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lo
w
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laten
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s
ig
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p
r
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s
s
in
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[
1
]
.
B
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f
if
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(
5
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n
etwo
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m
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(
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ar
ch
itectu
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es,
wh
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s
p
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s
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n
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a
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ten
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a
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[
2
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.
At
th
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s
am
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tim
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m
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g
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co
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p
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s
tr
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en
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a
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d
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tim
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p
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s
in
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,
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h
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(
UAV
)
-
ass
is
ted
s
en
s
in
g
ap
p
licatio
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s
[
3
]
.
Pre
s
en
t
in
n
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v
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n
s
in
ar
r
ay
d
esig
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th
at
in
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co
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m
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ac
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MI
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if
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t
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lo
ca
lizatio
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ac
cu
r
ac
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an
d
an
g
u
lar
r
eso
lu
tio
n
[
4
]
,
[
5
]
.
Sp
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s
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ten
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tell
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No
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[
6
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h
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to
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ass
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MI
MO
in
f
r
astru
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[
5
]
.
Sti
ll,
th
eir
d
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d
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ce
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n
lar
g
e
am
o
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n
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s
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s
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ap
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tech
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ased
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ess
in
r
ea
l
-
tim
e
en
v
ir
o
n
m
en
ts
[
7
]
.
I
n
p
r
ac
tical
s
itu
atio
n
s
,
f
ac
to
r
s
s
u
ch
as
n
o
n
-
u
n
if
o
r
m
n
o
is
e,
m
u
tu
al
c
o
u
p
lin
g
,
an
d
h
ar
d
war
e
is
s
u
es
m
ak
e
DOA
esti
m
atio
n
ev
en
less
ac
cu
r
ate.
Su
g
g
ested
f
ast
s
en
s
o
r
ar
r
ay
p
r
o
ce
s
s
in
g
tech
n
iq
u
es
aim
to
r
ed
u
ce
co
m
p
u
tatio
n
al
o
v
er
h
ea
d
;
h
o
wev
er
,
th
eir
ac
cu
r
ac
y
is
co
m
p
r
o
m
is
ed
in
n
o
is
y
,
s
n
ap
s
h
o
t
-
co
n
s
tr
ain
e
d
en
v
ir
o
n
m
en
ts
[
8
]
.
Ad
v
an
ce
d
r
a
d
ar
ar
c
h
itectu
r
e
s
,
s
u
ch
as
f
r
eq
u
en
cy
d
iv
er
s
i
ty
ar
r
ay
(
FDA
)
-
MI
MO
s
y
s
tem
s
,
h
av
e
b
ee
n
d
ev
elo
p
ed
to
im
p
r
o
v
e
tar
g
et
lo
ca
lizatio
n
b
y
lev
e
r
ag
in
g
ad
d
itio
n
al
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
,
m
ak
in
g
r
ed
u
ce
d
-
d
im
en
s
io
n
p
r
o
ce
s
s
in
g
,
an
d
im
p
r
o
v
in
g
DOA
esti
m
atio
n
ac
cu
r
ac
y
[
9
]
.
Pro
p
o
s
ed
tech
n
iq
u
es
f
o
r
r
ed
u
ce
d
co
m
p
lex
ity
th
r
ee
-
d
im
en
s
io
n
al
DOA
esti
m
ate
in
au
d
ito
r
y
an
d
elec
tr
o
m
a
g
n
et
ic
s
en
s
o
r
s
s
ee
k
to
o
p
tim
ize
co
m
p
u
tin
g
ef
f
icien
c
y
wh
ile
k
ee
p
in
g
s
p
atial
r
eso
lu
tio
n
[
7
]
.
No
n
eth
eless
,
th
ese
tech
n
iq
u
es
f
r
e
q
u
en
tly
p
r
esu
p
p
o
s
e
o
p
tim
al
n
o
is
e
s
ce
n
ar
io
s
an
d
ac
cu
r
ate
ar
r
a
y
ca
lib
r
atio
n
.
No
is
e
-
awa
r
e
DOA
esti
m
atio
n
h
as a
ttra
cted
co
n
s
id
er
ab
le
d
em
a
n
d
in
r
ec
en
t
y
ea
r
s
.
Sp
ec
tr
u
m
-
ad
ap
tiv
e
an
d
co
lo
r
ed
-
n
o
is
e
-
r
esil
ien
t
esti
m
ate
m
eth
o
d
o
lo
g
ies
h
av
e
b
ee
n
d
ev
is
ed
to
allev
iate
th
e
ef
f
ec
ts
o
f
n
o
n
-
u
n
if
o
r
m
n
o
is
e
co
n
d
itio
n
s
[
1
0
]
.
A
lo
t
o
f
r
esear
ch
h
as
s
h
o
wn
th
at
m
an
y
class
ical
an
d
m
o
d
er
n
DOA
esti
m
ate
m
eth
o
d
s
d
o
n
'
t
wo
r
k
well
in
m
ix
ed
-
f
ield
an
d
n
o
n
-
id
ea
l
s
itu
atio
n
s
,
esp
ec
ially
in
lar
g
e
MI
MO
s
y
s
tem
s
[
1
1
]
.
R
esear
ch
er
s
h
av
e
u
s
ed
d
is
tr
ib
u
ted
MI
MO
s
etu
p
s
an
d
r
o
tatin
g
a
r
r
ay
d
esig
n
s
t
o
im
p
r
o
v
e
ac
cu
r
ac
y
in
in
d
o
o
r
an
d
f
ad
in
g
e
n
v
ir
o
n
m
en
ts
.
H
o
wev
er
,
t
h
ese
m
eth
o
d
s
in
cr
ea
s
e
co
m
p
lex
ity
[
1
2
]
.
C
al
ib
r
atio
n
-
b
ased
tech
n
iq
u
es
ca
n
m
ak
e
esti
m
ates
m
o
r
e
ac
cu
r
at
e,
b
u
t
t
h
ey
r
eq
u
ir
e
p
r
ec
is
e
h
ar
d
war
e
alig
n
m
en
t a
n
d
m
o
r
e
p
o
wer
f
o
r
p
r
o
ce
s
s
in
g
[
1
3
]
.
I
n
teg
r
ated
s
en
s
in
g
an
d
co
m
m
u
n
icatio
n
(
I
SAC
)
s
y
s
tem
s
h
av
e
s
tr
en
g
th
en
e
d
th
e
c
o
n
n
ec
tio
n
b
etwe
en
s
ig
n
al
d
esig
n
an
d
DOA
esti
m
atio
n
,
h
ig
h
lig
h
tin
g
th
e
n
ee
d
f
o
r
m
ix
ed
o
p
tim
izatio
n
m
eth
o
d
s
[
1
4
]
.
C
h
an
g
in
g
an
ten
n
a
s
etu
p
s
t
o
esti
m
ate
s
ig
n
al
d
ir
ec
tio
n
h
as
m
ad
e
MI
MO
s
y
s
tem
s
m
o
r
e
f
lex
ib
le,
esp
ec
ially
in
n
o
is
y
s
ettin
g
s
.
Sp
ar
s
e
r
ec
o
n
s
tr
u
ctio
n
m
eth
o
d
s
u
s
e
th
e
f
ac
t
th
at
s
i
g
n
als
u
s
u
ally
co
m
e
f
r
o
m
o
n
ly
a
f
ew
d
ir
ec
tio
n
s
,
s
o
th
ey
ca
n
esti
m
ate
wh
er
e
s
ig
n
a
ls
co
m
e
f
r
o
m
with
f
ewe
r
m
ea
s
u
r
em
en
ts
[
1
1
]
.
B
u
t
t
r
ad
itio
n
a
l
s
p
ar
s
e
s
o
lv
er
s
d
o
n
o
t
h
an
d
le
n
o
is
e
well
an
d
ca
n
g
iv
e
wr
o
n
g
r
esu
lts
[
1
5
]
,
a
u
to
m
atica
lly
s
elec
t
th
e
m
o
s
t
i
m
p
o
r
tan
t
p
a
r
ts
o
f
a
s
ig
n
al.
