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2000, IEEE Signal Processing Magazine

IEEE Signal Processing Magazine

Space-time adaptive processing: a knowledge-based perspective for airborne radar2006 •

Radar systems are confronted with increasingly complex objectives in a highly non cooperative interference environment. To meet the challenge, sensor systems are forced to utilize multidimensional signal processing techniques. In fact, conventional signal processing perform poorly due to lack of knowledge of highly dimensional statistic requirements. On the other hand, traditional adaptive signal processing techniques break down or have suboptimal performance in these cases. A possible approach is optimal or suboptimal Space-Time Adaptive Processing (STAP) techniques. This article presents an introduction to STAP which was originally developped for detecting slow moving objectives from airborne radars. STAP is a data domain implementation of an optimal filter solution. The optimum filter is designed based on the known covariance matrix and the known Doppler-angle

IEE Proceedings - Radar, Sonar and Navigation

Localised three-dimensional adaptive spatial–temporal processing for airborne radar2003 •

IEEE Transactions on Aerospace and Electronic Systems

Adaptive antenna space-time processing techniques to suppress platform scattered clutter for airborne radar1995 •

Advanced airborne radar may require adaptive space-time processing (STP) to detect small targets at long ranges. STP is a multidimensional adaptive filter that resolves received radar data into a spectrum of plane waves in angular and Doppler Frequency coordinates. The platform of an airborne radar can scatter incident signals into the antenna, spreading the spectra of the clutter signals so that it overlaps the target signal and therefore increases the false alarm rate. To reduce the processing requirements of a full STP filter, a suboptimal architecture with fewer degrees of freedom is demonstrated and compared with the optimal architecture.

Space-time adaptive processing (STAP) has a huge computational complexity and a large training samples requirement, which limit its practical applications. The traditional post- Doppler adaptive processing methods such as factored approach (FA) and extended factored approach (EFA) can significantly reduce the computational complexity and the training sample requirement in adaptive processing, and maintain nearly the same performance as the optimal STAP. However, because training samples are restricted in real-world environ- ments, their performances can be considerably degraded in the large-scale antenna array. To solve this problem, the post-Doppler adaptive processing method based on the spatial domain reconstruction is proposed. In this method, the spatial clutter data after Doppler filtering is reconstructed as a matrix that has close columns and rows. The spatial weights vector in FA or EFA is also re-expressed as the product of two shorter weight vectors. Then the cyclic minimizer is applied to find the desired solution. Experimental results show that the proposed method has the advantages of fast convergence and small training samples requirement. It has greater moving target detection ability especially under the condition for large-scale antenna array and small training samples support than FA and EFA

International Conference on Aerospace Sciences and Aviation Technology

A New-Partially Adaptive Space-Time Filtering Technique for Interference Suppression in Phased Array Radar Systems2003 •

IEEE Transactions on Aerospace and Electronic Systems

Multi-Waveform Space-Time Adaptive Processing2017 •

IET Radar, Sonar & Navigation

Models and performance evaluation for multiple-input multiple-output space–time adaptive processing radar2009 •

Proceedings of the 2004 IEEE Radar Conference (IEEE Cat. No.04CH37509)

Adaptive beam-domain processing for space-based radars2018 •

The training data selection and update are crucial steps for the space-time adaptive processing (STAP) operation, since contaminated training data result in a decreased clutter suppression performance, an incorrect constant false alarm rate (CFAR) threshold and target cancellation by self-whitening. This paper presents a promising algorithm that selects the training data by applying a moving window, taking into account the changes of the clutter statistics over space and time. The goal is to improve the clutter suppression capability and, thus, to increase the number of true detections. The benefits of the proposed algorithm are verified using real 4-channel X-band radar data acquired by the DLR’s airborne F-SAR.

