Digital Signal Processing Reference
In-Depth Information
0
-5
-10
-15
-20
-25
-100
-80
-60
-40 -20 0
Angle of arrival (degrees)
20
40
60
80
100
FIgure 14.15
CANAL spectrum, by LMS algorithm for one horizontally polarized interferer
from -40 degrees.
M
2N
∑∑
1
1
Λ
1
−
H
H
H
weea
=
()
θ
=
ee
+
eee
()θ
a
(14 .49)
ak
k
i
i
j
j
k
2
2
σ
σ
i
n
i
=
1
jM
= +
1
For large JNR, σ
i
2
σ
n
2
and equation (14.49) can be simplified as
2N
∑
1
1
1
H
H
H
w
=
e ea
()
θ
=
ee a
()
σ
θ
=
(
Ieea
−
)
(),
θ
(14 . 50)
ak
j
j
k
nn
k
j
j
k
2
2
2
σ
σ
n
n
n
jM
=+
1
where
e
n
and
e
j
are long matrices representing the 2
N
-by-(2
N
-
M
) and 2
N
-by-
M
eigen-
vector matrices corresponding to the noise and the jammer eigenvalues, respectively. It
is noted that the nulling weight matrix is orthogonal to the jammer subspace, and the
MUSIC spectrum can be directly obtained as
1
P
()
θ
=
.
(14 . 51)
L
∑
2
H
a
()
θ
w
ai
i
=
1
If
L
= 1, then the problem simplifies to looking for peaks by displaying the inverse
spectrum. If
L
> 1, the common nulls are emphasized, whereas spurious system nulls are
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