Computationally efficient adaptive radar pulse compression system
One aspect of this disclosure relates to a method for processing a received, modulated radar pulse to resolve a radar target from noise or other targets. According to an embodiment of the method, a radar return signal is received and samples of the radar return signal are obtained. A minimum mean-square error (MMSE) pulse compression filter is determined for each successive sample. The MMSE filter is separated into a number of components using contiguous blocking, where each component includes a piecewise MMSE pulse compression filter segment. An estimate of radar range profile is obtained from an initialization stage or a previous stage. The piecewise MMSE pulse compression filter segments are applied to improve accuracy of the estimate. The estimate is repeated for two or three stages to adaptively suppress range sidelobes to a level of a noise floor. Other aspects and embodiments are provided herein.
1. A method for estimating the range profile of a physical system that characterizes the location of scatterers in the physical system as designated by a plurality of range cells, comprising:
transmitting an energy pulse waveform to the physical system, wherein a discrete-time version of the transmitted waveform is denoted as the column vector s=[s 0 s 1 . . . s N ] T having length N, where N is an integer;
receiving a return signal produced by scattering of the transmitted waveform by the physical system as represented by the convolution of the transmitted waveform with the impulse response of the physical system, the received return signal being denoted in discrete notation at the l th range cell as:
y ( l )= x T ( l ) s+v ( l )
for l=0, . . . , L+N−2, where x(l)=[x(l) x(l−1) . . . x(l−N+4] T is the portion of the range profile that the transmitted waveform s convolves with at delay l, v(l) is a sample of an additive noise signal, and L is the number of range cells of interest;
computing an estimate {circumflex over (x)}(l) of the impulse response of the physical system and thereby the range profile as:
{circumflex over (x)} ( l )= {tilde over (w)} H ( l ) y ( l )
where {tilde over (w)}(l) is a piecewise Minimum Mean-Square Error (MMSE) pulse compression filter;
computing {tilde over (w)}(l) by combining M number of length-K filter segments corresponding to M number of length-K segments of the received signal y(l), and wherein the m th length-K filter segment {tilde over (w)} m (l) is computed as:
w
~
m
(
ℓ
)
=
(
E
[
y
~
m
(
ℓ
)
y
~
m
H
(
ℓ
)
]
)
-
1
E
[
1
M
y
~
m
(
ℓ
)
x
*
(
ℓ
)
]
for m=0, 1, . . . , M−1, where {tilde over (y)} m (l) is the m th length-K segment of the N contiguous samples of the received signal y(l); and,
combining the filter segments {tilde over (w)} m (l) in a manner corresponding to the segmentation of the received signal y(l) that approximates a range-dependent MMSE filter w(l) obtained by minimizing the MMSE cost function
J ( l )= E[|x ( l )− w H ( l ) y ( l )| 2 ]
for each individual range cell l=0, 1, . . . , L−1.
2. The method of claim 1 wherein
K
=
N
M
such that the K-length segments are of the same length.
3. The method of claim 2 wherein the received signal y(l) is segmented in a decimated manner such that:
{tilde over (y)} m ( l )=[ y ( l+m ) y ( l+M+m ) . . . y ( l+N− 2 M+m ) y ( l+N−M+m )] T
for m=0, 1, . . . , M−1; and,
wherein the filter segments are computed as:
w
~
m
(
ℓ
)
=
1
M
ρ
^
(
ℓ
)
(
C
~
m
(
ℓ
)
+
R
~
m
)
-
1
s
m
where {circumflex over (ρ)}(l)=|{circumflex over (x)}(l)| 2 is the estimated power of x(l), {tilde over (R)} m =E[{tilde over (v)} m (l){tilde over (v)} m H (l)] is a decimated noise covariance matrix based on a decimated segmentation of the noise signal v(l) like that of the received signal y(l), and the decimated signal correlation matrix {tilde over (C)} m (l) is:
C
~
m
(
ℓ
)
=
∑
i
=
0
M
-
1
∑
k
=
-
K
+
1
K
-
1
ρ
^
(
ℓ
+
Mk
-
i
+
m
)
s
i
,
k
s
i
,
k
H
where s i,k is the i th decimated segment of s delay shifted by k based on a decimated segmentation of s like that of the received signal y(l).
