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An Improved Time-Reversal-Based Target Localization for Through-Wall Microwave Imaging

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http://jecei.srttu.edu
Journal of Electrical and Computer Engineering Innovations
JECEI, Vol. 1, No. 2, 2013
Regular aper
89 J. Elec. Comput. Eng. Innov. 2013, Vol. 1, No. 2, pp. 89-97
S TTU
An Improved Time-Reversal-Based Target Localization for Through-Wall Microwave Imaging
A. B. Gorji
1,*
and B. Zakeri
1
1
Faculty of Electrical and Computer Engineering, Babol Noshirvani University of Technology, Babol, Iran
*
Corresponding Author’s Information: amin.gorji@stu.nit.ac.ir
ARTICLE INFO
ABSTRACT
ARTICLE HISTORY:
Received 27 October 2013 Revised 28 November2013 Accepted 4 December 2013
Recently, time reversal (TR) method, due to its high functionality in heterogeneous media has been widely employed in microwave imaging (MI) applications. One of the applications turning into a great interest is through-wall microwave imaging (TWMI). In this paper, TR method is applied to detect and localize a target obscured by a brick wall using a numerically generated data. Regarding this, it is shown that when the signals acquired by a set of receivers are time reversed and backpropagated to the target-embedded media, finding the optimum time frame which the constituted image represents a true location of the target becomes infeasible. Indeed, there are situations pertinent to the target distance ratio that the previously-used
Maximum field method
and
Entropy-based methods
may fail to select the optimum time frame. As a result, an improved method which is based on
initial reflection from the target
is proposed. According to different target locations described in this research, the results show this method prevails over the shortcomings of the former methods.
KEYWORDS:
Finite-difference time-domain Optimum focusing Target distance ratio Target initial reflection Through-wall microwave imaging Time reversal
1. I
NTRODUCTION
Recently, in the field of microwave imaging (MI), the great interest on detection and localization of objects through walls and obstacles has been emerging. This phenomenon basically arises from various unique civilian and military applications, including non-destructive detection tests, earthquake search and rescue missions, hostage operations or hostile threat assessment situations [1]. In fact, a through-wall microwave imaging (TWMI) system would be capable of collecting information of the total media consisting of target(s) and wall(s), performing a comprehensive process on it, and also identify and localize the target. Encouraging results have been obtained with backscattering algorithms [2], synthetic-aperture-radar (SAR) [3], polarimetric-based techniques [4], tomographic approach [5], and high-speed imaging algorithm known as Envelope [6]. However, among the processing algorithms, time reversal (TR) methods have shown that would exploit ultra wide band (UWB) signals and the concept of multipath components in the intervening media to ameliorate the detection capabilities [7]. Originally, TR has been utilized in acoustics [8].Also, it has been introduced in Electromagnetics and more research has been carried out on subsurface object imaging [9], wireless communication systems [10], bio-malignant tissue detection [11, 12], and through-wall imaging of the obscured targets [13-15]. In TR method, a source radiates a signal which propagates through a media including the target. The waves are then reflected and the corresponding data are recorded by an array of receivers. By extracting the target-only responses from the data, reversing them in time and synthetically propagating them back, an image of the scene can be extracted at each time frame. Consequently, by utilizing an appropriate approach to take an optimum time frame, detection
A. B. Gorji et al.
90
and localization of the target becomes possible. Furthermore, in TWMI applications, TR entails to detect targets through materials including plywood, drywall, solid/hollow brick and concrete which their relative high permittivity or inhomogeneous structure may result in further burden for selecting the optimum time frame. In this paper, we embark on solving the problem of finding an optimum time frame which represents an exact image of the target. In this regard,
Maximum Electric-field (E-field) Method
[13] and
Entropy-based Methods
[11, 14] have been recently employed in both TWMI and breast cancer detection scenarios. These methods may guarantee a maximum amplitude or a tightly focused image corresponding to the detected location of the target. However, we show that there are situations pertinent to the distance ratio of the target in which the preceding methods may fail to image the exact location of the target. As a result, an improved method, based on
initial reflection from the target
is proposed which is robust to the effect of this parameter and prevails over the previous methods. The rest of the paper is organized as follows: in Section II a general description of TR method is presented. In Section III, the geometry of TWMI scenarios along with the specifications of computational setup is introduced which is carried out numerically using finite-difference time-domain (FDTD) [16]. In Section IV, the methods of finding an optimum time frame together with our proposed method are fully addressed. The results regarding the functionality of the methods to successfully localize the target according to different distance ratios of the target are demonstrated in Sections V. Finally, in Section VI a summary of the present work and the future contributions is drawn.