[Joseph R. Guerci and Edward J. Baranoski]
© EYEWIRE
Knowledge-Aided
Adaptive Radar
at DARPA
[An overview]
F
or the past several years, the Defense Advanced
Research Projects Agency (DARPA) has been pioneering the development of the first ever real-time knowledge-aided (KA) adaptive radar architecture. The
impetus for this program is the ever increasingly complex missions and operational environments encountered by
modern radars and the inability of traditional adaptation methods to address rapidly varying interference environments. The
DARPA KA sensor signal processing and expert reasoning
(KASSPER) program has as its goal the demonstration of a high
performance embedded computing (HPEC) architecture capable
1053-5888/06/$20.00©2006IEEE
of integrating high-fidelity environmental knowledge (i.e., priors) into the most computationally demanding subsystem of a
modern radar: the adaptive space-time beamformer. This is no
mean feat as environmental knowledge is a memory quantity
that is inherently difficult (if not impossible) to access at the
rates required to meet radar front-end throughput requirements. In this article, we will provide an overview of the
KASSPER program highlighting both the benefits of KA adaptive radar, key algorithmic concepts, and the breakthrough lookahead radar scheduling approach that is the keystone to the
KASSPER HPEC architecture.
IEEE SIGNAL PROCESSING MAGAZINE [41] JANUARY 2006
BACKGROUND ON SPACE-TIME ADAPTIVE PROCESSOR
Even for a nonspecialist, it is not hard to qualitatively imagine
the enormous challenges presented to modern airborne radar
systems when attempting to separate ephemeral ground target
echoes (associated with moving vehicles, for example) from
overwhelming land clutter returns, which can be eight or more
orders-of-magnitude stronger than the desired target, especially in highly complex and nonstationary clutter environments (e.g., urban clutter) [1]–[4]. The lion’s share of this signal
separation/detection task falls to the real-time, space-time adaptive processor (STAP) [5]–[7].
STAP attempts to filter out the clutter and noise returns by
an adaptive multidimensional finite impulse response (FIR) filter structure, as depicted in Figure 1, consisting of M time taps
to support Doppler filtering, and N spatial taps to support
angle processing. By judicious setting of the complex weights,
{wi, j }, a two-dimensional (2-D) angle-Doppler adaptive antenna pattern can be obtained that maximizes the return from a
desired target resolution cell, while
simultaneously minimizing the
returns from clutter and possibly
N Antenna Elements
jamming. A notional example of this
es T
Antenna
process is depicted in Figure 2(a)
s
T
T
l
Pu
N
M
2
1
and (b), where the clutter plus noise
xNM
.
×
×
×
T
T
T
wNM
power spectrum of Figure 2(a) is filxN+1
x2N
xN+2 .
PRI
tered by the pattern in Figure 2(b).
.
.
×
w2N
wN+2
×
Delay ×
xN
wN+1
Note that an airborne radar is
x2
x
.
.
×
× 1 w1. +
×
wN +
w2 +
assumed as evidenced by the angleDoppler coupled clutter ridge which
Σ +
Σ +
Σ +
+
+
+
is the result of aircraft motion [7].
Σ +
Σ +
Σ +
The multidimensional adaptive
FIR filter thus consists of a total of
+
NM taps [or spatio-temporal
degrees-of-freedom (DOFs)]. The
+ Σ +
spatial DOFs could be the outputs
of individual antenna array elements (as part of an electronically
y = w'x
scanned array for example), subarrays, or outputs of a beamformer
[FIG1] Space-time (angle-Doppler) beamformer consisting of N independent antenna
channels and M time taps (pulse returns) comprising the coherent processing interval (CPI). A
[7]; while the temporal DOFs could
specific angle-Doppler pattern is obtained by judicious selection of the complex linear
be the sampled pulse returns or
combiner weights. For other space-time variations of the above architecture (e.g., postDoppler bins [7]. In any case, the
Doppler beamspace), see [6] and [7].
−10
D
D
Di opp
str le
ibu r C
tio lut
ν= 0
n ter
(Impulse
−20
−30
ν≠
−40
0.5
No
rm
0
ν=0
Target
e
0
ize 0
idelob
ν≠
eting S
p
d
m
o
C
r
Do
Clutte 0
pp
le −0.5
Angle
r
alized
−0.5
Norm
al
0.5
θJ = –60°
1
θJ = –30°
θJ = +45°
2
3
Jammer Nulls
0
−10
−20
−30
ch
−40
ot
0
t
ut
Cl
N
er
−50
−60
Relative Amplitude (dB)
0
1-
Normalized Doppler
Relative Amplitude (dB)
n
tributio
tter Dis
tial Clu
a
p
S
1-D
−70
0.5
−0.5
−0.5
−80
0
Normalized Angle
(a)
0.5
(b)
[FIG2] (a) Notional clutter spectrum for an airborne MTI radar and (b) the optimal 2-D space-time filter response for a boresight aligned
target with a normalized Doppler of 0.25 [7].
IEEE SIGNAL PROCESSING MAGAZINE [42] JANUARY 2006
optimum STAP weights vector, w ∈ C NM , that maximizes
the signal-to-interference-plus-noise ratio (SINR), satisfies
the matrix Weiner-Hopf equation
w = R−1 s,
(1)
ed by the STAP algorithm, and L data samples are used in the
