M
SE
6.
CO
NCLU
SI
O
N
E
s
ti
m
a
tio
n
clo
s
ed
s
p
ac
e
s
o
u
r
ce
n
u
m
b
er
p
r
o
b
lem
ca
n
b
e
m
et
i
n
m
a
n
y
f
ield
s
a
s
r
ad
ar
,
s
o
n
ar
an
d
co
m
m
u
n
icatio
n
.
I
n
t
h
i
s
p
ap
er
,
a
n
e
w
tec
h
n
iq
u
e
co
m
b
i
n
i
n
g
MU
SIC
an
d
s
p
atial
s
a
m
p
li
n
g
ap
p
r
o
ac
h
is
b
ein
g
d
em
o
n
s
tr
ated
w
i
th
s
i
m
u
lated
ca
s
es
to
o
u
tp
er
f
o
r
m
t
h
e
co
n
v
en
t
io
n
a
l
MU
SIC
m
eth
o
d
i
n
s
ep
ar
atin
g
clo
s
el
y
s
p
ac
ed
s
o
u
r
ce
s
.
W
e
co
m
p
ar
ed
o
u
r
n
e
w
tec
h
n
iq
u
e
to
s
tan
d
ar
d
MU
SIC.
Un
d
er
th
e
ass
u
m
p
tio
n
o
f
n
u
m
b
er
o
f
s
en
s
o
r
s
m
u
s
t
b
e
lar
g
er
t
h
an
t
h
e
n
u
m
b
er
o
f
s
o
u
r
ce
s
,
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
i
m
p
r
o
v
e
s
t
h
e
d
etec
tio
n
o
f
t
w
o
clo
s
el
y
s
o
u
r
ce
s
at
lo
w
SN
R
an
d
i
m
p
r
o
v
es
t
h
e
r
eso
l
u
tio
n
w
i
th
les
s
co
m
p
u
ta
tio
n
al
co
s
t
,
t
h
a
t’
s
w
h
y
;
it
f
its
w
i
t
h
r
ea
l
ti
m
e
i
m
p
le
m
e
n
tatio
n
.
H
o
w
e
v
er
,
th
e
SS
-
MU
SI
C
i
m
p
r
o
v
es
t
h
e
r
eso
lu
tio
n
b
u
t
it
d
o
esn
’
t
i
m
p
r
o
v
e
t
h
e
esti
m
atio
n
ac
c
u
r
ac
y
.
RE
F
E
R
E
NC
E
S
[1
]
T
.
Ba
o
,
M
o
h
a
m
m
e
d
El
Ko
rso
,
H.
H.
Ou
slim
a
n
i,
“
Cra
m
é
r
–
Ra
o
Bo
u
n
d
A
n
d
S
tatisti
c
a
l
R
e
so
lu
ti
o
n
L
im
it
In
v
e
stig
a
ti
o
n
F
o
r
Ne
a
r
-
F
ield
S
o
u
r
c
e
L
o
c
a
li
z
a
ti
o
n
”
,
El
se
v
ier
Dig
it
a
l
S
ig
n
a
l
Pro
c
e
ss
in
g
,
(
2
0
1
5
),
p
p
1
2
-
17.
[2
]
S
.
M
a
rc
o
s,
“
L
e
s
m
é
th
o
d
e
s
à
Ha
u
te
Ré
so
lu
ti
o
n
,
traitem
e
n
t
d
’a
n
ten
n
e
s
e
t
a
n
a
l
y
se
sp
e
c
trale
”
,
(Éd
it
io
n
s
He
r
m
è
s
1
9
9
8
)
2
n
d
Ed
.
[3
]
N.
Ne
m
ri,
H.
W
.
Ba
d
ri,
R.
G
h
a
y
o
u
la,
H.
T
ra
b
e
lsi
,
A
.
G
h
a
rs
a
ll
a
h
,
“
S
y
n
th
e
sis
a
n
d
I
m
p
le
m
e
n
tatio
n
(In
S
T
M
8
S
)
o
f
P
h
a
se
d
Circu
lar
A
n
te
n
n
a
A
rra
y
s
Us
in
g
T
a
g
u
c
h
i
M
e
th
o
d
”
,
In
te
rn
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
m
p
u
te
r
En
g
i
n
e
e
ri
n
g
(
IJ
ECE
),
J
u
n
e
2
0
1
6
,
DO
I:
1
0
.
1
1
5
9
1
/i
jec
e
.
v
6
i3
.
9
1
9
3
[4
]
R.
Ch
a
v
a
n
n
e
s,
“
A
p
p
li
c
a
ti
o
n
d
e
s
M
é
th
o
d
e
s
d
’é
g
a
li
sa
ti
o
n
a
u
R
a
d
a
r
T
ra
n
sh
o
rizo
n
No
stra
d
a
m
u
s
”
,
P
h
D
th
e
sis
T
e
le
c
o
m
P
a
ris,
2
0
1
1
.
[5
]
A
.
Zee
sh
a
n
,
A
.
If
ti
k
h
a
r,
“
T
h
re
e
De
c
a
d
e
s
o
f
De
v
e
lo
p
m
e
n
t
in
DO
A
Esti
m
a
ti
o
n
T
e
c
h
n
o
lo
g
y
”
,
T
EL
KOM
NIKA
In
d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
,
V
o
l
1
2
No
8
,
2
0
1
4
,
p
a
g
e
s 6
2
9
7
-
6
3
1
2
.
[6
]
S
.
K.
Bo
d
h
e
,
B
.
G
.
Ho
g
a
d
e
,
S
h
a
il
e
sh
D.
Na
n
d
g
a
o
n
k
a
r,
“
Be
a
m
f
o
r
m
in
g
Tec
h
n
iq
u
e
s
f
o
r
S
m
a
rt
A
n
ten
n
a
u
sin
g
Re
c
tan
g
u
lar
A
rra
y
S
tru
c
tu
re
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
E
CE)
,
Vo
l.
4
,
No
.
2
,
A
p
ril
2
0
1
4
,
p
p
.
2
5
7
~
2
6
4
.
[7
]
T
.
D.
W
a
n
g
,
L
.
G
a
n
,
P
.
W
e
i,
H.
S
.
L
iao
,
“
DO
A
Esti
m
a
ti
o
n
o
f
Co
h
e
re
n
tl
y
Distrib
u
ted
S
o
u
rc
e
s
b
a
se
d
o
n
b
lo
c
k
S
p
a
re
s Co
n
stra
i
n
t
w
it
h
M
e
a
su
re
m
e
n
t
M
a
tri
x
Un
c
e
rtain
ty
”
,
IEI
CE
E
lec
tro
n
.
Exp
re
ss
1
0
(
2
0
1
3
)
2
0
1
2
0
8
6
3
.
[8
]
H.
A
k
a
ik
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