2. C
LASSIC
TR
M
ETHOD
Time Reversal (TR) technique is an imaging method based on the invariance of Maxwell`s equations under time reversal, which is known in electromagnetics as the principle of reciprocity. In general, the procedure for detection and localization of the target based on TR consists of three main steps shown in Fig. 1. After, a source radiates a signal through a media including the targets, the reflected waves from the media are recorded by an array of receiving antennas which ideally should be placed all around the media to capture all the possible directions of the reflected waves. However, unlike this full-aspect configuration [17], in other types of scenarios, it is presumably impossible to entirely surround the media and a limited number of arrays are particularly feasible.
Figure 1: General scheme of TR method.
Then, the reflected waves from the media are recorded by an array of receiving antennas which ideally should be placed all around the media to capture all the possible directions of the reflected waves. However, unlike this full-aspect configuration [17], in other types of scenarios, it is presumably impossible to entirely surround the media and a limited number of arrays are particularly feasible. This limited-aspect configuration is in prevalent use for the applications including TWMI and subsurface objects imaging. Thereupon, the aim of forward propagation step is to collect the data of the media and process them in order to image and localize the targets. Accordingly, the data can be generated either analytically [7], numerically [11-13], or physically via on-site measurement [14], in which the first two suffices when one deals with the development of imaging algorithms such that spending time and energy on practical measurements is almost cumbersome. Next, the target-only response must be extracted from the recorded signal at each array receiver. Since the recorded signal of the media consists of background clutter plus target, assuming that the background is stationary, its solo signature with no target in present can be calculated and collected at each receiver. Now, let`s assign
E
T
and
E
B
as the total and background reflected signals, respectively. Then, for each receiver, the target-only (scattered) response
E
S
is obtained as
T BS
E E E
(1) This method of extracting the target response is called background subtraction method. In fact, extracting the target response is the basis of all TR processing methods including Classic TR [11], DORT [9, 18], MUSIC [19] and TRAIC [20]. In scenarios in which
E
B
cannot be obtained in a separate run, the target response is directly extracted from the total response by applying a time-window on the total signal [9] or Matched-Filter analysis [21]. However, these methods
Target Background TRA Background
Accurate Time-Reversal-Based Target Localization for Through-Wall Microwave Imaging …
91 J. Elec. Comput. Eng. Innov. 2013, Vol. 1, No. 2, pp. 89-97
will surely yield to more mathematical efforts. Additionally, in moving target scenarios, the information about
E
B
may not be required and corresponding target response can be achieved using the total response subtraction of two successive moving target runs. This method is called differential TR and is fully addressed in [22]. In the final step, based on TR processing method used in the previous step, imaging and localization of the target become possible. By time-reversing (phase conjugating in frequency domain) the target responses at each array receiver and synthetically propagating them back to the background media (no target), the wave focuses on the location of formerly existing target, approximately recreating the image of the target. It is obvious that this step is performed analytically by using Green functions named Point Spread Functions (PSF) [23] or numerically including FDTD [11-13], TLM [24], and Ray-Tracing methods [25]. Despite this, unlike the imaging applications, physical back propagation of the waves may occur in applications involving actual retransmission of signals like destruction of kidney stones with ultrasonic waves [26].
3. G
EOMETRY AND
C
OMPUTATIONAL
S
ETUP
A. Geometry of TWMI Problem
The geometry of TWMI problem which is considered in this investigation is depicted in Fig 2. A standard commercial solid brick cell with dimensions 20×10 cm (length × width) is used here to construct a single layer wall with 10 cm thickness and 120 cm vertical length. Based on the measurement results reported in [27], the relative permittivity and conductivity of the brick wall is nearly consistent in the entire frequency spectrum of the measurement. As a result, regarding to the center frequency of excitation source, these values are set to ε
r
=4.8 and σ=0.001 S/m. A linear array of 16 isolated z-directed electric dipoles with equidistant separation of 6 cm are placed just 20 cm before the wall to act as the receiving probes. These arrays are called time reversal array (TRA) and will participate in synthetically back propagation step. The distance between the first and the last probe is called aperture size
a
which is equal to 90 cm for this array. A z-directed electric dipole atthe center of the array line is placed as the transmitter (and as monostatic receiver) to radiate the excitation pulse toward the scene in TM
z
mode. Also, throughout this work, a cylindrical disk scattererwith diameter D=6 cm and ε
r
=47 will be introduced as a target in different locations behind the wall, generally specified as near distance and far distance with respect to aperture size
a
. More discussion about this issue will be given in part D.