formation of (2). Ideally, if the snapshot data samples were
drawn from a Gaussian independent and identically distributed (i.i.d.) stochastic process, then (2) corresponds to the
maximum likelihood (ML) covariance estimate, i.e.,
R̂ = arg max f (x i : i = 1, . . . , L | R),
(3)
where s ∈ C NM is the desired target signal of interest (i.e.,
{R }
steering vector [7]), and R ∈ C NM×NM is the clutter-plusjamming-plus-noise covariance matrix [7], which is guaranwhere f (x i : i = 1, . . . , L | R) denotes the probability density
teed to be positive definite in
function (pdf) of L snapshots conpractice due to the omnipresent
ditioned on R. Reed, Mallet, and
receiver noise [7].
Brennan (RMB) have shown that
THE IMPETUS FOR THIS PROGRAM
A meditation of (1), in the
in this case, the expected SINR
IS THE EVER INCREASINGLY COMPLEX
context of practical real-world
loss ratio (adaptive/ideal), ρ, due
MISSIONS AND OPERATIONAL
considerations, leads one to
to
finite sample estimation is [10]
ENVIRONMENTS
immediately recognize a set of
serious fundamental issues [7].
L − NM + 2
L ≥ NM,
(4)
ρ=
■ R is potentially very large (due to the product NM).
L+1
■ R cannot be known a priori since it depends on the clutter
where it is assumed that there are at least NM samples. Note
and jamming environment. It must therefore be estimated, at
that ρ → 1 as NM → ∞ as expected. A useful rule-of-thumb
least in part, on the fly.
derived from (4) is that, to achieve a loss no greater than 3 dB,
■ Due to the unknown statistics of the radar interference,
at least on order of 2NM i.i.d. samples are required. For an
R must be determined adaptively from the data.
N = 16, M = 16, case, this corresponds to an assumption that
■ The need for immediate results will require (1) to be impleat least 512 i.i.d. samples are available that share identical statismented on the aircraft in real time.
tics with the cell under test.
A first-generation solution to these issues essentially consists of
In practice, the L training samples are derived from a subset
the following elements [5]–[7]:
of the total space-time data cube measured during a coherent
■ selection of the STAP domain (e.g., pre-Doppler element
processing interval (CPI) [5]. One such commonly discussed
space and post-Doppler beamspace [7])
scheme is depicted in Figure 3. Unfortunately, as will be made
■ selection of a rank-reduction method since a full dimensional implementation of (1) is not only very difficult and costly but
often not a good idea since adding adaptive DOFs (ADOFs) can
actually hurt performance in nonstationary environments
−
[1]–[3], [7]
−
■ selection of a covariance estimation scheme (implicit or
−
Array
explicit) [5]–[7]
Snapshot Vector
■ a real-time computing architecture [8].
X i+2
Although many ingenious solutions to the first, second, and
fourth items have been devised, they have been predicated on a
X i+1
single basic approach to the third: sample covariance estimation
derived from local radar measurements [5]–[7]. In practice, this
Range
Test Cell
Xi
estimation is generally implicit since the solution to a real-time
computing architecture generally consists of a data domain
implementation (e.g., a QR-factorization implemented via a parX i −1
Guard Cells
allel pipelined computing architecture [8], [9]) in which a covariance matrix is not explicitly formed. It is, nonetheless,
X i −2
mathematically equivalent to replacing R in (1) with a sample
−
estimate R̂ generally of the form
−
−
R̂ =
1
L
x i x′i ,
(2)
i∈{L data samples }
where x i ∈ C NM is a space-time snapshot [7] data vector for
the ith range bin measured by the radar in the domain select-
[FIG3] An example data selection strategy for estimating a
sample space-time covariance matrix. L data samples are selected
from range bins in proximity to a range cell under test (ith range
bin in this example). The actual test cell, and cells adjacent to it
(guard cells), may be excluded to avoid contamination from the
actual target signal [5].
IEEE SIGNAL PROCESSING MAGAZINE [43] JANUARY 2006
readily apparent in the next section, real-world clutter often violates any such stationarity assumptions.
KA-STAP
Range Bin
BACK TO “BAYES-ICS”
EXAMPLES OF REAL-WORLD CLUTTER
In this section, we describe in some detail basic ways in which
It is obvious that real-world ground clutter is not well modprior knowledge can be incorporated into the most demanding
eled by a homogenous stationary stochastic process [1]–[3].
component of a modern moving target indication radar: the
Variations in underlying terrain, foliage, land-sea interfaces,
space-time adaptive beamformer. Though radar centric, the
and urban/manmade strucmethods discussed in the followtures, as well as nonlinear array
ing were specifically chosen due
responses (e.g., circular and/or
to their general applicability in