T
h
is
h
elp
s
th
em
p
er
f
o
r
m
b
etter
i
n
n
o
is
y
en
v
ir
o
n
m
en
t
s
[
1
6
]
.
T
o
m
ak
e
s
y
s
tem
s
m
o
r
e
r
o
b
u
s
t,
r
esear
ch
e
r
s
h
av
e
d
ev
el
o
p
ed
m
et
h
o
d
s
th
at
f
o
cu
s
o
n
f
i
n
d
in
g
s
im
p
ler
s
o
lu
tio
n
s
,
s
u
ch
as
ℓ₀
-
n
o
r
m
m
in
im
izatio
n
an
d
m
atr
ix
co
m
p
letio
n
.
H
o
wev
er
,
th
ese
m
eth
o
d
s
o
f
ten
lead
to
o
p
tim
izatio
n
p
r
o
b
lem
s
th
at
ar
e
n
o
t c
o
n
v
ex
[
1
7
]
.
R
ec
en
t
r
esear
ch
h
as
g
iv
e
n
i
m
p
o
r
tan
ce
to
lo
w
c
o
m
p
lex
it
y
p
r
ed
ictio
n
tech
n
iq
u
es
an
d
te
n
s
o
r
-
b
ased
f
o
r
m
u
latio
n
s
to
in
cr
ea
s
e
th
e
ac
cu
r
ac
y
o
f
DOA
p
r
ed
ictio
n
in
m
ass
iv
e
MI
MO
an
d
r
a
d
ar
s
y
s
tem
s
[
1
8
]
.
T
ec
h
n
iq
u
es
th
at
ca
n
m
a
n
ag
e
b
o
th
co
h
er
en
t
an
d
u
n
c
o
r
r
ela
ted
s
o
u
r
ce
s
d
em
o
n
s
tr
ate
en
h
an
ce
d
ac
cu
r
ac
y
b
u
t
en
co
u
n
ter
s
ca
lin
g
ch
allen
g
es
in
ex
ten
s
iv
e
ar
r
ay
s
[
1
9
]
.
So
m
e
tech
n
iq
u
es
u
s
e
th
e
s
y
s
tem
’
s
lay
o
u
t
to
f
in
d
an
d
tr
ac
k
s
ig
n
al
s
o
u
r
ce
s
in
I
SAC
s
y
s
tem
s
,
b
u
t
th
ey
ar
e
less
ef
f
ec
tiv
e
wh
en
th
er
e
is
a
lo
t
o
f
n
o
is
e
[
2
0
]
.
Div
id
in
g
th
e
an
ten
n
a
a
r
r
ay
a
n
d
s
teer
in
g
s
ig
n
als
to
g
eth
er
ca
n
im
p
r
o
v
e
ac
cu
r
ac
y
,
b
u
t
th
is
also
s
lo
ws
d
o
wn
th
e
s
y
s
tem
an
d
m
a
k
es
it
m
o
r
e
co
m
p
lex
[
2
1
]
.
Oth
e
r
m
et
h
o
d
s
,
s
u
c
h
as
C
USE
-
T
D,
b
r
ea
k
d
o
wn
s
ig
n
al
d
ata
in
s
p
ec
ial
way
s
an
d
wo
r
k
well
ev
en
in
d
if
f
icu
l
t
s
itu
atio
n
s
,
b
u
t
th
ey
r
eq
u
ir
e
a
lo
t
o
f
c
o
m
p
u
tin
g
p
o
wer
[
2
2
]
.
Ma
ch
in
e
lear
n
i
n
g
-
b
ased
MI
MO
r
ec
eiv
er
s
ca
n
i
m
p
r
o
v
e
s
ig
n
al
d
ir
ec
tio
n
an
d
a
cc
u
r
ac
y
,
b
u
t
th
e
y
also
n
ee
d
s
i
g
n
if
ican
t
co
m
p
u
tin
g
r
eso
u
r
ce
s
[
2
3
]
.
Dee
p
lear
n
in
g
ca
n
h
elp
f
i
n
d
s
ig
n
al
s
o
u
r
ce
s
in
th
r
ee
d
im
en
s
io
n
s
,
m
ak
in
g
th
e
s
y
s
tem
m
o
r
e
r
o
b
u
s
t in
m
o
v
i
n
g
v
e
h
ic
les a
n
d
ch
an
g
i
n
g
en
v
i
r
o
n
m
e
n
ts
,
b
u
t th
ese
m
et
h
o
d
s
a
r
e
s
til
l h
a
r
d
t
o
u
s
e
i
n
r
ea
l
t
im
e
[
2
4
]
.
New
s
ig
n
al
p
r
o
ce
s
s
in
g
m
eth
o
d
s
f
o
r
elec
tr
o
m
ag
n
etic
v
ec
t
o
r
s
en
s
o
r
(
E
MV
S
)
-
MI
MO
r
a
d
ar
h
elp
th
e
s
y
s
tem
h
an
d
le
n
o
is
e
b
etter
,
b
u
t
th
ey
r
eq
u
ir
e
c
o
m
p
lex
h
ar
d
war
e.
B
ea
m
s
p
ac
e
-
b
ased
ch
an
n
el
esti
m
atio
n
m
eth
o
d
s
wo
r
k
well
f
o
r
m
illi
m
eter
-
wav
e
s
y
s
tem
s
,
b
u
t
th
e
y
ca
n
b
e
af
f
ec
ted
b
y
n
o
is
e
an
d
r
o
u
n
d
in
g
er
r
o
r
s
[
2
5
]
.
Op
tim
izatio
n
m
eth
o
d
s
lik
e
g
r
e
y
wo
lf
o
p
tim
i
za
tio
n
(
GW
O)
ar
e
n
o
w
m
o
r
e
i
m
p
o
r
tan
t
f
o
r
s
o
lv
in
g
DOA
est
im
atio
n
p
r
o
b
lem
s
.
B
ec
au
s
e
o
f
th
is
,
GW
O
is
a
s
tr
o
n
g
o
p
tio
n
f
o
r
a
d
ju
s
tin
g
h
y
p
er
p
ar
am
eter
s
wh
en
n
ee
d
ed
.
E
v
en
th
o
u
g
h
th
er
e
h
av
e
b
ee
n
b
ig
i
m
p
r
o
v
em
en
ts
in
f
in
d
i
n
g
wh
er
e
s
ig
n
als
co
m
e
f
r
o
m
,
cu
r
r
en
t
m
eth
o
d
s
s
till
h
av
e
p
r
o
b
lem
s
in
lar
g
e
MI
MO
s
y
s
tem
s
.
C
o
m
m
o
n
alg
o
r
ith
m
s
lik
e
MU
SIC
an
d
E
SP
R
I
T
ar
e
ea
s
ily
af
f
ec
ted
b
y
n
o
is
e,
ca
n
m
ak
e
m
is
tak
es,
an
d
d
o
n
o
t
w
o
r
k
as
well
wh
en
s
ig
n
als
ar
e
s
im
ilar
o
r
wh
en
th
e
r
e
is
n
o
t
m
u
c
h
d
ata.
Me
th
o
d
s
t
h
at
u
s
e
s
p
ar
s
e
r
ec
o
v
er
y
,
lik
e
o
r
th
o
g
o
n
al
m
atch
in
g
p
u
r
s
u
it
(
OM
P),
ar
e
m
o
r
e
ac
cu
r
ate,
b
u
t
th
ey
d
o
n
o
t
wo
r
k
as
well
wh
en
th
e
r
e
is
a
lo
t
o
f
n
o
is
e
o
r
wh
e
n
th
in
g
s
ch
an
g
e
q
u
ick
ly
.
M
o
s
t
r
ec
en
t
s
p
ar
s
e
B
ay
esian
lear
n
in
g
(
SB
L
)
m
eth
o
d
s
f
o
cu
s
o
n
m
ak
in
g
r
esu
lts
s
p
ar
s
e,
b
u
t
t
h
ey
o
f
ten
d
o
n
o
t
d
o
en
o
u
g
h
to
r
ed
u
ce
er
r
o
r
s
o
r
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ar
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ay
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eg
r
ess
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o
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atio
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tically
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en
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izatio
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esti
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o
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ess
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en
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ap
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a
n
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atio
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eth
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s
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r
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m
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k
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s
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m
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b
y
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o
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g
ex
p
e
n
s
iv
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m
atr
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es.
