Mitigating low duty factor electronic attack (EA)
A method for mitigating low duty factor electronic attack (EA) includes taking M samples of each of N pulses of radar return energy. The method includes forming an M×N pulse sample data matrix (PSDM) using the M samples and N pulses of the radar return energy including in-phase and quadrature phase components of the radar return energy and jamming data from the low duty factor EA. The method includes defining a 2N×1 vector for each row of the PSDM. The method includes computing a 4N×1 vector separating the in-phase and quadrature phase measurements of the jamming data from the low duty factor EA into a respective half of the 4N×1 vector using the 2N×1 vector and a measurement matrix dictionary. The method includes extracting the jamming data from the 4N×1 vector and forming a clean M×N PSDM that is free of the jamming data using the 4N×1 vector.
1. A method for mitigating low duty factor electronic attack (EA) in a radar system, the method comprising:
receiving N pulses of radar return energy, the N pulses of radar return energy including jamming data from the low duty factor EA;
digitizing the received N pulses of radar return energy;
taking M samples of each of the digitized N pulses of the radar return energy;
forming an M×N pulse sample data matrix (PSDM) using the M samples and digitized N pulses of the radar return energy, wherein each cell of the PSDM includes an in-phase and quadrature phase measurement of the radar return energy and jamming data from the low duty factor EA;
defining a 2N×1 vector for each row of the PSDM, the 2N×1 vector separating the in-phase and quadrature phase measurements in each cell of the PSDM into a respective half of the 2N×1 vector;
computing a 4N×1 vector, the 4N×1 vector separating the in-phase and quadrature phase measurements of the jamming data from the low duty factor EA into a respective half of the 4N×1 vector using the 2N×1 vector and a measurement matrix dictionary;
extracting the jamming data from the 4N×1 vector; and
forming a clean M×N PSDM using the 4N×1 vector, the clean PSDM being substantially free of the jamming data from the low duty factor EA.
2. The method of claim 1 further comprising forming the measurement matrix dictionary, A, as a 2N×4N measurement matrix, wherein the 2N×4N measurement matrix dictionary is defined according to:
A
m
,
n
=
{
cos
(
2
π
mn
/
N
)
if
0
≤
n
<
N
and
0
≤
m
<
N
-
sin
(
2
π
mn
/
N
)
if
N
≤
n
<
2
N
and
0
≤
m
<
N
sin
(
2
π
mn
/
N
)
if
0
≤
n
<
N
and
N
≤
m
<
2
N
cos
(
2
π
mn
/
N
)
if
N
≤
n
<
2
N
and
N
≤
m
<
2
N
1
if
n
≥
2
N
and
m
=
n
0
else
,
where A is the measurement matrix dictionary, m and n are indices in the measurement matrix dictionary A, and N is a number of pulses emitted by the radar system.
3. The method of claim 2 , wherein the 2N×1 vector is defined according to:
y (m) :=[Re y m,1 ,Re y m,2 . . . ,Re y m,n ,Im y m,1 ,Im y m,2 . . . ,Im y m,n ] T ,
where y (m) is the 2N×1 vector corresponding to the m th row of the PSDM, Re is the in-phase measurement of the radar return energy, and Im is the quadrature phase measurement of the radar return energy, T denotes a transpose step.
4. The method of claim 3 wherein the 4N×1 vector is computed according to:
x
(
m
)
=
arg
min
x
||
x
||
l
1
s
.
t
.
||
Ax
-
y
(
m
)
||
l
2
≤
ɛ
,
where x (m) is 4N×1 vector corresponding to the m th row of the PSDM, A is the measurement matrix dictionary, l 1 and l 2 refer to l 1 and l 2 norms, ε is a non-negative number based on a measurement model uncertainty and a thermal noise level, and y (m) is the 2N×1 vector corresponding to the m th row of the PSDM.
5. The method of claim 4 wherein x (m) is chosen by minimizing:
∑
n
=
0
4
N
-
1
|
x
n
(
m
)
|
,
and
satisfying the inequality:
∑
l
=
0
2
N
-
1
(
∑
n
=
0
4
N
-
1
A
l
,
n
x
n
(
m
)
-
y
i
(
m
)
)
2
≤
ɛ
,
where x n (m) is the n-th element in the vector X (m) and y 1 (m) is the 1-th element in the vector y (m) .
6. The method of claim 5 wherein extracting the jamming data from the 4N×1 vector x (m) includes defining the jamming data according to:
j k (m) =x k+2N (m) +√{square root over (−1)} x k+3N (m) k= 0,1,2, . . . , N− 1,
where j k (m) is an N×1 vector of complex numbers representing the jamming data corresponding to the m th row of the PSDM.