LOOK-AHEAD RADAR SCHEDULING IS
tilted arrays [24], [25]), all conmany other adaptive sensor sigTHE KEYSTONE TO THE KASSPER
tribute to stationarity violanal processing systems such as
HPEC ARCHITECTURE
tions. Consequently, significant
sonar, lidar, and other multidideviations from predicted ideal
mensional sensor arrays, where
performance are to be expected—their exact nature of course
environmental clutter (as opposed to say random thermal
depends intimately on the interference [3].
receiver noise) is a dominant source of interference. We will
Figure 4 shows a comparison between actual measured
describe two broad categories of KA processing: Case I—
radar returns for the DARPA Mountain Top experimental UHF
Intelligent Training and Filter Selection (ITFS) and Case II—
radar [11] located at the White Sands Missile Range in New
Bayesian Filtering and Data Prewhitening. The former
Mexico [Figure 4(a)] and what would have been measured if
consists of primarily indirect exploitation of prior knowledge
the terrain were homogenous [Figure 4(b)]. This form of
sources (such as training data selection), while the latter entails
inhomogeneity leads to either over or under nulling of the
direct filtering of the incoming multidimensional data stream
clutter [7], with resulting poor detection or false alarm rate
based on prior information.
performance, respectively.
Figure 5 shows data from an experimental X-band airborne
CASE I—ITFS
radar [12]. Clearly evident are distinct bright clutter discretes
In the ITFS approach, prior knowledge of the interference envithat will not be adequately nulled if an averaging process like (2)
ronment is used to optimize two adaptive filtering processes: the
is simply applied.
filter selection and the filter training strategy. In the case of
For details on the many deleterious effects of nonstationary
radar clutter, this is accomplished by first conducting an envinon-Gaussian, real-world clutter, the reader is referred to the
ronmental segmentation analysis based on whatever prior terproceedings of the KASSPER workshops [13], available via the
rain/clutter database is available. Everything from digital terrain
internet at www.darpa.mil/spo/programs/kassper.htm.
and elevation data, land cover/land use (LCLU) to synthetic
aperture radar (SAR) imagery; even hyperspectral imagery can
be used [1]. Land clutter tends to be clumpy, that is it
tends to be locally similar but with distinct and often
abrupt boundaries (see Figure 6 for example). Clearly
600
600
from physical principles, an adaptive filter should not
attempt to lump all these regions together and apply a
500
500
single filtering strategy. Instead, a segmentation analysis
should be performed and an adaptive filter tailored to that
400
400
region should be applied.
Generally speaking, the filter selection stage deter300
300
mines what type of adaptive filter is best suited to a
given segmented region. In the case of STAP filtering
200
200
for clutter suppression in radar, a pivotal step is the
domain in which the actual filtering is performed (e.g.,
100
100
pre- or post-Doppler or element or beamspace [5]–[7])
and the number of ADOFs, which manifests itself ultimately in the size of the adaptive filter. For example, in
0
200
0
200
−200
−200
the case of the principal components (PC) method, the
Doppler (Hz)
Doppler (Hz)
number of ADOFs refers to the number of significant
(a)
(b)
eigenvectors to be included in the adaptive weight cal[FIG4] Comparison between (a) real-world clutter from the DARPA
culation. Similarly, for the multistage Weiner filter, the
Mountain Top radar and (b) returns assuming homogenous clutter [7].
number of stages is the metric for ADOFs [14]. What is
The colormap scale is in decibels and ranges from 0 (noise floor, dark
critical is that the number of ADOFs be matched to the
blue) to 70 dB (dark red).
IEEE SIGNAL PROCESSING MAGAZINE [44] JANUARY 2006
Scatterer Power (dB)
600
20
400
10
20
600
200
0
0
−200
−10
−400
−20
Down Range (m)
Down Range (m)
Resolution Cell Power (dB)
10
400
200
0
0
−10
−200
−20
−400
−600
−600
−30
−30
−600 −400 −200 0 200 400 600 800 1,000
Cross Range (m)
−600−400 −200 0 200 400 600 800 1,000
Cross Range (m)
(b)
(a)
[FIG5] Example real-world X-band radar measurements corresponding to a geographical location with discrete clutter (see [14] for
details). (a) Hi-resolution geo-registered reflectivity image. (b) Corresponding discrete map.
Range Bin %
available training data (and of course the real-time computing
this approach is the Bayesian covariance estimation approach of
architecture). A general rule of thumb, which has its origins in
Anderson [16].
the RMB result (4) but is rigorously proved by Smith [27], is
Wishart [17] established that the elements of a sample
that there be on order 2k i.i.d. samples available for training