T
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le
1
.
C
o
m
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C
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p
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h
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O
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d
SB
L
SR
to
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DOA
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ately
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itio
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s
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s
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al
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tio
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s
to
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im
p
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e
r
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eiv
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ig
n
als
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d
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g
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th
eir
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g
les.
A
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ay
esian
least
s
q
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ar
es
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eg
r
ess
io
n
m
o
d
el
with
Gau
s
s
ian
p
r
io
r
s
is
u
s
ed
to
esti
m
ate
s
p
ar
s
e
s
o
u
r
ce
co
ef
f
icien
ts
.
Hy
p
er
p
a
r
am
eter
s
co
n
tr
o
l
th
e
e
f
f
ec
ts
o
f
s
p
ar
s
ity
an
d
n
o
is
e.
GW
O
i
s
u
s
ed
to
ad
ap
tiv
ely
tu
n
e
th
ese
h
y
p
e
r
p
ar
am
eter
s
b
y
m
i
n
im
izin
g
t
h
e
B
ay
esian
r
ec
o
n
s
tr
u
ctio
n
er
r
o
r
.
T
h
is
m
ak
es
co
n
v
er
g
en
ce
a
n
d
esti
m
atio
n
m
o
r
e
ac
cu
r
ate.
Af
ter
th
e
o
p
tim
i
ze
d
s
p
ar
s
e
co
ef
f
icien
ts
ar
e
u
s
ed
to
m
ak
e
a
s
p
atial
s
p
ec
tr
u
m
,
p
ea
k
d
etec
tio
n
is
u
s
ed
to
f
in
d
DOAs.
T
h
is
h
y
b
r
id
ar
ch
itectu
r
e
is
s
ca
lab
le
f
o
r
h
u
g
e
MI
MO
ap
p
licatio
n
s
an
d
o
f
f
er
s
s
tr
o
n
g
p
er
f
o
r
m
an
ce
in
p
o
o
r
SNR
an
d
lim
ited
s
n
ap
s
h
o
ts
.
2
.
1
.
M
a
s
s
iv
e
m
ultiple
-
inp
ut
m
ultiple
-
o
utput
s
y
s
t
em
m
o
d
el
C
o
n
s
id
er
an
ten
n
a
elem
en
ts
in
a
u
n
if
o
r
m
lin
ea
r
ar
r
ay
(
UL
A)
d
ep
lo
y
ed
at
th
e
b
ase
s
tatio
n
o
f
a
m
ass
iv
e
MI
MO
s
y
s
tem
[
5
]
.
L
et
≪
n
ar
r
o
wb
a
n
d
f
a
r
-
f
ield
s
o
u
r
ce
s
ar
r
iv
in
g
at
a
n
ten
n
a
ele
m
en
ts
f
r
o
m
u
n
k
n
o
wn
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ir
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tio
n
s
as g
iv
en
i
n
(
1
)
.
=
[
1
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2
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…
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]
(
1
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T
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e
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ig
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ℎ
s
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t is m
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as g
iv
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n
in
(
2
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y
(
)
=
A
(
)
s
(
)
+
n
(
)
(
2
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y
(
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∈
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1
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A
(
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=
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a
(
1
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,
…
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a
(
)
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if
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ld
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ix
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s
(
)
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×
1
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en
o
tes s
o
u
r
ce
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m
b
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,
n
(
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(
0
,
2
I
)
is
ad
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itiv
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wh
ite
Gau
s
s
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2
.
2
.
Sp
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k
T
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is
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etize
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a
f
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r
id
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f
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tio
n
s
as
in
(
3
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.
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h
is
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s
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o
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co
m
p
lete
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ictio
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ar
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as in
(
4
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.
Θ
=
{
̃
1
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2
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̃
}
,
≫
(
3
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Φ
=
[
a
(
̃
1
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a
(
̃
2
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,
…
,
a
(
̃
)
]
∈
ℂ
×
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
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2
5
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-
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3
8
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,
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4
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Au
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6
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4
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T
h
e
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ig
n
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ef
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r
m
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lated
as in
(
5
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.
Y
=
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X
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N
(
5
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W
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e
Y
∈
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th
e
m
ea
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u
r
em
en
t
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atr
ix
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d
X
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is
th
e
s
p
ar
s
e
s
ig
n
al
m
atr
ix
,
∼
(
0
,
2
)
r
ep
r
esen
ts
n
o
is
e.
On
ly
r
o
ws o
f
X
ar
e
n
o
n
-
ze
r
o
,
co
r
r
esp
o
n
d
i
n
g
t
o
th
e
tr
u
e
DOAs
[
4
]
.
2
.
3
.
Sp
a
rse
B
a
y
esia
n
lea
s
t
s
qu
a
re
s
re
g
re
s
s
io
n m
o
del
I
n
th
e
p
r
o
p
o
s
ed
SB
L
SR
[
1
7
]
f
r
am
ewo
r
k
,
s
p
ar
s
ity
in
th
e
a
n
g
u
lar
d
o
m
ain
is
en
f
o
r
ce
d
b
y
m
o
d
elin
g
ea
ch
r
o
w
o
f
t
h
e
s
o
u
r
ce
co
ef
f
i
cien
t
m
atr
ix
X
with
a
ze
r
o
-
m
ea
n
co
m
p
lex
Gau
s
s
ian
p
r
i
o
r
,
as
ex
p
r
ess
ed
in
(
6
)
.
T
h
e
v
a
r
ian
ce
h
y
p
er
p
ar
am
ete
r
s
co
n
t
r
o
l
th
e
ac
tiv
ity
o
f
ea
ch
p
o
ten
tial
d
ir
ec
tio
n
,
e
n
a
b
lin
g
a
u
to
m
atic
r
elev
an
ce
d
eter
m
i
n
atio
n
b
y
p
r
o
m
o
tin
g
s
p
ar
s
ity
in
th
e
s
o
lu
tio
n
.
T
h
e
s
tatis
tical
r
elatio
n
s
h
ip
b
etwe
en
th
e
o
b
s
er
v
ed
m
ea
s
u
r
em
en
ts
an
d
th
e
s
p
ar
s
e
co
ef
f
icien
ts
is
ca
p
tu
r
ed
th
r
o
u
g
h
th
e
Gau
s
s
ian
lik
elih
o
o
d
f
u
n
ctio
n
g
iv
en
in
(
7
)
,
wh
ich
ass
u
m
es a
d
d
itiv
e
wh
ite
Gau
s
s
ian
n
o
is
e
with
v
ar
ian
ce
2
.
(
X
∣
)
=
∏
=
1
(
x
∣
0
,
I
)
(
6
)
(
Y
∣
X
,
2
)
=
(
Y
∣
Φ
X
,
2
I
)
(
7
)
B
y
ap
p
ly
in
g
B
ay
es’
th
eo
r
em
an
d
m
in
im
izin
g
t
h
e
m
ea
n
s
q
u
ar
e
er
r
o
r
,
th
e
p
o
s
ter
io
r
m
e
an
o
f
is
o
b
tain
ed
as
(
8
)
.
B
y
jo
i
n
tly
e
x
p
lo
itin
g
th
e
p
r
io
r
an
d
lik
eli
h
o
o
d
m
o
d
els,
th
e
p
o
s
ter
io
r
d
is
tr
ib
u
tio
n
o
f
X
is
d
er
iv
ed
,
an
d
th
e
B
ay
esian
lea
s
t
s
q
u
ar
es
esti
m
ato
r
in
(
9
)
y
ie
ld
s
th
e
p
o
s
ter
io
r
m
ea
n
o
f
th
e
s
p
ar
s
e
co
ef
f
icien
ts
.
