Feature Enhancement of Robust Adaptive Target Detection...
Transcript of Feature Enhancement of Robust Adaptive Target Detection...
Feature Enhancement of Robust Adaptive Target Detection withthe Y-configured Multisensor Imaging Radar
Y. Shkvarko and V. EspadasDepartment of Electrical Engineering. CINVESTAV Unidad Guadalajara
Av. Del Bosque 1145 Col. El Bajío, Zapopan, Jalisco, México
E-mail: [email protected]
Abstract— A new Descriptive Experiment Design Regulari-zation-based Robust Adaptive Beamforming (DEDR-RAB)approach is presented for high resolution array radarimaging of multiple targets with the Y-configured Multi-sensor Imaging Radar (MIR). Our approach is based onthe advanced minimum risk inspired DEDR framework forenhanced radar imaging and optimization of the MIR resolu-tion performances. We adopt the celebrated GeoSTAR sensorarray configuration that provides a desirable low side lobesshape of the point spread function (PSF) attained employingthe conventional matched spatial filtering (MSF) techniquefor radar image formation. The effectiveness (signal to inter-ference plus noise ratio, SINR) of the new aggregated DEDR-RAB radar imaging method is corroborated via extendedsimulations of different DEDR-related imaging techniques.The results are indicative of the superior operational effi-ciency of high resolution localization of the multiple closelyspaced targets with the new DEDR-RAB methodology.
Keywords: descriptive experiment design regularization, target
detection, beamforming, multi-sensor imaging radar
1. IntroductionBeamforming is a pervading task in remote sensing (RS)
imaging applications. The adaptive beamformers (ABF) se-
lect a weight vector as a function of the data to optimize
the performance subject to various constraints, these ABF
can have better resolution and much better interference
rejection capability than the data-independent beamformers.
However the ABF are much more sensitive to errors, such as
steering vector errors caused by imprecise sensor calibration
than the data-independent beamformers [1]. The latter has
spurred development of various ABFs and devise RABs for
enhancing the RS images, and many sophisticated techniques
are now available (see, for example [1], [2] and the refer-
ences therein). Crucial still unresolved ABFs issues relate
to robust enhanced imaging in harsh operational scenarios
characterized by possible imperfect array calibration, partial
sensor failure and/or uncertain noise statistics [3].
We address a new DEDR-RAB approach for attain-
ing virtual high-resolution performances of radar imag-
ing with differently configured mm-band array radars. Our
new aggregated DEDR-RAB approach is a robust adap-
tive beamforming-oriented generalization of the conven-
tional MSF method for radar image formation [4] based on
the advanced descriptive experiment design regularization
framework for radar imagery enhancement [5], [6]. At an
initial stage, we optimize the sensor array configuration
employing the celebrated GeoSTAR geometry [7] to attain
the desired shape of the MSF system PSF, that is, we secure
lowest possible side-lobes level ba-lanced over the minimum
effective width of the main PSF beam by optimizing the
antenna inter-element spacing. At a reconstructive stage, the
low resolution MSF image is next enhanced via performing
the new aggregated DEDR-RAB post-processing aimed at
attaining the overall super-high resolution remote sensing
(RS) performances. The effectiveness of the new aggre-
gated DEDR-RAB radar imaging method is corroborated
via extended simulations of the multiple target localization
experiment of different DEDR-related imaging techniques
using the specialized elaborated software that we refer to
as ’Virtual Remote Sensing Laboratory’ (VRSL) [8]. The
latter are indicative of the superior operational efficiency
of the imaging radar system that employs the new DEDR-
RAB method adapted to the DEDR-optimized GeoSTAR
configuration over other tested competing techniques [1] -
[9]. In this study, the robustness of the ABF is performed
by aggregating it with the DEDR-based minimum variance
distortionless response (MVDR) digital beamforming ap-
proach that exploits structural information on the desired
image map sparsity over the RS scene [10]. The developed
aggregated DEDR-RAB technique is implemented in an
implicit iterative form to enhance the overall imaging and
target localization performances.
2. MIR conceptThe MIR-Y antenna array is shown in Fig. 1a and
corresponding uv samples (Fig. 1b), in this case, u and vspecify the normalized (so-called visibility domain) coor-
dinate representation format, u = x/λo, and v = y/λo.