covariance matrix [L R̂] i, j formed from an outer product sum of
the adaptive weights (e.g., sample covariance estimation),
L Gaussian i.i.d. samples, i.e.,
where k is the number of effective ADOFs.
L
1
Once a basic filtering structure has been selected, a training
x i x′i
(5)
R̂ =
strategy can be selected and optimized for that choice. Basically,
L i=1
all or a subset of the samples from the locally stationary region
obey a Wishart distribution (actually complex Wishart [18]) of
are utilized in the weight training stage. In the case of PC, all of
degree L, i.e., R̂ ∼ W(L R̂, L).
the range bins—including the cell under test—might be included
since it has been shown that this approach is robust to target cancellation. In contrast, a multibin post-Doppler
approach without a PC technique might need to take extra
Scan % = 4,796
care and introduce exclusion and guard cells to prevent
1,000
target signal cancellation [5].
80
Figure 7 illustrates the impact that ITFS can have
900
when applied to real-world data. As described in [15],
800
70
the multichannel airborne radar measurement
700
(MCARM) data set (see Figure 6) included a number of
significant highways, i.e., moving clutter. If one simply
60
600
applied traditional sample averaging techniques such
500
as those previously described, one could suffer signifi50
400
cant detection losses at roadway speeds [15]. Using an
intelligent training and adaptation scheme that essen300
40
tially took account of the road networks, a significant
200
improvement in detection was achieved.
100
CASE II—BAYESIAN FILTERING AND
DATA PREWHITENING
In the Bayesian approach to radar STAP, prior knowledge
is used directly by the filter to aid in adapting to nonstationary clutter. A convenient pedagogical framework for
30
−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4
Fractional Doppler Frequency
[FIG6] Measured range-Doppler returns for the MCARM dataset [12]
showing the highly segmented nature of radar clutter returns.
IEEE SIGNAL PROCESSING MAGAZINE [45] JANUARY 2006
If a prior estimate of the covariance matrix exists, R̂0 , it is
not unreasonable to assume it too is Wishart distributed [16].
The rationale for this is simple. If it is based on prior radar
observations, then it is also of the form (5). Anderson has
shown that in this case, the Bayesian estimate (maximum a
posteriori) for the covariance matrix is given by [16]
An obvious yet useful generalization of (6) is
R̂ = α R̂0 + β R̂1
α + β = 1,
which is the familiar colored loading or blending approach of
[19] and [20]. The practical advantages of (7) relative to (6) are
many. For example, the data used to form the prior covariance
might lose its relevance with time—the so-called stale weights
problem [21]. In that case, even though R̂0 might have been
formed from L0 samples, it effectively has less information and
should be commensurately deweighted. A common method for
accomplishing this, borrowed from Kalman filtering, is the
fading memory approach in which case α, in (7), is
R̂ = max f (x i : i = 1, . . . , L | R) f(R)
R
=
1
L0 R̂0 + L1 R̂1 ,
L0 + L1
(6)
where f (R) denotes the prior pdf associated with the prior
covariance estimate R̂0 based on L0 samples, and thus is
W(L0 R̂0 , L0 ); and R̂1 denotes the ML estimate based on L1
samples. Equation (6) has an obvious intuitive appeal: the a
posteriori covariance estimate is formed as a weighted sum of
the prior and current estimates with weighting factors proportional to the amount of data used in the formation of the
respective sample covariances.
α = e−γ t L0 ,
(8)
where t is the time elapsed since the prior covariance estimate
was formed, and the positive scalar γ is the fading memory
constant [22].
Sliding Window: 2×DoF with Four Guard Cells
Knowledge-Based Training
MCARM 5_575, Doppler 10,
Symmetric Window
MCARM 5_575, Doppler 10,
Data Selective Training
25
25
Target Not Detected
20
15
10
5
0
HWY9
15
10
5
0
−5
−5
−10
15
Target
20
M_MSMI (dB)
M_MSMI (dB)
(7)
16
17
18
19
20
21
−10
15
16
Range (Miles)
(a)
13
71
15
6
300
42
1
17
18
19
20
21
Range (Miles)
(b)
Cells Excluded
Rationale
13.5–14 Miles
Rt. 15
16–17.5 Miles
Rt. 13
19–20 Miles
Rt. 9 in Sidelobe Region,
Radial Alignment
21–22 Miles
Rt. 9 in Main lobe
9
(c)
(d)
[FIG7] Illustration of the impact prior knowledge (in this case, prior road network data) can have on improving detection performance
for the MCARM dataset [15]. (a) STAP filter residue without KA processing. (b) Target, which was previously undetected, is clearly visible
after intelligent training [15]. (c) Local map of region indicating locations of road networks. (d) A training cell exclusion rule based on the
map data.
IEEE SIGNAL PROCESSING MAGAZINE [46] JANUARY 2006
In a more general setting, the blending parameters (α, β)