T
h
e
d
iag
o
n
al
m
atr
ix
Γ
,
f
o
r
m
e
d
b
y
th
e
h
y
p
er
p
ar
a
m
eter
s
,
ad
ap
tiv
ely
weig
h
ts
th
e
c
o
n
tr
i
b
u
tio
n
o
f
ea
ch
d
ictio
n
ar
y
ato
m
,
lead
in
g
to
ac
cu
r
ate
an
d
n
o
is
e
-
r
esil
ien
t D
OA
esti
m
atio
n
.
(
∣
,
,
2
)
∝
(
∣
,
2
)
(
∣
)
(
8
)
X
̂
=
Γ
Φ
(
ΦΓ
Φ
+
2
I
)
−
1
Y
(
9
)
W
h
er
e
∈
ℂ
×
d
en
o
tes
th
e
r
ec
eiv
ed
s
ig
n
al
m
atr
ix
,
Φ
∈
ℂ
×
is
th
e
s
en
s
in
g
(
s
teer
in
g
)
m
atr
ix
,
∈
ℂ
×
r
ep
r
esen
ts
th
e
s
p
ar
s
e
s
o
u
r
ce
co
ef
f
icien
t
m
atr
ix
,
an
d
d
en
o
tes
ad
d
itiv
e
n
o
is
e.
T
h
e
h
y
p
er
p
ar
am
eter
v
ec
to
r
=
[
1
,
2
,
…
,
]
co
n
tr
o
ls
s
p
ar
s
ity
,
an
d
Γ
=
d
iag
(
)
.
T
h
e
n
o
is
e
v
ar
ian
ce
is
d
en
o
te
d
b
y
2
.
2
.
4
.
G
re
y
wo
lf
o
ptim
iza
t
i
o
n
-
ba
s
ed
hy
perpa
ra
m
et
er
o
pti
m
iza
t
io
n
T
o
f
u
r
th
er
im
p
r
o
v
e
s
p
ar
s
ity
en
f
o
r
ce
m
e
n
t
an
d
ac
ce
ler
ate
co
n
v
er
g
en
ce
,
GW
O
is
in
co
r
p
o
r
ated
to
o
p
tim
ize
th
e
B
ay
esian
h
y
p
e
r
p
ar
am
eter
v
ec
to
r
,
as d
ef
in
ed
in
(
1
0
)
.
T
h
e
o
p
tim
izatio
n
p
r
o
ce
d
u
r
e
is
g
u
id
ed
b
y
a
f
itn
ess
f
u
n
ctio
n
in
d
icate
d
in
(
1
1
)
,
th
at
d
ec
r
ea
s
es
th
e
r
ec
o
n
s
t
r
u
ctio
n
er
r
o
r
.
T
h
e
f
ir
s
t
p
ar
t
o
f
th
e
f
itn
ess
f
u
n
ctio
n
g
u
ar
an
tees th
at
th
e
o
b
s
er
v
e
d
m
ea
s
u
r
em
en
ts
an
d
th
e
r
ec
o
n
s
tr
u
cted
s
ig
n
als ar
e
ex
ac
tly
alig
n
ed
.
T
h
e
n
ex
t
p
ar
t
c
o
n
tr
o
ls
h
i
g
h
h
y
p
er
p
a
r
am
eter
v
al
u
es
to
im
p
a
r
t
s
p
ar
s
ity
r
eg
u
lar
izatio
n
.
GW
O
f
o
llo
ws
th
e
s
o
cial
an
d
p
r
ed
at
o
r
y
c
h
ar
ac
ter
o
f
ey
wo
lv
es,
with
th
e
alp
h
a,
b
eta,
an
d
d
elta
wo
lv
es
lead
in
g
th
e
s
ea
r
ch
p
r
o
ce
s
s
[
1
3
]
.
Usi
n
g
r
ep
ea
ted
p
o
s
itio
n
ad
ju
s
tm
en
ts
an
d
en
ci
r
clin
g
s
tr
ateg
ies,
GW
O
ad
ap
ti
v
ely
o
p
tim
izes
th
e
h
y
p
er
p
ar
am
eter
s
,
f
ac
ilit
atin
g
ef
f
ec
tiv
e
s
p
ar
s
ity
r
eg
u
latio
n
,
en
h
an
ce
d
esti
m
atio
n
p
r
ec
is
io
n
,
a
n
d
c
o
n
s
is
ten
t
co
n
v
er
g
en
ce
in
DOA
esti
m
at
io
n
.
I
n
co
n
t
r
ast
to
co
n
v
en
tio
n
al
SB
L
S
R
,
wh
er
e
h
y
p
er
p
ar
a
m
eter
s
ar
e
u
p
d
ated
u
s
in
g
f
ix
ed
o
r
h
eu
r
is
tic
r
u
les,
th
e
p
r
o
p
o
s
ed
m
eth
o
d
em
p
lo
y
s
G
W
O
to
i
ter
ativ
ely
u
p
d
ate
th
e
h
y
p
er
p
ar
am
eter
v
ec
to
r
.
At
ea
c
h
iter
atio
n
,
ca
n
d
id
ate
s
o
lu
tio
n
s
r
ep
r
esen
t
d
if
f
er
en
t
h
y
p
er
p
ar
am
eter
co
n
f
ig
u
r
atio
n
s
,
an
d
th
eir
f
itn
ess
is
ev
alu
ated
u
s
in
g
t
h
e
o
b
jectiv
e
f
u
n
ctio
n
in
(
1
0
)
.
B
ased
o
n
th
e
p
o
s
itio
n
s
o
f
t
h
e
al
p
h
a,
b
eta,
a
n
d
d
elta
wo
lv
es,
th
e
h
y
p
er
p
ar
am
eter
s
ar
e
ad
ap
tiv
el
y
u
p
d
ated
to
m
i
n
im
ize
r
ec
o
n
s
tr
u
ctio
n
e
r
r
o
r
,
l
ea
d
in
g
to
im
p
r
o
v
e
d
s
p
ar
s
ity
an
d
esti
m
atio
n
ac
cu
r
a
cy
.
=
[
1
,
2
,
…
,
]
(
1
0
)
ℱ
(
)
=
∥
Y
−
Φ
X
̂
∥
2
+
∑
=
1
(
1
1
)
T
h
e
co
n
v
er
g
en
ce
b
eh
a
v
io
r
o
f
th
e
p
r
o
p
o
s
ed
a
p
p
r
o
ac
h
is
s
u
p
p
o
r
ted
b
y
th
e
in
h
e
r
en
t
p
r
o
p
er
ties
o
f
GW
O,
wh
ich
b
alan
ce
s
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
th
r
o
u
g
h
ad
ap
tiv
e
co
e
f
f
icien
t
u
p
d
ates.
T
h
is
m
ec
h
an
is
m
en
ab
les th
e
alg
o
r
ith
m
to
av
o
id
lo
ca
l m
in
im
a
an
d
co
n
v
er
g
e
to
war
d
a
n
ea
r
-
o
p
tim
al
s
o
lu
tio
n
.
C
o
m
b
in
ed
with
th
e
B
ay
esian
r
eg
r
ess
io
n
f
r
a
m
ewo
r
k
,
wh
ich
e
n
s
u
r
es
s
tab
le
esti
m
atio
n
th
r
o
u
g
h
p
r
i
o
r
m
o
d
e
lin
g
,
th
e
p
r
o
p
o
s
e
d
GW
O
-
S
B
L
S
R
ex
h
ib
its
co
n
s
is
t
en
t c
o
n
v
e
r
g
en
ce
ac
r
o
s
s
d
if
f
er
e
n
t n
o
is
e
an
d
s
n
a
p
s
h
o
t c
o
n
d
itio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
GWO
-
o
p
timiz
ed
s
p
a
r
s
e
B
a
ye
s
ia
n
lea
s
t sq
u
a
r
es reg
r
ess
io
n
fo
r
…
(
A
n
n
e
Go
w
d
a
A
leri
B
yreg
o
w
d
a
)
3435
2
.
5
.