Figure 2: FDTD computational setup used for TWMI. The source (dot) and TRA (stars) are shown. The brick wall has 10 cm thickness. The target will be introduced at different locations. The aperture size and target distance are also denoted by
a
and
L
, respectively.
B. Computational Setup for TR Method
Both forward-propagation and back-propagation steps of TR method are carried out numerically using two-dimensional finite-difference-time-domain (FD-TD) method. The computational domain has a dimension of N
x
×N
y
=180×130 grid points, with a uniform spatial discretization of Δ=1 cm and a time step of Δt=16 ps (the Courant factor S
c
=c*Δt/Δx is chosen to be 0.5). The maximum of runtime is also set to maxtime=800Δt which is sufficiently enough for the incident wave to travel from the source to the right end of the domain in a round-trip. The boundary condition used is also a convolutional perfectly matched layer (CPML) formulated with recursive-convolution technique to provide reflectionless truncation of the computation domain. The thickness of CPML is set to 5Δ at all four sides of the boundaries. It is also worth noting that in medium with high losses or dispersion, the performance of TR imaging based on conventional FDTD may become degraded due to double attenuation in forward and back propagation steps. To dispel this problem, a modification on FDTD update equations must be performed at back-propagation step in order to compensate losses or dispersion caused by the back-ground media [11, 28].
C. Excitation Source
In general, various constraints and specifications including particular electrical characteristics of the media, signal penetration through wall materials, target dimensions, and also portability of the setup will determine the best operating frequency range for microwave penetrating radar (MPR) systems. Practically, such systems operate in the range of 0.5-
Sample Target Wall PML
A. B. Gorji et al.
92
10 GHz [29] and a minimum system bandwidth of about 30% with respect to the center frequency is essential for providing a sufficient resolution in target detection [4]. In this work, a UWB modulated Gaussian pulse is considered as the excitation source by
2
().sin2()
s p
p s
t t t
P t e f t t
(2) Where
t
p
and
t
s
are temporal width and temporal shift, respectively, which specify the spectrum bandwidth of
P
(
t
) and also
f
p
is the center frequency. These parameters are then assigned as
f
p
=4.6 GHz,
t
p
=0.16 ns and
t
s
=2*
t
p
. The excitation pulse and its frequency spectrum is also plotted in Fig. 3.
D. Final Settings
Assume that the target is located at a distance
L
away from the source. We may further investigate TR method according to the distance
L
with respect to
a
; simply
L/a
(srcinated from classical diffraction limit). As a result, there will be three distance ratios as near distance
L/a
<1, medium distance
L/a
=1, and far distance
L/a
>1. Finally, to fully understand the capability of TR method, two general near and far distance settings shown in Table 1 will be specified in this paper.
4. F
OCUSING
M
ETHODS
After exciting the source and collecting the data of reflected signals, we obtain target-only responses by using background subtraction methods. The target responses are then time reversed and backpropagated into the background media. Accordingly, the comput-ationally backpropagated fields constitute an image of the scene at each frame of the time. Next, we embark on solving a problem of finding an
optimum timeframe
which represents an image of the scene with exact focusing on the location of the target.
A. Maximum E-field Method
As reported by Zheng et al. [13], in this method the maximum E-field amplitude of the imaging domain is found at each time frame and it is plotted along the time axis. The optimum time frame is then selected as a time which corresponds to the maximum of this plot, as
&
maxmax01
:()(),
opt
t t E t E t t t t t t
(3)
Figure 3: Modulated Gaussian excitation signal source and the corresponding frequency spectrum,
f
p
=4.6 GHz,
t
p
=0.16 ns,
t
s
=2*
t
p.
T
ABLE
1 F
INAL
S
ETTINGS FOR
TR
P
ROCESSING
Setting 1 Setting 2 Target Location (x,y)
(70,40) (160,85)
Target Distance Ratio
near far
B. Entropy-based Methods
In the ideal full-aspect configuration, the behavior of backpropagated waves on target location is such that it first converges toward the target and a time lag behind that, it diverges from it. In order to find a time frame which is corresponding to the convergence-divergence instant, a minimum entropy criterion will be defined as in (5) and (6) reported by Cresp et al [14] and Kosmas et al [11], respectively.