could be chosen based on the relative confidence in the estimates. For example, R̂0 could be derived from a physical scattering model of the terrain. In which case it is also typically of the
form (5) with the distinction that the outer products represent
clutter patch steering vectors weighted by the estimated reflectivity [7], [23], i.e.,
Nc
1
G i v i v′i .
R̂0 =
Nc i=1
(9)
Nc clutter patches have been utilized in the formation of R̂0
(typically corresponding to a particular iso-range ring [7]),
where v i ∈ C NM is the space-time (angle-Doppler) steering
vector corresponding to the ith clutter patch and G i its
corresponding power [7]. Such information could be available a priori from SAR imagery [24] (essentially a high-resolution clutter reflectivity map) or physics-based models [23].
How the confidence metric applies, in the form of the weighting parameter α, is difficult to ascribe in practice since the quality
of the a priori estimate is vulnerable to a number of error sources.
A straightforward remedy is to choose α adaptively so as to maximally whiten the observed interference data. For example:
min ZL(α),
(10)
{α}
where
′
ZL(α) =
yi yi − I
(11)
i
and
− 1
2
xi.
y i = α R̂0 + β R̂1
(12)
In (10)–(12), x i is the space-time snapshot vector for the ith
range bin; (α R̂0 + β R̂1 )(−1/2) is the whitening matrix corresponding to a particular α; y i is the vector residue with dim(y i )
= dim (x i ); and the summation in (11) is performed over a suitable subset of the radar observations for which R̂0 is believed
valid. If an a priori covariance estimate is available for each
range bin, then the vector residue (12) can be replaced with
− 1
2
xi
y i = α R̂0 (i) + β R̂1
(13)
where R̂0 (i ) is the a priori estimate for the ith range bin.
The above adaptive α approach is but a special case of an
entire class of direct filtering methods incorporating prior
information, viz., data prewhitening (or simply data detrending). In a more general setting, the space-time vector residues,
{y i }, can be viewed as a detrended vector time series using prior
knowledge in the form of a covariance based whitening filter.
The major potential advantage of this is to remove (or attenuate) the major quasi-deterministic trends in the data (e.g., clutter discretes and mountains) so that the resulting residue
vector time series is less nonstationary or inhomogeneous.
An interesting example of this can be found in [12]. In this
prewhitening example, a CLEAN algorithm was applied to the APTI
data set of Figure 5(a), resulting in the discrete map of Figure 5(b). A
deterministic covariance [23] was then formed as in (9), from which a
square root whitening filter matrix could be derived. Figure 8 shows
a log exceedance plot of the difference between the unwhitened data
and the prewhitened data. Note the presence of spiky clutter as
evidence by the so-called fat-tails in the unwhitened data.
In the next section, we address the seemingly daunting challenge of incorporating prior knowledge—an inherently memory
intensive process—into a high performance embedded computer.
100
Fraction Exceeding Value
STAP Only
STAP w/Prewhitening
10−1
c = r / √|r | 2 + |x | 2
10−2
s = x / √|r | 2 + |x | 2
10−3
r ⇐ √|r | 2 + |x | 2
x´ = –sr + cx
Better Behaved "Tail"
10−4
r = c*r + s*x
13 dBI
10−5
−10
x
x
−5
0
5
10
15
Pixel SINR (dB)
20
25
30
r
c,s
c,s
r
c,s
x´
[FIG8] Illustration of the effectiveness of the prewhitening
approach on real-world data [24]. Prewhitening the data
corresponding to Figure 5 resulted in a significant reduction in
the tails of the clutter residue.
[FIG9] An example of computer array implementing a data
domain reformulation of the sample matrix-based Weiner-Hopf
equation (from [8]).
IEEE SIGNAL PROCESSING MAGAZINE [47] JANUARY 2006
REAL-TIME KA-STAP: THE DARPA KASSPER PROGRAM
OBSTACLES TO REAL-TIME KA-STAP
As mentioned previously, ingenious real-time computing
architecture solutions have been devised to implement the
sample matrix based (ML) solutions to STAP. In particular,
to achieve the enormous throughput burden of a modern
multichannel STAP radar, highly parallel HPEC systems
based on so-called data domain reformulations of the
Weiner-Hopf equation (1) have been devised [8], [9]. Figure
9 shows one such architecture based on a QR-factorization
solution to (1) and (5).
The basic parallel processing architecture of Figure 9 solves
the adaptive Weiner-Hopf equation
R̂ w = s
by first performing a QR-factorization of the data matrix consisting of L space-time snapshots [7], then solving two triangular
systems of equations (back substitution). More specifically, since
R̂ ∝ X X ′ ,
(15)
where X ∈ CNMLx is defined as
X [ x1
xL ]
(16)
(14) can be solved in two steps involving the R matrix of the QR
factorization, i.e., if
QX ′ =
r
,
⊘
(17)
(14)
pr
o
to xima
Ac te
ce Nu
ss m
Me be