Dire
ct
io
n
-
of
-
a
r
riv
a
l
esti
m
a
t
io
n
Up
o
n
ac
q
u
ir
in
g
th
e
o
p
tim
ize
d
s
p
ar
s
e
co
ef
f
icien
t
esti
m
ates,
th
e
DOA
in
f
o
r
m
atio
n
is
d
er
iv
ed
b
y
f
o
r
m
u
latin
g
a
s
p
atial
p
o
we
r
s
p
ec
tr
u
m
f
r
o
m
th
e
r
etr
iev
e
d
c
o
ef
f
icien
ts
.
As
s
h
o
wn
in
(
1
2
)
,
t
h
e
s
q
u
ar
e
d
ℓ
2
-
n
o
r
m
o
f
ea
ch
esti
m
ated
c
o
ef
f
icien
t
v
ec
to
r
lin
k
e
d
to
th
e
d
is
cr
et
ized
an
g
u
lar
g
r
id
is
u
s
ed
to
m
ak
e
th
e
s
p
atial
s
p
ec
tr
u
m
[
1
4
]
.
T
h
e
p
ea
k
s
in
t
h
is
s
p
ec
tr
u
m
s
h
o
w
th
at
th
er
e
ar
e
s
o
u
r
ce
s
o
f
s
ig
n
als.
T
h
en
,
as
s
h
o
wn
in
(
1
3
)
,
th
e
DOAs
ar
e
f
o
u
n
d
b
y
f
in
d
in
g
th
e
an
g
u
lar
g
r
id
p
o
in
ts
th
at
ar
e
co
n
n
ec
ted
to
th
e
m
ai
n
s
p
ec
tr
al
p
ea
k
s
.
T
h
is
p
ea
k
-
s
ea
r
ch
-
b
ased
esti
m
atio
n
lin
k
s
th
e
s
p
ar
s
e
r
ec
o
n
s
tr
u
ctio
n
r
esu
lts
d
ir
ec
tly
t
o
th
e
r
ea
l
s
o
u
r
ce
d
ir
ec
tio
n
s
,
s
o
th
er
e
is
n
o
n
ee
d
to
b
r
ea
k
d
o
wn
th
e
eig
en
v
al
u
es.
(
̃
)
=
∥
x
̂
∥
2
2
(
1
2
)
̂
=
a
r
g
ma
x
̃
(
̃
)
(
1
3
)
2
.
6
.
G
re
y
wo
lf
o
ptim
iza
t
i
o
n
-
o
ptim
ized
s
pa
rse
B
a
y
esia
n le
a
s
t
s
qu
a
re
s
re
g
re
s
s
io
n
T
h
e
GW
O
-
o
p
tim
ized
s
p
ar
s
e
l
ea
s
t
s
q
u
ar
es
r
eg
r
ess
io
n
m
eth
o
d
in
itiates
b
y
cr
ea
tin
g
an
o
v
e
r
co
m
p
lete
s
teer
in
g
d
ictio
n
ar
y
u
s
in
g
th
e
d
is
cr
etize
d
an
g
u
lar
g
r
id
an
d
s
ettin
g
th
e
B
ay
esian
h
y
p
e
r
p
ar
am
eter
s
an
d
g
r
ey
wo
lf
p
o
p
u
latio
n
as
d
escr
ib
ed
in
A
lg
o
r
ith
m
1
.
Du
r
in
g
ea
ch
iter
atio
n
,
s
p
ar
s
e
s
o
u
r
ce
co
ef
f
i
cien
ts
ar
e
co
m
p
u
ted
u
tili
zin
g
th
e
SB
L
SR
p
o
s
ter
io
r
m
ea
n
f
o
r
m
u
latio
n
.
A
f
itn
es
s
f
u
n
ctio
n
c
o
m
b
in
in
g
r
ec
o
n
s
tr
u
ctio
n
er
r
o
r
a
n
d
s
p
ar
s
ity
r
eg
u
lar
izatio
n
is
th
en
ev
alu
ated
f
o
r
all
wo
lv
es,
a
n
d
t
h
e
co
r
r
ec
t
s
o
lu
tio
n
s
a
r
e
id
e
n
tifie
d
as
,
,
an
d
wo
lv
es.
T
h
e
h
y
p
e
r
p
ar
am
ete
r
s
ar
e
a
d
ap
tiv
ely
m
o
d
if
ie
d
ac
c
o
r
d
in
g
to
th
e
g
r
ey
w
o
lf
lead
e
r
s
h
ip
h
ier
ar
c
h
y
an
d
en
cir
clin
g
m
ec
h
an
is
m
to
d
ir
ec
t
th
e
s
ea
r
ch
to
war
d
s
th
e
i
d
ea
l
s
o
lu
tio
n
.
T
h
is
iter
ativ
e
s
tep
last
s
u
n
til
th
e
co
n
v
er
g
en
ce
cr
iter
io
n
is
ac
h
ie
v
ed
.
A
s
p
atial
p
o
wer
s
p
ec
tr
u
m
is
o
b
tain
ed
f
r
o
m
th
e
o
p
tim
i
ze
d
co
ef
f
icien
ts
,
an
d
th
e
DOA
ar
e
p
r
ed
icted
b
y
f
in
d
in
g
d
o
m
in
atin
g
s
p
ec
tr
al
p
ea
k
s
,
r
esu
ltin
g
in
p
r
ec
is
e
an
d
r
eliab
le
esti
m
ates.
Alg
o
r
ith
m
1
.
GW
O
-
o
p
tim
ized
SB
L
S
R
Input
Number of antennas
, number of snapshots
, angular grid
Θ
̃
, received signal
matrix
Y
, steering dictionary
Φ
, population size
, convergence threshold
, maximum
iterations
↑
Output
Estimated DOAs
̂
Step 1
Start
Step 2
Construct the overcomplete steering dictionary
Φ
using the discretized angular
grid
Θ
̃
Step 3
Initiali
ze Bay
esian
hyper
p
arameter
s
(
0
)
=
[
1
(
0
)
,
2
(
0
)
,
…
,
(
0
)
]
and set i
terati
o
n counte
r
=
1
Step 4
Initialize Grey Wolf population (α, β, δ, and ω wolves) with candidate
hyperparameter vectors
Step 5
For loop (Repeat until convergence)
Step 6
Estimate sparse coefficients
X
̂
(
)
using SBLSR:
X
̂
(
)
=
Γ
(
)
Φ
(
Φ
Γ
(
)
Φ
+
2
I
)
−
1
Y
Step 7
Evaluate fitness function for each wolf:
ℱ
(
)
=
∥
Y
−
Φ
X
̂
(
)
∥
2
+
∑
=
1
Step 8
Identify α, β, and δ wolves based on minimum fitness values
Step 9
Update hyperparameters
(
)
using GWO encircling and hunting mechanisms
Step 10
Check convergence: If
∥
(
)
−
(
−
1
)
∥
<
or
≥
↑
, then terminate
Step 11
Increment iteration counter
=
+
1
and repeat Step 5
Step 12
Construct spatial spectrum
(
̃
)
=
∥
x
̂
∥
2
2
Step 13
Estimate DOAs by locating dominant peaks in the spatial spectrum
Step 14
Stop
3.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
T
h
e
s
ettin
g
s
ar
e
a
u
to
m
atica
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ly
ad
ju
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ted
u
s
in
g
th
e
g
r
ey
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lf
lead
er
s
h
ip
s
tr
u
ctu
r
e
an
d
s
ea
r
ch
alg
o
r
ith
m
t
o
id
en
tif
y
th
e
o
p
ti
m
al
s
o
lu
tio
n
.
T
h
e
o
p
tim
ized
p
ar
am
eter
s
ar
e
s
u
b
s
eq
u
en
tly
u
s
ed
to
c
o
n
s
tr
u
ct
a
s
p
atial
p
o
wer
s
p
ec
tr
u
m
,
f
r
o
m
wh
ich
th
e
DOAs
ar
e
d
eter
m
in
ed
b
y
id
en
tif
y
in
g
th
e
p
r
o
m
in
e
n
t
p
ea
k
s
.
T
h
e
DOA
er
r
o
r
is
esti
m
ated
u
s
in
g
(
1
4
)
.