7. The method of claim 6 wherein the clean M×N PSDM is defined according to:
z m,k =y k (m) −j k (m) ,
where z m,k is the clean M×N PSDM.
8. A system for mitigating low duty factor electronic attack (EA) in a radar system, the system comprising:
one or more processors;
a radar receiver configured to receive N pulses of radar return energy, the N pulses of radar return energy including jamming data from the low duty factor EA;
an analog-to-digital converter configured to digitize the received N pulses of radar return energy; and
a memory, the memory including executable code representing instructions that when executed cause the system to:
take M samples of each of the digitized N pulses of the radar return energy,
form an M×N pulse sample data matrix (PSDM) using the M samples and digitized N pulses of the radar return energy, wherein each cell of the PSDM includes an in-phase and quadrature phase measurement of the radar return energy and jamming data from the low duty factor EA,
define a 2N×1 vector for each row of the PSDM, the 2N×1 vector separating the in-phase and quadrature phase measurements in each cell of the PSDM into a respective half of the 2N×1 vector,
compute a 4N×1 vector, the 4N×1 vector separating the in-phase and quadrature phase measurements of the jamming data from the low duty factor EA into a respective half of the 4N×1 vector using the 2N×1 vector and a measurement matrix dictionary,
extract the jamming data from the 4N×1 vector, and
form a clean M×N PSDM using the 4N×1 vector, the clean PSDM being substantially free of the jamming data from the low duty factor EA.
9. The system of claim 8 wherein the memory further includes executable code representing instructions that when executed cause the system to form the measurement matrix dictionary, A, as a 2N×4N measurement matrix, wherein the 2N×4N measurement matrix dictionary is defined according to:
A
m
,
n
=
{
cos
(
2
π
mn
/
N
)
if
0
≤
n
<
N
and
0
≤
m
<
N
-
sin
(
2
π
mn
/
N
)
if
N
≤
n
<
2
N
and
0
≤
m
<
N
sin
(
2
π
mn
/
N
)
if
0
≤
n
<
N
and
N
≤
m
<
2
N
cos
(
2
π
mn
/
N
)
if
N
≤
n
<
2
N
and
N
≤
m
<
2
N
1
if
n
≥
2
N
and
m
=
n
0
else
,
where A is the measurement matrix dictionary, m and n are indices in the measurement matrix dictionary A, and N is a number of pulses emitted by the radar system.
10. The system of claim 9 , wherein the 2N×1 vector is defined according to:
y (m) :=[Re y m,1 ,Re y m,2 . . . ,Re y m,n ,Im y m,1 ,Im y m,2 . . . ,Im y m,n ] T ,
where y (m) is the 2N×1 vector corresponding to the m th row of the PSDM, Re is the in-phase measurement of the radar return energy, and Im is the quadrature phase measurement of the radar return energy, T denotes a transpose step.
11. The system of claim 10 wherein the 4N×1 vector is computed according to:
x
(
m
)
=
arg
min
x
||
x
||
l
1
s
.
t
.
||
Ax
-
y
(
m
)
||
l
2
≤
ɛ
,
where x (m) is 4N×1 vector corresponding to the m th row of the PSDM, A is the measurement matrix dictionary, l 1 and l 2 refer to l 1 and l 2 norms, ε is a non-negative number based on a measurement model uncertainty and a thermal noise level, and y (m) is the 2N×1 vector corresponding to the m th row of the PSDM.
12. The system of claim 11 wherein x (m) is chosen by minimizing:
∑
n
=
0
4
N
-
1
|
x
n
(
m
)
|
,
and
satisfying the inequality:
∑
l
=
0
2
N
-
1
(
∑
n
=
0
4
N
-
1
A
l
,
n
x
n
(
m
)
-
y
i
(
m
)
)
2
≤
ɛ
,
where x n (m) is the n-th element in the vector X (m) and y 1 (m) is the 1-th element in the vector y (m) .
13. The system of claim 12 wherein extracting the jamming data from the 4N×1 vector x (m) includes defining the jamming data according to:
j k (m) =x k+2N (m) +√{square root over (−1)} x k+3N (m) k= 0,1,2, . . . , N− 1,
where j k (m) is an N×1 vector of complex numbers representing the jamming data corresponding to the m th row of the PSDM.
14. The system of claim 13 wherein the clean M×N PSDM is defined according to:
z m,k =y k (m) −j k (m) ,
where z m,k is the clean M×N PSDM.