This MIR array (GeoSTAR, Geo Synthesized Thinned Array
Radiometer) is composed of 24 (M = 24) antenna ele-
ments as in [7], where it is addressed in as a concept to
provide high resolution imaging of distributed RS scenes in
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Fig. 1: (a) Antenna array layout with sensor numbering (M = 24) for Y-shaped GeoSTAR configuration, (b) corresponding
uv samples fot inter-element spacing dA(1) = 0.5λo; carrier frequency fo=24GHz
microwave and mm wavebands. In this work, the particular
system under consideration is operated at two separate yet
concurrent frequencies of 24 GHz and 36 GHz with dual
polarization (Vertical V and Horizontal H). At one instant,
radio frequency (RF) pulses of a specified pulse width (PW)
are transmitted concurrently at 24 and 36 GHZ in either V
polarization or H polarization. These pulses are “calibrated"
to maintain coherency so that their amplitudes and phases
are constant for different pulses. The transmitting antenna
is switched between V and H polarizations; i.e., V and H
transmitted pulses are delayed by a certain time. For each
frequency (24 or 36 GHZ), transmitted V polarized and H
polarized RF pulses are separated by a half of the fixed pulse
repetition time (PRT/2). The V polarized RF pulses and H
polarized RF pulses are repeated after every PRT.
Each antenna element receives signals of V and H polar-
izations. It follows that, we can send V pulses and receive
the same polarization mode (VV) or receive H polarization
(VH); similarly, we have HH and HV modes. The operation
range of the MIR system is in the order of 1 m to 100 m,
with a range resolution cell of 0.3 m, so we have 165 range
gates for processing. The sensors provide two measurements
for each data snapshot, In-phase (I) and Quadrature (Q).
The crucial issue relates to the formation of the empirical
estimate (Yr) sensor data cross-correlation matrix (Yr) for
each range gate r = 1, . . . , Rr = 165. To form the full rank
cross-correlation matrix (Yr) we need to perform averaging
over a great number J of independent recorded sensor array
data realizations. These independent realizations are to be
recorded using J transmitted pulses for each range gate
r = 1, . . . , Rr = 165
To form the full-rank sensor data covariance matrix (Yr),the minimal number of independent recordings J should be
not less than the number of sensors (M = 24), thus for each
range gate J > M , (i.e. J > 24) independent realizations are
to be recorded for each range gate r = 1, . . . , Rr = 165.
In the case of J < 24, the data covariance matrix is rank-
deficient; this means that if we apply the robust beamforming
processing for sensor focusing, we inevitably will face the
problem of huge artifacts (so called ghosts on the speckle
corrupted scene images). In the radar terminology [2], these
artifacts (speckle and ghost targets) will inevitably increase
the false alarm rate.
3. Low Resolution StageThe general mathematical formalism of the problem at
hand and the DEDR framework that we employ in this
section is similar in notations and structure to those in the
previous studies [4], [5], [6], and some crucial elements are
repeated for convenience of the reader.
3.1 Problem FormalismThe mathematical model of the power spectrum distribu-
tion (the so-called spatial spectrum pattern, SSP) restoration
problem is stated as follows. Consider the unknown con-
tinuous spatial distribution of the extended radiating source
within the given spatial domain (interval of analysis) Θ � θdefined by the instantaneous complex amplitudes e(t, θ) of
the source. In a convenient discrete-form representation,
we consider the discretized interval of spatial analysis Θwith a set of K prescribed spatial directions {θk; k =1, 2, ...,K} ∈ Θ. The vector
e(t) = vec{ek(t) = e(t, θk); k = 1, ...,K} (1)
composed with the complex amplitudes of the source signals
from all K spatial directions is referred to as the vector of
random unknown instantaneous source complex amplitudes.
For the Y- configured MIR at hand, the phase at the mth
antenna element as a result of the kth source is ωkym where
ωk = 2π sin(θk) and ym = is the location of the elemental
phase center with respect to the midpoint of the array
in wavelengths (λ). We assume the statistically uncertain
scenario where tth time sampled signal at the mth element
of the array for a fixed range gate r is
um(t) =
K∑
k=1
ek(t)gm(θk)exp(iωkym) + nm(t) (2)
where gm(θk) is the pattern response of the mth array
element in the direction θk and nm(t) is the tth sample
of the adopted Gaussian noise from the mth array element.
This noise component is modeled as a random variable
independent of both time index t and the element index m.