=
√
1
∑
‖
̂
−
θ
‖
2
=
1
(
14
)
W
h
er
e
th
e
p
ar
am
eter
r
ef
er
s
to
th
e
n
u
m
b
e
r
o
f
M
o
n
te
C
ar
lo
it
er
atio
n
s
,
in
th
is
s
tu
d
y
,
θ
an
d
̂
ar
e
th
e
r
ea
l a
n
d
p
r
ed
icted
r
esu
lts
o
f
th
e
DOA
m
ea
s
u
r
em
en
t
m
o
d
els,
r
esp
ec
tiv
ely
.
T
ab
le
2
s
h
o
ws
th
e
p
ar
am
eter
s
th
at
wer
e
em
p
lo
y
ed
in
th
is
s
im
u
latio
n
in
v
esti
g
atio
n
.
All
r
o
o
t
m
ea
n
s
q
u
ar
e
er
r
o
r
(
R
MSE
)
r
esu
lts
ar
e
av
er
ag
ed
o
v
er
m
u
ltip
le
Mo
n
te
C
ar
lo
t
r
ials
(
1
,
000
–
5
,
0
0
0
r
u
n
s
)
to
en
s
u
r
e
s
tatis
tical
r
eliab
ilit
y
.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
h
as
also
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
15
,
No
.
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Au
g
u
s
t 2
0
2
6
:
3
4
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3436
b
ee
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ated
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n
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e
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e
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le
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p
ar
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ab
le
2
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am
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o
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P
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a
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(AWGN)
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p
e
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i
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e
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t
o
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o
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v
e
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W
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e
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a
t
i
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5
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o
1
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,
0
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5
,
000
Ev
a
l
u
a
t
i
o
n
p
a
r
a
me
t
e
r
R
M
S
E
3
.
1
.
M
o
nte
ca
rlo
it
er
a
t
io
n
v
a
ried
f
ro
m
1
,
0
0
0
t
o
5
,
0
0
0
Fig
u
r
e
1
illu
s
tr
ates
th
e
R
MSE
p
er
f
o
r
m
an
ce
as
a
p
ar
am
eter
o
f
th
e
n
u
m
b
er
o
f
elem
e
n
ts
f
o
r
d
if
f
e
r
en
t
DOA
esti
m
atio
n
te
ch
n
iq
u
es,
in
clu
d
in
g
th
e
p
r
o
p
o
s
ed
GW
O
-
SB
L
S
R
,
co
n
v
en
tio
n
al
SB
L
SR
,
C
USE
-
TD
[
2
0
]
,
H2
AD
[
2
3
]
,
a
n
d
th
e
o
r
etica
l CR
L
B
.
T
wo
s
im
u
latio
n
s
ce
n
ar
io
s
ar
e
co
n
s
id
er
ed
: M
o
n
te
C
ar
lo
(
Mc
)
s
ize
o
f
1
,
0
0
0
as
in
Fig
u
r
e
1
(
a)
an
d
M
o
n
te
C
ar
lo
(
Mc
)
s
ize
o
f
5
,
0
0
0
as
in
Fig
u
r
e
1
(
b
)
.
I
n
b
o
th
ca
s
es,
an
o
v
er
all
r
ed
u
ctio
n
in
R
MSE
is
in
d
icate
d
as
th
e
s
en
s
o
r
n
u
m
b
er
i
n
cr
ea
s
es,
o
win
g
to
th
e
im
p
r
o
v
e
d
s
p
atial
r
eso
lu
tio
n
an
d
en
h
an
ce
d
ar
r
ay
a
p
er
tu
r
e
.
T
h
e
co
n
s
is
ten
t
p
er
f
o
r
m
an
ce
tr
en
d
s
ac
r
o
s
s
d
if
f
er
en
t
SNR
lev
els,
s
en
s
o
r
co
n
f
ig
u
r
atio
n
s
,
a
n
d
Mo
n
te
C
ar
lo
tr
ials
.
(
a)
(
b
)
Fig
u
r
e
1
.
R
MSE
in
r
elatio
n
t
o
th
e
n
u
m
b
er
o
f
an
ten
n
as a
cr
o
s
s
d
if
f
er
en
t
m
eth
o
d
s
f
o
r
: (
a
)
Mc
s
ize
o
f
1
,
0
0
0
(
b
)
Mc
s
ize
o
f
5
,
0
0
0
Fo
r
Mc
s
ize
o
f
1
,
0
0
0
,
th
e
p
r
o
p
o
s
ed
GW
O
-
SB
L
SR
ex
h
ib
its
l
o
wer
R
MSE
co
m
p
ar
ed
to
t
h
e
b
en
ch
m
ar
k
tech
n
iq
u
es
ac
r
o
s
s
all
s
en
s
o
r
co
n
f
ig
u
r
atio
n
s
,
d
em
o
n
s
tr
atin
g
im
p
r
o
v
ed
r
o
b
u
s
tn
ess
u
n
d
e
r
lim
ited
s
tatis
t
ical
av
er
ag
in
g
.
W
h
en
th
e
Mc
s
ize
is
r
aised
to
5
,
0
0
0
,
all
tech
n
iq
u
es
y
ield
m
o
r
e
s
tab
le
R
MSE
v
alu
es
d
u
e
to
in
cr
ea
s
ed
s
tatis
tica
l
r
eliab
ilit
y
.
B
u
t
th
e
GW
O
-
SB
L
S
R
s
till
o
u
tp
er
f
o
r
m
s
an
d
is
v
er
y
clo
s
e
to
th
e
C
R
L
B
.
T
h
e
s
m
aller
R
MSE
g
ap
in
th
e
h
ig
h
er
Mc
s
ce
n
ar
io
s
h
o
ws
h
o
w
s
tab
le
an
d
ef
f
icien
t
th
e
o
p
tim
ized
SB
L
SR
f
r
am
ewo
r
k
is
at
co
n
v
er
g
in
g
.
T
h
ese
f
in
d
in
g
s
in
d
icate
th
at
t
h
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
wo
r
k
s
b
etter
f
o
r
p
r
ed
ictin
g
DOA
an
d
ca
n
h
a
n
d
le
m
o
r
e
s
en
s
o
r
s
,
ev
en
wh
e
n
th
e
Mo
n
to
C
ar
lo
co
n
d
itio
n
s
v
ar
y
.
3
.
2
.
Va
ri
a
t
io
n in
s
ig
na
l
-
to
-
n
o
is
e
ra
t
io
v
a
lues
Fo
r
alter
n
ativ
e
DOA
esti
m
at
i
o
n
alg
o
r
ith
m
s
,
Fig
u
r
e
2
s
h
o
ws
th
e
R
MSE
at
d
if
f
er
en
t
S
NR
v
alu
es
b
etwe
en
1
0
d
B
an
d
-
1
0
d
B
.
T
h
e
R
MSE
co
r
r
esp
o
n
d
in
g
to
ea
ch
SNR
lev
el
is
p
r
esen
ted
in
Fig
u
r
e
s
2
(
a)
to
2
(
e)
.
I
m
p
r
o
v
ed
s
ig
n
al
q
u
ality
a
n
d
h
ig
h
er
s
p
atial
r
eso
lu
tio
n
wi
th
m
o
r
e
s
en
s
o
r
s
r
esu
lt
in
lo
wer
R
MSE
f
o
r
all
ap
p
r
o
ac
h
es
at
h
i
g
h
er
SNR
lev
els
(
1
0
d
B
an
d
5
d
B
)
.
No
tw
ith
s
tan
d
in
g
,
t
h
e
p
r
o
p
o
s
ed
G
W
O
-
S
B
L
SR
ex
h
ib
its
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
GWO
-
o
p
timiz
ed
s
p
a
r
s
e
B
a
ye
s
ia
n
lea
s
t sq
u
a
r
es reg
r
ess
io
n
fo
r
…
(
A
n
n
e
Go
w
d
a
A
leri
B
yreg
o
w
d
a
)
3437
n
ea
r
ly
f
lawless
esti
m
atio
n
p
er
f
o
r
m
an
ce
,
co
n
s
is
ten
tly
o
b
tain
in
g
th
e
lo
west
R
MSE
ac
r
o
s
s
all
s
en
s
o
r
co
m
b
in
atio
n
s
an
d
m
ain
tain
in
g
a
clo
s
e
p
r
o
x
im
ity
t
o
th
e
C
R
L
B
.