mo r of
ry Cl
Co ock
nte C
nts ycle
s
then the unknown adaptive weight vector w can be solved in
two steps:
1
5–10
r ′ a =s
Registers
Internal, or L1
Cache
L2, L3
25–50
Ap
Faster Speed
Higher Cost
<1
102–103
106– ∞
Memory
Disk
Larger Size
Lower Cost
Tape
[FIG10] Illustration of the time scales involved in accessing
different memory storage media.
Real-Time Data Stream
Causal
Processor
KA-STAP Output
Noncausal
Processor
[FIG11] Example of a KA-HPEC architecture exploiting the
high degree of radar determinism with look-ahead time-scales
on the order of seconds. The noncausal processor, running in
parallel with a more conventional HPEC STAP processor, is used
to look-ahead and detect regions of the radar field of regard
requiring KA processing—and thus modifications to the normal
adaptive weights calculations.
r w =a.
(18)
With such architectures, tens to hundreds of giga floating point
operations (GFLOPs) of real-time computing power can be
achieved in hardware that can fit on an airborne radar aircraft.
Though marvels of modern technology, these machines are
cyber savants: they can solve (1) and (5) at blinding speeds in a
strict pipelined fashion but grind to a snail’s pace if the data
flow is disrupted for nonpipelined operations. This is a major
fundamental obstacle to implementing KA or general Bayesian
approaches which are inherently memory intensive (prior
information needs to be stored). Figure 10 shows the order-ofmagnitude time scales for accessing different memory storage
devices. Thus, to create a real-time KA HPEC (KA-HPEC, pronounced K-PEC) architecture, a major breakthrough in memory management must be achieved since much of the prior
information (e.g., terrain maps, road networks, and discrete
maps) will reside on mass storage (and thus slow) media.
SOLUTION: LOOK-AHEAD SCHEDULING
The key KA-HPEC breakthrough in the DARPA KASSPER project is based on a basic fundamental insight. There is a significant degree of determinism and thus predictability to radar
clutter returns, particularly if the prediction horizon is only on
the order of seconds.
For example, let t0 denote the present time of the airborne radar depicted in Figure 11. Let t0 + δ t denote a time
slightly in the future—say δ t = 1 s. Then in practice, the following are true:
1) The location of the aircraft at t0 + δ t can be predicted to a
very high degree of accuracy assuming that no radical
maneuvering is occurring.
2) The future state of the radar (look-direction, frequency,
and PRF) at t0 + δ t is also known to a very high degree of
accuracy.
IEEE SIGNAL PROCESSING MAGAZINE [48] JANUARY 2006
The justification for the first assertion
is simply that given the full kinematic
KASSPER Hardware Architecture
state vector of the aircraft (position,
speed, and heading), Newtonian
Holds Receiver Data, Platform
mechanics insures fairly deterministic
Data, etc to Be Read by the
Signal Processor
behavior—particularly for just a few
KASSPER
seconds into the future. Justification for
Timing and Control etc. Signal Processor
the second assertion arises from the
simple fact that modern airborne radar
systems typically utilize a radar scheduler. Since the radar is computer conControl
trolled, it must have a tasking schedule.
I/Q Data,
The scheduler is highly deterministic
INS Data,
GPS Data,
when considering a future time horizon
Air Data,
Display
on the order of seconds.
Sensor Data
etc.
Why are the above assertions so critiStorage
"Knowledge"
cal to solving the memory access probData
lem described previously? Simple: they
allow for look-ahead scheduling. More
specifically, they allow for noncausal proHolds a-priori
cessing whose prediction horizon is
Knowledge to
commensurate with the memory access
be Read by the
Surrogate for
Signal
delays! To see how this can be exploited
Actual Radar
Processor
"Knowledge"
System
by a KA-HPEC architecture, consider
Storage
Figure 11. In this instantiation, a noncausal look-ahead computer is running
in parallel with a more conventional [FIG12] The MIT Lincoln Laboratory 96-node real-time KASSPER HPEC system.
causal STAP HPEC processor. The noncausal processor is used to spot trouble before it occurs
and perform the necessary memory retrieval and prePlatform Moves
to This Site ...
computations to ensure that the right weight modificaNew Boundary Tiles
Loaded to Cache from
... From This Tile
tion scheme is ready to go when the data appear.
Mass Storage
Note that the KA information arising from the noncausal look-ahead processor can often be integrated into
the casual (conventional) STAP processor via a straightOld Boundary Tiles
Discarded from Cache
forward augmentation of the sample snapshot matrix X
defined in (16). For example, if R̂K A ∈ CNM×NM is an a
priori estimate of the covariance matrix, then the [FIG13] Illustration of the environmental database manipulation illustrating