The previous equation of observation (2) can be put in the
following vectorial form:
u(t) = Se(t) + n(t); t = 1, ..., T (3)
where n(t) represents the observation noise and S is the
signal formation matrix (SFO) defined as
S = matrix{Smk = gm(θk)exp(iωkym)} (4)
where m = 1, ...,M ; k = 1, ...,K. In (3), u(t), e(t) y n(t)represent zero-mean complex vectors composed of the sam-
ple coefficients {ek(t), nm(t), um(t); k = 1, . . . ,K;m =1, . . . ,M}. These vectors are characterized by the correla-
tion matrices [4]
Ru =< SReS+ > +Rn (5)
where
Re = D(b) (6)
is the diagonal matrix with the vector-form SSP b at its
principal diagonal {bk = b(θk) = < ek(t)ek(t)∗ > = <
|ek(t)|2 >; k = 1, . . . ,K} and Rn = N0I, respectively,
where I defines the identity matrix, N0 is the observation
white noise power, superscript + stands for Hermitian con-
jugate and < · > defines averaging.
3.2 DEDR-MSF MethodThe low resolution RS imaging problem is stated generally
as follows: to form the image of the tag b̂(θk) as a function
of the spatial scene coordinates applying the MSF method
[4], i.e.
b̂(θk) = s(θk)+Yrs(θk); k = 1, ..., K (7)
in which the image is formed as an MSF estimate of the SSP
distribution over the remotely sensed scene at a particular
rth range gate. In the pursued here non-parametric problem
treatment, the resolution quality is assessed by the shape of
the resulting system PSF associated with the MSF image (7)
of a single point-type target located at the scene origin at the
corresponding range gate r ∈ R. In particular, the desired
system PSF is associated with the shape that provides the
lowest possible side lobes (and grating lobes) level balanced
over the minimum achievable effective width of the PSF
main beam [2].
In (7), s(θk) is the kth array steering vector composed of
the corresponding kth row (k = 1, ...,K) of the regular SFO
matrix S and the estimate Yr (M -by-M ) of the array spatial
correlation matrix is computed via performing averaging
over the J snapshots as:
Yr = {R̂u} =1
J
J∑
j=1
uju+j . (8)
Based on (7), let us next analyse the PSF of the MIR
imaging system attainable with the employment of the con-
ventional GeoSTAR-configured Y-shaped array. In Fig. 2, we
present the PSF related to the MSF-based single target (TAG)
imaging procedure (7) employing the GeoSTAR-configured
Y-shaped sensor array radar. The PSF cross-section in the x-
y imaging scene provide explicit information on the spatial
resolution cells achievable with such configured imaging
sensor array that employ the conventional 2-D MSF method
(7) for RS image formation. The PSF in Fig. 2 is presented
with an inter-element spacing dA = 2λo, i.e., equal to
the double of the carrier wavelength. Note that the most
important characteristics of this PSF is the width of the
main beam and the maximum level of the secondary lobes
(including the suppressed grating lobes).
The next feature enhanced RS imaging problem at hand
is to develop the framework (in this study, the DEDR-RAB
method) and the related technique(s) for high-resolution
estimation (feature-enhanced reconstruction) of the SSP b,
we tackle this situation in the next section.
4. DEDR-RAB TechniqueThe clasical robust adaptive MVDR method [10] adapted
for the high-resolution spatial spectrum pattern estimation as
a solution to the problem b̂ = estMVDR{b|u} results in the
non-linear solution dependent strategy [10]:
b̂(θk) =1
s+(θk)R−1u s(θk)
; k = 1, ...,K (9)
optimal (in the MVDR sense) for the theoretical model-
dependent covariance matrix inverse R−1u . In the practical
RS target imaging scenarios, the unknown exact (model)
covariance matrix is substituted by its J-sample maximum
likelihood estimate (8) that results in the corresponding
MVDR estimation algorithm [1], [10]
b̂(θk) =1
s+(θk)Y−1r s(θk)
; k = 1, ...,K (10)
feasible for the full rank Yr only. From Bayes Minimum
Risk Estimation Strategy [5], [6] and from simple algebra,
Fig. 2: Point Spread function (PSF) for 24 element
Y-shaped configured multisensor imaging radar with
dA = 2λo inter-element spacing for 30m range gate.
it is easy to corroborate that the theoretical model-based
strategy (10) is algorithmically equivalent to the solution
with respect to b of the non-linear equation
D(b̂) = {W(b̂) YrW+(b̂)}diag (11)
with the solution operator (SO)
W(b̂) = K(b̂)S+R−1n . (12)
Since Rn = N0I, the last SO becomes:
W(b̂) = K(b̂)S+ (13)
where K(b̂) = (Ψ+N0R−1e )−1 and Ψ = S+S represents the
matrix-form PSF of the MSF low-resolution image formation
system [2].The DEDR framework [5], [6] suggests the worst case
statistical performances optimization approach to the prob-
lem of b̂ = estMVDR{b|u} with the model uncertain-
ties regarding the statistics of the SFO perturbations that
yields the robust (13). The RAB modification of the DEDR
(DEDR-RAB) is constructed by replacing in (13) N0 by
the composite (loaded) NΣ = N0 + β. The latter is the
observation noise power N0 augmented by factor β ≥ 0adjusted to the regular SFO Loewner ordering factor and the
statistical uncertainty bound for the for the SFO perturbation
(see [5] for details). Finally, we can define the new DEDR-
RAB as:
D(b̂) = {(S+S+NΣR−1e )−1S+YrS(S+S+NΣR−1
e )−1}diag(14)
Fig. 3: Point Spread function (PSF) for 24 element
Y-shaped configured multisensor imaging radar with
dA = 2λo inter-element spacing for 30m range gate.