22,
(,)(,)
n nijni j
E i j p E i j
(4)
ln()max()
n nij ijnij
p p ENT n p
(5)
22,4,
(,)()(,)
ni jni j
E i j ENT n E i j
(6) Where
n
represents the time frame, (
i,j
) the grid cell coordinates and the summation is over the entire imaging domain. The defined entropy is calculated at each time frame and a time instant when it becomes minimized is selected as the optimum time frame. Unlike the previous method, minimum entropy method guarantees a tightly focused image rather than maximum field amplitude at the focusing point.
0100200300400500600700800-1-0.500.51
t (
t)
P ( t )
0.5123456789100246810
A b s . M a g n i t u d e
f (GHz)
Zheng
Cresp
Kosmas
Accurate Time-Reversal-Based Target Localization for Through-Wall Microwave Imaging …
93 J. Elec. Comput. Eng. Innov. 2013, Vol. 1, No. 2, pp. 89-97
C. Target Initial reflection Method
In this work, we examine the functionality and efficiency of the above focusing methods and investigate the situations in which they may fail to image the exact location of the target. As a result, an alternative optimum time focusing method which is valid for all situations and prevails over the shortcomings of other methods should be utilized. In this part we are attempting to characterize this proposed method, namely
Target Initial Reflection Method
. Let`s again postulate the geometry of the wall and an arbitrary located target as in Fig. 4. Now, we want to follow the transmitted wave starting at the beginning source point, propagating into the scene, possessing interactions with the wall and the target, and then reflecting back to the receiving arrays. In addition, we will monitor the target response waveforms of three particular receivers; the source receiver, which corresponds to a receiver at the source point (
R
S
), the nearest receiver to the target (
R
N
), and the farthest receiver away from the target (
R
F
). The excited source after a delay of
t
d
reaches to the peak value. In its path toward the target, it travels the route
A
1
B
1
,
B
1
C
1
and
C
1
D
, where
D
is the point which the transmitted wavefront is incident on the target. The target scatters the fields and a portion of them are received by the arrays. For the source receiver
R
S
, the scattered wave travels
DC
1
,
C
1
B
1
and
B
1
A
1
, likewise the wave travels
DC
2
,
C
2
B
2
and
B
2
A
2
to reach to nearest receiver
R
N
, and
DC
3
,
C
3
B
3
and
B
3
A
3
to reach to farthest receiver
R
F
. The detailed waveforms monitored by each of these three receivers are shown in Fig. 5. The received waves are then time-reversed and back-propagated, which is analogous to start the propagation from the right end of each waveform (maxtime) and move toward the left (Fig. 5). According to the depicted waveforms, the first antenna starting backpropagation process is the farthest one, it travels along the path toward the target up until the time the nearest antenna as the last antenna starts backpropagation. Based on Fig. 5 it is derived the two waveforms will simultaneously reach the target location
D
if they both travel only the remained time amount of
t
2
which is the stacked time for the scattered waveform to travel from the target
D
to the nearest receiver at
A
1
. As a result, these two waveforms together with the waveform from the rest of the arrays will arrive at the same time to point
D
and their amplitudes are constructively added to each other to construct a contrasted image of the location of the target. More detailed route path of backpropagated waveforms are shown in Fig. 4. In other words, the optimum time frame is a time instant in which the nearest receiver
R
N
is powered on
Figure 4: Detailed route path of forward and back propagated waveforms for source receiver (R
S
), nearmost receiver (R
N
), and farthest receiver (R
F
).
Figure 5: Signal waveforms monitored by each of source receiver (R
S
), nearmost receiver (R
N
), and farthest receiver (R
F
). Time reversing and backpropagating the waveforms are analogous to start the propagation from the right end of the axis.
and then continues traveling for
t
2
sec. To formulize the optimum time, we may write
1221
()()
opt d d
maxtimemaxtime
t - t t t t t t
(7) where
t
1
is the stacked time for the source waveform to travel from starting point
A
1
to target
D
or vice versa. According to the waveform of the source receiver
11
22
r d r d
t t t t t t
(8)
R
N
is powered on
Source signal
R
S
R
N
R
F
Target reflection
maxtime

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