the sliding window approach to migrating data from mass storage to RAM
Bayesian linear combiner of (7) can be implemented by
and ultimately to cache.
X=
(1/2)
√
βX1
√
βXL
√ 12
α R̂K A ,
(19)
where R̂K A ∈ CNM×NM is the matrix square-root of R̂K A. This
KA instantiation really drives home the point that prior information is mathematically tantamount to having more data.
Figure 12 shows the MIT Lincoln Laboratory KASSPER
HPEC system, a real-time 96 noe parallel processing architecture implementing the noncausal look-ahead scheduling
scheme of Figure 11 [26]. The system has the capability of
receiving real-time in-phase and quadrature (I&Q) digitized
samples from multiple receive channels over the full range
extent of a radar and implementing a variety of KA algorithms
throughout the entire radar signal processing chain from
STAP to constant false alarm rate.
Though when it comes to real-time HPEC, the devil is most
certainly in the details; Figure 13 gives the basic gist of how
the look-ahead scheduling is implemented. As the aircraft
moves, a sliding window of data is migrated from a mass storage medium (e.g., disk drives) to a more readily accessible
location (e.g., RAM). Depending on the particulars of the radar
tasking, a first-pass decision is made as to what regions require
KA processing. For example, if the radar is scheduled to point
in a direction where a major road network is known to exist,
essential details regarding this road network (orientation and
range extent) are extracted and exploited in potentially several
stages of the radar signal processing chain. Given the lookahead time buffer, this is all accomplished prior to the actual
radar event. The exact extent of the sliding window depicted in
IEEE SIGNAL PROCESSING MAGAZINE [49] JANUARY 2006
Figure 13 depends (of course) on the particular radar parameters (min/max range and altitude).
THE FUTURE: NEXT GENERATION
INTELLIGENT ADAPTIVE SENSORS
The heart of the DARPA KASSPER program is an architecture for performing KA/Bayesian adaptive sensor signal processing. It is not a specific set of algorithms. Indeed, this
article and the entire special issue are merely scratching the
surface of potential instantiations not only for radar but for
any sensor interacting with the environment. For example,
multichannel sonar systems face an analogous set of problems when attempting to detect small target echoes or emanations in a background of largely environmentally induced
noise. If environmental databases were available (bathymetry
and sea state), KA processing could be employed. The same
is true of automated target detection sensors working in the
EO/IR (electro-optical/infrared) regime (e.g., hyperspectral
and lidar). Though radar centric, it is hoped that this article
will spark interest in others outside of radar and usher in, or
should we say, re-usher in real-time Bayesian adaptive sensor signal processing.
AUTHORS
Joseph R. Guerci is director of the Special Projects Office of
DARPA. In this capacity, he is responsible for leading the
development of some of the nation’s most advanced technologies and systems aimed at meeting emerging national
defense needs. An alumnus of Polytechnic University of New
York with a Ph.D. in systems engineering, he has more than
60 peer-reviewed publications, eight U.S. patents, and is the
author of Space-Time Adaptive Processing for Radar. He is
also a Member of the IEEE Radar Systems Panel and a
Fellow of the IEEE.
Edward J. Baranoski is a program manager in the
Special Projects Office at the DARPA where his focus is on
next generation sensors and signal processing. From 1990
through 2004, he worked at MIT Lincoln Laboratory, serving on the technical staff developing space-time adaptive
processing algorithms and as group leader of the Embedded
Digital Systems Group and ISR Systems Group. He has previously worked at the Johns Hopkins Applied Physics
Laboratory. He received his B.S. degree from Drexel
University, the M.S. degree from the George Washington
University, and the Ph.D. degree from Carnegie Mellon
University, all in electrical and computer engineering. He
was an Associate Editor for IEEE Transactions on Antennas
and Propagation and has served on the IEEE Underwater
Acoustics Signal Processing and Sensor Array and
Multichannel (SAM) Technical Committees, serving as VP of
the SAM Technical Committee from 2000–2003, and was
cochair of the first IEEE Sensor Array and Multichannel
(SAM 2000) Signal Processing Workshop.
REFERENCES
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[19] J.S. Bergin, C.M. Teixeira, P.M. Techau, and J.R. Guerci, “STAP with knowledge-aided data pre-whitening,” in Proc. 2004 IEEE Radar Conf., Apr. 2004, pp.
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