4. The method of claim 2 wherein the received signal y(l) is segmented into contiguous blocks such that:
{tilde over (y)} m ( l )=[ y ( l+Km ) y ( l+Km+ 1) . . . y ( l+Km+K− 2) y ( l+Km+K− 1)] T
for m=0, 1, . . . , M−1; and,
wherein the filter segments are computed as:
w
~
m
(
ℓ
)
=
1
M
ρ
^
(
ℓ
)
(
C
~
m
(
ℓ
)
+
R
~
m
)
-
1
s
m
where {circumflex over (ρ)}(l)=|{circumflex over (x)}(l)| 2 is the estimated power of x(l), {tilde over (R)} m =E[{tilde over (v)} m (l){tilde over (v)} m H (l)] is a blocked noise covariance matrix based on a blocked segmentation of the noise signal v(l) like that of the received signal y(l), and the blocked signal correlation matrix {tilde over (C)} m (l) is
C
~
m
(
ℓ
)
=
∑
k
=
-
N
+
1
K
-
1
ρ
^
(
ℓ
+
k
+
Km
)
s
k
s
k
H
where s k is the k th delay shift of the K-length blocked segment of the transmitted waveform s based on a blocked segmentation of s like that of the received signal y(l).
5. The method of claim 1 wherein
K
≠
N
M
such that the K-length segments are of varying length.
6. The method of claim 1 further comprising initializing the value of {circumflex over (x)}(l) by a matched filter method as:
{circumflex over (x)} ( l )= s H y ( l )
wherein the value of {circumflex over (x)}(l) is then updated as:
{circumflex over (x)} ( l )= {tilde over (w)} H ( l ) y ( l )
using the piecewise MMSE pulse compression filter {tilde over (w)}(l).
7. The method of claim 1 further comprising initializing the value of {circumflex over (x)}(l) and then iteratively computing the value of {circumflex over (x)}(l) as:
{circumflex over (x)} ( l )= {tilde over (w)} H ( l ) y ( l )
using the piecewise MMSE pulse compression filter {tilde over (w)}(l) for a plurality of stages in order to adaptively suppress range sidelobes to a desired level.
8. The method of claim 1 wherein the transmitted energy pulse waveform is selected from a radar pulse, an acoustic pulse, and a laser pulse.
9. A system for estimating the range profile of a physical system that characterizes the location of scatterers in the physical system as designated by a plurality of range cells, comprising:
a transmitter for transmitting an energy pulse waveform to the physical system, wherein a discrete-time version of the transmitted waveform is denoted as the column vector s=[s 0 s 1 . . . s N ] T having length N, where N is an integer;
a receiver for receiving a return signal produced by scattering of the transmitted waveform by the physical system as represented by the convolution of the transmitted waveform with the impulse response of the physical system, the received return signal being denoted in discrete notation at the l th range cell as:
y ( l )= x T ( l ) s+v ( l )
for l=0, . . . , L+N−2, where x(l)=[x(l) x(l−1) . . . x(l−N+1)] T is the portion of the range profile that the transmitted waveform s convolves with at delay l, v(l) is a sample of an additive noise signal, and L is the number of range cells of interest; and,
a processor programmed to:
compute an estimate {circumflex over (x)}(l) of the impulse response of the physical system and thereby the range profile as:
{circumflex over (x)} ( l )= {tilde over (w)} H ( l ) y ( l )
where {tilde over (w)}(l) is a piecewise Minimum Mean-Square Error (MMSE) pulse compression filter;
compute {tilde over (w)}(l) by combining M number of length-K filter segments corresponding to M number of length-K segments of the received signal y(l), and wherein the m th length-K filter segment {tilde over (w)} m (l) is computed as:
w
~
m
(
ℓ
)
=
(
E
[
y
~
m
(
ℓ
)
y
~
m
H
(
ℓ
)
]
)
-
1
E
[
1
M
y
~
m
(
ℓ
)
x
*
(
ℓ
)
]
for m=0, 1, . . . , M−1, where {tilde over (y)} m (l) is the m th length-K segment of the N contiguous samples of the received signal y(l); and,
combine the filter segments {tilde over (w)} m (l) in a manner corresponding to the segmentation of the received signal y(l) that approximates a range-dependent MMSE filter w(l) obtained by minimizing the MMSE cost function
J ( l )= E[|x ( l )− w H ( l ) y ( l )| 2 ]
for each individual range cell l=0, 1, . . . , L−1.