Ho
wev
er
,
th
e
R
MSE
o
f
s
tan
d
ar
d
SB
L
SR
i
s
h
ig
h
er
,
an
d
th
e
p
er
f
o
r
m
a
n
ce
o
f
C
USE
-
T
D
[
2
0
]
a
n
d
H2
AD
[
2
3
]
d
if
f
e
r
s
s
u
b
s
tan
tially
,
p
a
r
t
icu
lar
ly
f
o
r
s
m
aller
s
en
s
o
r
ar
r
ay
s
.
As
th
e
S
NR
d
ec
r
ea
s
es
to
0
d
B
,
-
5
d
B
,
an
d
-
1
0
d
B
,
n
o
is
e
b
ec
o
m
es
m
o
r
e
n
o
ticea
b
le,
wh
ich
r
aises
th
e
R
MSE
f
o
r
all
m
eth
o
d
s
.
I
n
th
ese
h
ar
d
-
to
-
h
ea
r
s
itu
atio
n
s
,
th
e
p
er
f
o
r
m
a
n
ce
d
i
f
f
er
en
ce
b
etwe
en
th
e
s
u
g
g
ested
GW
O
-
SB
L
S
R
an
d
b
en
ch
m
ar
k
tec
h
n
iq
u
es
is
q
u
i
te
n
o
ticea
b
le.
T
h
e
im
p
r
o
v
e
d
SB
L
S
R
ef
f
ec
tiv
ely
m
an
ag
es
n
o
is
e,
m
ain
tain
in
g
l
o
w
an
d
s
tab
le
R
MSE
v
alu
es
a
cr
o
s
s
d
if
f
er
en
t
s
en
s
o
r
co
u
n
ts
.
GW
O
-
b
ased
tu
n
in
g
en
ab
les r
o
b
u
s
t p
er
f
o
r
m
an
ce
e
v
en
in
ch
allen
g
in
g
s
ig
n
al
tr
a
n
s
m
is
s
io
n
en
v
ir
o
n
m
e
n
ts
.
(
a)
(
b
)
(
c)
(
d
)
(
e)
Fig
u
r
e
2
.
R
MSE
in
r
elatio
n
t
o
th
e
n
u
m
b
er
o
f
s
en
s
o
r
s
ac
r
o
s
s
d
if
f
er
en
t te
ch
n
iq
u
es a
t: (
a)
SNR
=1
0
d
B
,
(
b
)
SNR
=5
d
B
,
(
c)
SNR
=0
d
B
,
(
d
)
SNR
=
-
5
d
B
,
an
d
(
e)
SNR
=
-
1
0
d
B
3
.
3
.
Dis
cus
s
io
n
T
ab
le
3
co
m
p
ar
es
th
e
R
MSE
v
alu
es
o
f
th
e
p
r
o
p
o
s
ed
GW
O
-
S
B
L
S
R
with
ex
is
tin
g
tech
n
iq
u
es
C
USE
-
TD
[
2
0
]
,
H2
AD
[
2
3
]
,
an
d
th
e
SB
L
SR
[
1
7
]
SNR
v
alu
es
v
ar
ied
f
r
o
m
-
1
0
d
B
t
o
1
0
d
B
.
As
SNR
in
cr
ea
s
ed
f
r
o
m
-
10
d
B
to
1
0
d
B
,
all
m
eth
o
d
s
s
h
o
w
a
c
o
n
s
id
er
ab
le
r
e
d
u
ctio
n
i
n
R
MSE
,
r
ef
lectin
g
im
p
r
o
v
e
d
p
r
ed
ictio
n
in
f
a
v
o
r
a
b
le
n
o
is
e
co
n
d
itio
n
s
.
T
h
e
o
b
s
er
v
ed
R
MSE
v
alu
es
ex
h
ib
it
lo
w
v
ar
iatio
n
ac
r
o
s
s
tr
ials
,
in
d
icatin
g
s
tab
le
co
n
v
er
g
e
n
ce
b
eh
av
io
r
.
At
lo
w
SNR
v
alu
es
-
1
0
d
B
an
d
-
5
d
B
,
wh
er
e
th
e
n
o
is
e
p
o
w
er
is
s
ev
er
ely
d
o
m
in
atin
g
s
ig
n
al
p
o
wer
,
th
e
p
r
o
p
o
s
ed
tec
h
n
iq
u
e
in
d
ic
ates
clea
r
R
MSE
r
ed
u
ctio
n
c
o
m
p
ar
ed
to
e
x
is
tin
g
m
eth
o
d
s
.
T
h
is
s
h
o
ws
th
a
t
G
W
O
-
b
a
s
e
d
h
y
p
e
r
p
a
r
a
m
e
t
e
r
o
p
t
i
m
i
z
a
ti
o
n
i
s
e
f
f
e
c
ti
v
e
a
t
r
e
d
u
c
i
n
g
e
r
r
o
r
s
c
a
u
s
e
d
b
y
n
o
i
s
e
,
as
s
h
o
w
n
i
n
F
i
g
u
r
e
3
.
T
h
e
o
p
tim
ized
SB
L
SR
k
ee
p
s
b
ea
tin
g
o
th
er
m
eth
o
d
s
at
m
o
d
er
ate
an
d
h
ig
h
SNR
lev
els
an
d
co
m
es
v
er
y
clo
s
e
to
th
e
th
e
o
r
etica
l
p
er
f
o
r
m
a
n
ce
lim
its
.
T
h
e
R
MSE
co
m
p
ar
is
o
n
g
r
a
p
h
t
h
at
g
o
es
with
th
is
s
h
o
ws
th
e
s
am
e
tr
en
d
an
d
clea
r
ly
s
h
o
ws
th
at
th
e
s
u
g
g
ested
GW
O
-
SB
L
SR
wo
r
k
s
b
etter
o
v
er
th
e
wh
o
le
SNR
r
an
g
e.
T
h
ese
r
esu
lts
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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2
2
5
2
-
8
9
3
8
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tif
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tell
,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t 2
0
2
6
:
3
4
3
1
-
3
4
4
0
3438
co
n
f
ir
m
th
at
th
e
u
p
d
ated
SB
L
SR
f
r
am
ewo
r
k
p
r
o
v
id
es
a
d
e
p
en
d
ab
le
an
d
n
o
is
e
-
r
esis
tan
t
way
to
esti
m
ate
DOA
f
o
r
lar
g
e
MI
MO
ap
p
licatio
n
s
.
T
ab
le
3
.
C
o
m
p
a
r
in
g
R
MSE
with
cu
r
r
e
n
t m
eth
o
d
s
S
N
R
(
i
n
d
B
)
R
M
S
E
i
n
C
U
S
E
-
TD
[
2
0
]
(
i
n
d
e
g
)
R
M
S
E
i
n
H
2
A
D
[
2
3
]
(
i
n
d
e
g
)
R
M
S
E
in
S
B
LSR
[
1
7
]
(
i
n
d
e
g
)
R
M
S
E
in
G
W
O
S
B
LS
R
[
P
r
o
p
o
s
e
d
]
(
i
n
d
e
g
)
-
10
2
.
0
1
1
.
7
7
1
.
4
7
1
.
4
-
5
1
.
8
6
1
.
7
2
1
.
2
2
1
.
0
2
0
1
.
5
2
1
.
3
4
0
.
8
2
0
.
7
2
5
1
.
3
3
1
.
2
1
0
.
6
5
0
.
6
2
10
0
.
7
6
0
.
8
6
0
.
5
7
0
.
4
2
Fig
u
r
e
3
.
R
MSE
v
er
s
u
s
SNR
p
er
f
o
r
m
an
ce
co
m
p
ar
is
o
n
4.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
p
r
esen
ts
an
im
p
r
o
v
ed
SB
L
SR
f
r
am
ewo
r
k
f
o
r
DOA
esti
m
atio
n
in
ex
ten
s
iv
e
MI
MO
s
y
s
tem
s
.