In Fig. 3, we present the PSF related to the DEDR-
RAB single target (TAG) imaging procedure (14) employing
the GeoSTAR-configured Y-shaped sensor array radar. The
PSF cross-section in the x-y imaging scene provide explicit
information on the spatial resolution cells achievable with
such configured imaging sensor array that employ (14) for
RS image formation. As in Fig.2, the PSF in Fig. 3 is
presented with an inter-element spacing dA = 2λo. Note the
difference between the two PSFs at hand, that is, the width
of the main beam and the maximum level of the secondary
lobes (including the suppressed grating lobes).
Fig. 4: Nominal multiple TAGs scene
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Fig. 5: Simulations protocols for the Y-configured MIR: (a)-(c) Low resolution scene image formed using the conventional
DEDR-MSF technique (7), SNR = 10 dB, for a range gate of r = 10m, 30m and 100m respectively; (d)-(f) Feature
enhanced image reconstructed employing the new aggregated DEDR-RAB method (14), SNR = 10 dB, for a range gate of
r = 10m, 30m and 100m respectively.
5. Target Localization ProtocolsWe corroborated the effectiveness of the new DEDR-
RAB technique (14) via simulation studies performed with
the ela-borated VRSL software. Three typical simulation
protocols of radar imaging of a scene composed of five
closely spaced targets (TAGs) in the range gates r = 10m,
30m and 100m (respectively, in columns) are presented in
Fig. 5 for the Y-configured MIR. In Fig. 4 we present the
nominal multiple TAGs scene. Figures 5a trough 5c show
the low resolution images of that scene formed using the
conventional DEDR-MSF technique (7) for the 10 dB signal-
to-noise ratio (SNR) typical for radar imaging scenarios [2]
with a signal interference (INR) of 20 dB. Similarly, figures
5d trough 5f present the feature enhanced (high-resolution)
images of the same scene reconstructed with the proposed
aggregated DEDR-RAB technique (14). The reported target
localization protocols are indicative of the drastically supe-
rior operational efficiency provided with method (14) that
employs the DEDR-optimized GeoSTAR-configured array
over other competing tested imaging array radar geometries
[3].
To maintain consistency with the adaptive beamforming
literature, we adopt the SINR as a measure of the effec-
tiveness of our new aggregated DEDR-RAB method. The
DEDR-MSF performs poorly against the new DEDR-RAB
method as the latter presents an impressive average SINR
of 30 dB compared to 12 dB for the DEDR-MSF when
the signal of interest SNR=10 dB and exists a signal of
interference of 20 dB. This is shown in Figures 6 and 7.
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Fig. 6: Comparison of the DEDR-MSF and DEDR-RAB
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INR=20 dB.
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Fig. 7: Comparison of the DEDR-MSF and DEDR-RAB
methods. Average SINR (dB) for a SNR=10 dB and
INR=20 dB.
6. ConclusionWe have addressed the new robust DEDR-RAB approach
for enhanced imaging of multiple target scenes in harsh
operational environments directly adapted to MIR imag-
ing systems, in this work particularly with Y-configured
GeoSTAR MIR. The presented high-resolution target local-
ization protocols are indicative of the superior operational ef-
ficiency of the Y-configured multimode imaging MIR system
with the adopted GeoSTAR array geometry. The reported
PSFs provide explicit information on the spatial resolution
achievable with such MIR system that employs the proposed
DEDR-RAB image formation technique. We demonstrated
via the analysis of behavior of SINR quality metric that
method (14) yields the best imaging performances. In future
studies, we intend to focus on the HW-SW co-design aimed
at the resolution enhancement of the DEDR imagery and
approaching the super-resolution imaging performances with
MAR systems.
This will push forward our capabilities in the hardware-
software codesign-based optimization of the RS and multi-
sensor radar systems paving a way toward adaptive superres-
olution sensing with the mm-waveband array radar systems.
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