10. The system of claim 9 wherein
K
=
N
M
such that the K-length segments are of the same length.
11. The system of claim 10 wherein the processor is programmed to segment the received signal y(l) is in a decimated manner such that:
{tilde over (y)} m ( l )=[ y ( l+m ) y ( l+M+m ) . . . y ( l+N− 2 M+m ) y ( l+N−M+m )] T
for m=0, 1, . . . , M−1; and,
wherein the processor is programmed to compute the filter segments:
w
~
m
(
ℓ
)
=
1
M
ρ
^
(
ℓ
)
(
C
~
m
(
ℓ
)
+
R
~
m
)
-
1
s
m
where {circumflex over (ρ)}(l)=|{circumflex over (x)}(l)| 2 is the estimated power of x(l), {tilde over (R)} m =E[{tilde over (v)} m (l){tilde over (v)} m H (l)] is a decimated noise covariance matrix based on a decimated segmentation of the noise signal v(l) like that of the received signal y(l), and the decimated signal correlation matrix {tilde over (C)} m (l) is:
C
~
m
(
ℓ
)
=
∑
i
=
0
M
-
1
∑
k
=
-
K
+
1
K
-
1
ρ
^
(
ℓ
+
Mk
-
i
+
m
)
s
i
,
k
s
i
,
k
H
where s i,k is the i th decimated segment of s delay shifted by k based on a decimated segmentation of s like that of the received signal y(l).
12. The system of claim 10 wherein the processor is programmed to segment the received signal y(l) into contiguous blocks such that:
{tilde over (y)} m ( l )=[ y ( l+Km ) y ( l+Km+ 1) . . . y ( l+Km+K− 2) y ( l+Km+K− 1)] T
for m=0, 1, . . . , M−1; and,
wherein the processor is programmed to compute the filter segments as:
w
~
m
(
ℓ
)
=
1
M
ρ
^
(
ℓ
)
(
C
~
m
(
ℓ
)
+
R
~
m
)
-
1
s
m
where {circumflex over (ρ)}(l)=|{circumflex over (x)}(l)| 2 is the estimated power of x(l), {tilde over (R)} m =E[{tilde over (v)} m (l){tilde over (v)} m H (l)] is a blocked noise covariance matrix based on a blocked segmentation of the noise signal v(l) like that of the received signal y(l), and the blocked signal correlation matrix {tilde over (C)} m (l) is
C
~
m
(
ℓ
)
=
∑
k
=
-
N
+
1
K
-
1
ρ
^
(
ℓ
+
k
+
Km
)
s
k
s
k
H
where s k is the k th delay shift of the K-length blocked segment of the transmitted waveform s based on a blocked segmentation of s like that of the received signal y(l).
13. The system of claim 9 wherein
K
≠
N
M
such that the K-length segments are of varying length.
14. The system of claim 9 wherein the processor is programmed to initialize the value of {circumflex over (x)}(l) by a matched filter method as:
{circumflex over (x)} ( l )= s H y ( l )
and then update the value of {circumflex over (x)}(l) as:
{circumflex over (x)} ( l )= {tilde over (w)} H ( l ) y ( l )
using the piecewise MMSE pulse compression filter {tilde over (w)}(l).
15. The system of claim 9 wherein the processor is programmed to initialize the value of {circumflex over (x)}(l) and then iteratively compute the value of {circumflex over (x)}(l) as:
{circumflex over (x)} ( l )= {tilde over (w)} H ( l ) y ( l )
using the piecewise MMSE pulse compression filter {tilde over (w)}(l) for a plurality of stages in order to adaptively suppress range sidelobes to a desired level.
16. The system of claim 9 wherein the transmitted energy pulse waveform is selected from a radar pulse, an acoustic pulse, and a laser pulse.