T
h
e
p
r
o
p
o
s
ed
a
p
p
r
o
ac
h
em
p
lo
y
s
GW
O
to
d
y
n
a
m
ically
o
p
tim
ize
B
ay
esian
h
y
p
er
p
a
r
am
eter
s
an
d
r
eg
r
ess
io
n
co
ef
f
icien
ts
with
in
th
e
SB
L
SR
m
o
d
el.
T
h
is
m
ak
es
it
p
o
s
s
ib
le
to
ef
f
ec
tiv
ely
e
n
f
o
r
ce
s
p
ar
s
ity
an
d
r
ed
u
ce
r
esid
u
al
er
r
o
r
e
v
en
wh
en
th
e
lev
el
o
f
n
o
is
e
ch
a
n
g
es.
T
h
is
in
teg
r
atio
n
m
ak
es
th
e
esti
m
ates
m
o
r
e
s
tab
le
an
d
ac
cu
r
ate
wh
ile
s
till
k
ee
p
i
n
g
th
e
s
tr
u
ctu
r
e
ea
s
y
to
co
m
p
u
te.
Simu
latio
n
r
esu
lts
s
h
o
w
th
at
th
e
p
r
o
p
o
s
e
d
GW
O
-
S
B
L
S
R
alwa
y
s
h
as
a
l
o
wer
R
MSE
th
an
tr
ad
itio
n
al
SB
L
S
R
an
d
o
th
er
DOA
esti
m
atin
g
alg
o
r
ith
m
s
,
n
o
m
atter
wh
at
SNR
lev
el,
s
en
s
o
r
s
etu
p
,
o
r
M
o
n
te
C
ar
lo
tr
ia
l
is
u
s
ed
.
W
h
en
it
co
m
es
to
b
o
th
c
o
h
er
e
n
t
a
n
d
u
n
co
r
r
elate
d
s
ig
n
als,
th
e
m
et
h
o
d
wo
r
k
s
v
er
y
well
an
d
g
et
s
r
esu
lts
th
at
ar
e
clo
s
e
to
th
e
C
r
am
ér
–
R
ao
lo
wer
b
o
u
n
d
(
C
R
L
B
)
.
T
h
e
s
tu
d
y
o
f
co
m
p
u
tatio
n
al
co
m
p
lex
ity
in
d
icate
s
th
at
en
h
an
ce
d
esti
m
atio
n
p
er
f
o
r
m
a
n
ce
is
ass
o
ciate
d
with
a
m
in
im
al
i
n
cr
ea
s
e
in
r
u
n
tim
e.
T
h
ese
r
e
s
u
lts
s
h
o
w
th
at
th
e
p
r
o
p
o
s
ed
im
p
r
o
v
ed
SB
L
SR
f
r
am
ewo
r
k
is
a
v
iab
le
an
d
s
c
alab
le
s
o
lu
tio
n
f
o
r
p
r
ac
tical
a
p
p
licatio
n
s
o
f
m
ass
iv
e
MI
M
O
an
d
MI
MO
r
ad
ar
.
Fu
tu
r
e
ef
f
o
r
ts
m
ay
ex
p
a
n
d
t
h
e
f
r
am
ewo
r
k
to
in
clu
d
e
wid
eb
an
d
s
ig
n
al
m
o
d
els
an
d
I
SAC
s
y
s
tem
s
.
T
h
e
p
r
ac
tical
ap
p
licab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
GW
O
-
SB
L
SR
f
r
a
m
ewo
r
k
ex
ten
d
s
to
r
ea
l
-
wo
r
ld
m
ass
iv
e
MI
MO
s
y
s
tem
s
in
5
G
an
d
b
ey
o
n
d
(
B
5
G)
wir
eless
co
m
m
u
n
icatio
n
s
,
wh
er
e
ac
c
u
r
ate
DOA
esti
m
atio
n
is
ess
en
tial
f
o
r
b
ea
m
f
o
r
m
in
g
a
n
d
u
s
er
l
o
ca
lizatio
n
.
T
h
e
c
o
m
p
u
tatio
n
al
s
tr
u
ctu
r
e
o
f
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
,
w
h
ich
av
o
id
s
ex
p
en
s
iv
e
m
at
r
ix
d
ec
o
m
p
o
s
itio
n
o
p
er
atio
n
s
,
m
ak
es
it
s
u
itab
le
f
o
r
s
ca
lab
le
im
p
lem
e
n
tatio
n
in
s
y
s
tem
s
with
a
lar
g
e
n
u
m
b
e
r
o
f
an
ten
n
a
el
em
en
ts
.
I
n
ad
d
itio
n
,
th
e
r
o
b
u
s
tn
ess
o
f
th
e
m
eth
o
d
u
n
d
er
lo
w
-
SNR
an
d
s
n
ap
s
h
o
t
-
lim
ited
co
n
d
itio
n
s
e
n
h
an
ce
its
s
u
itab
ilit
y
f
o
r
d
y
n
am
ic
wir
eless
en
v
ir
o
n
m
en
ts
.
Fu
r
th
er
m
o
r
e,
th
e
p
r
o
p
o
s
ed
f
r
a
m
ewo
r
k
ca
n
b
e
ef
f
ec
tiv
ely
in
te
g
r
ated
i
n
to
em
er
g
in
g
I
SAC
s
y
s
tem
s
,
wh
er
e
jo
in
t
r
ad
ar
s
en
s
in
g
an
d
co
m
m
u
n
icatio
n
f
u
n
ctio
n
alities
r
eq
u
ir
e
r
eliab
le
d
ir
ec
tio
n
esti
m
atio
n
.
T
h
e
ad
ap
tiv
e
h
y
p
er
p
ar
am
eter
o
p
tim
izatio
n
en
a
b
led
b
y
GW
O
s
u
p
p
o
r
ts
r
ea
l
-
tim
e
o
p
er
atio
n
an
d
im
p
r
o
v
es
esti
m
atio
n
s
tab
ilit
y
,
m
ak
in
g
th
e
ap
p
r
o
ac
h
p
r
o
m
is
in
g
f
o
r
p
r
ac
tical
d
ep
lo
y
m
e
n
t in
n
e
x
t
-
g
e
n
er
a
tio
n
wir
eless
an
d
r
ad
ar
p
latf
o
r
m
s
.
ACK
NO
WL
E
DG
M
E
N
T
S
W
e
s
in
ce
r
ely
ac
k
n
o
wled
g
e
SJ
B
I
n
s
titu
te
o
f
T
ec
h
n
o
lo
g
y
a
n
d
th
e
f
ac
u
lty
m
em
b
er
s
f
o
r
th
eir
v
alu
ab
le
s
u
p
p
o
r
t a
n
d
en
c
o
u
r
a
g
em
en
t th
r
o
u
g
h
o
u
t th
is
r
esear
ch
wo
r
k
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
No
f
u
n
d
in
g
is
r
aised
f
o
r
th
is
r
e
s
ea
r
ch
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
GWO
-
o
p
timiz
ed
s
p
a
r
s
e
B
a
ye
s
ia
n
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u
a
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…
(
A
n
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Go
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a
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leri
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o
w
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)
3439
AUTHO
R
CO
NT
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B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
t
r
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u
to
r
R
o
les
T
a
x
o
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o
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y
(
C
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to
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o
g
n
ize
in
d
iv
i
d
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
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ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
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co
llab
o
r
atio
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.
Na
m
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o
f
Aut
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b
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fro
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fro
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it
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g
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ll
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ffil
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lag
a
v
i.
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r
re
se
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rc
h
in
tere
sts
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d
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g
it
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l
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o
m
m
u
n
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m
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m
s,
with
a
p
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lar
f
o
c
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s
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n
5
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tec
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h
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h
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s
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sh
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d
m
o
re
th
a
n
1
7
re
se
a
rc
h
a
rti
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in
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ter
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ti
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c
a
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tac
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.
7
@
g
m
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.
c
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m
.
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