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Transmitting-Mode Time Reversal Imaging Using MUSIC Algorithm for Surveillance in Wireless Sensor Network Xiao-Fei Liu, Bing-Zhong Wang, Member, IEEE, and Joshua Le-Wei Li, Fellow, IEEE Abstract—The electromagnetic time reversal (TR) detection and imaging using multiple signal classification (MUSIC) is extended to the Maxwell equations problems with the transmitting-mode configurations, where the transmitter and receiver arrays are bistatic and the arrays elements are arbitrarily distributed. Based on this type of setup, the multistatic response matrix is derived in detail for target-scattering by relatively small anisotropic spheres located in the imaging domain. Then the electromagnetic transmitting-mode MUSIC algorithm is proposed by defining the pseudo-spectrum deduced from the Maxwell equations. By such extension, following advantages are achieved: a) leading to more accurate location and higher imaging resolution because the noncoincident arrays actually increase the effective aperture of the array; b) making the algorithm more flexible and practical; c) enlarging the coverage area of the detection system due to the reciprocal mapping between the transmitter and receiver spaces; and d) overcoming one special problem that the echo-mode encounters when one target is atop another one in the upright direction of the transceiver antenna array even they are far-separated. Based on these advantages, we have numerically discussed typical applications of the proposed method for surveillance in wireless sensor network. Through examples, the validity, the improvement, and the extended potential of the electromagnetic transmitting-mode time reversal MUSIC method are verified. Index Terms—Electromagnetic scattering, green function, image analysis, inverse problems, multisensor systems.
I. INTRODUCTION HE TIME reversal method, as a novel detection and imaging technique exploiting the multipath effect in the forward scattering and inverse scattering of electromagnetic wave, has attracted a lot of attention in recent years. The major adopted methods in literature include, although not limited only to, the time reversal mirror method [1]–[4](TRM), the time reversal operator decomposition (DORT) [5]–[8], and the time reversal multiple signal classification (TR-MUSIC) [9]–[11].
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Manuscript received May 19, 2010; revised February 15, 2011; accepted July 20, 2011. Date of publication September 15, 2011; date of current version January 05, 2012. This work was supported in part by the High-Tech Research and Development Program of China (2006AA01Z275, 2008AA01Z206) and in part by the State Scholarship Fund from the China Scholarship Council (No. 2008607035). J. L.-W. Li was supported by the University of Electronic Science and Technology of China, Chengdu, under the Chinese Government’s 1000Talent Plan. X.-F. Liu and B.-Z. Wang are with the Institute of Applied Physics, University of Electronic Science and Technology of China, Chengdu, 610054, China (e-mail:
[email protected];
[email protected]). J. L.-W. Li is with the Institute of Electromagnetics and School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2167903
These methods were originally developed and improved in acoustic wave research. The TR-MUSIC algorithm was, however, recently extended to characterize electromagnetic fields [12]–[17] and employed to applications to subsurface detection, medical imaging, distributed sensing, radar systems and so on. It was reported that the TR-MUSIC algorithm evades the iterative back-propagation process required in TRM and overcomes the difficulty in dealing with non-well-separated targets for DORT. In addition, the TR-MUSIC is valid for detections and imaging of multiple targets and extended targets with one step processing. However, the first transmitting-mode investigation, extension from the mostly discussed echo-mode, of the TR-MUSIC algorithm is carried out under the frame of Helmholtz equation with non-coincident and arbitrary array elements distributions by E. A. Marengo and F. K. Gruber [18]. Their excellent works discussed the comprehensive theory of a nonlinear inverse scattering problem combined with the TR-MUSIC or an alternative signal subspace method in detail for estimating the locations and scattering strengths or reflectivities of the targets. By considering the applications in wireless sensor network (WSN), we further extend the studies in this paper to Maxwell equations for the electromagnetic transmitting-mode TR-MUSIC with array configuration of irregular elements distribution because the node locations in WSN are often arbitrary and the transmitter and receiver are generally bistatic. Therefore, the vector fields, the dyadic Green’s functions and the tensors of EM parameters are introduced for the analysis. Similar to the DORT method, the transmitting-mode TR-MUSIC method also starts from the multistatic response matrix or the transfer matrix. The difference is that the latter utilizes the so-called noise space of the multistatic response matrix while the former uses the signal space. Therefore, the location and the imaging of the targets can be achieved by taking the orthogonality between the eigenvectors in the noise space and the Green’s function vectors, which are extractable from the background media. The following four improvements are expected by proposing the transmitting-mode algorithm. • Firstly, the new configuration of arrays accurately increases the effective aperture so that the resolution could be further enhanced as compared to that of the echo-mode algorithm. • Secondly, the degree of freedom in the choices (among the transmitter pseudo-spectrum, the receiver pseudo-spectrum or both) is apparently increased. Because of this and also the reciprocal mapping, the detection and surveillance coverage is enlarged.
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The vector wave equations satisfied by the electric field and magnetic field in a homogenous and isotropic medium have their following solutions: (1a) (1b) Fig. 1. Physical configuration of simulation model.
• In addition, the proposed method could overcome the problem that the echo-mode encounters where one target is atop another one in the upright direction of the transceiver antenna array even they are well- or far-separated. • At last, the algorithm becomes now more flexible and practical, especially for the highlighted applications to wireless sensor network. The detection targets are anisotropic in our analytical derivation, without any loss of generality. However, the isotropic targets are compatible in applications by alteratively defining the tensors of the electromagnetic parameters and . The remaining part of the paper is so organized subsequently. In Section II, the construction of the multistatic response matrix is discussed in detail from the electromagnetic scattering point of view. It is then followed by the investigation of the eigenvalue structure, whereas the MUSIC pseudo-spectrum is defined for the transmitting-mode TR-MUSIC algorithm. Then, the imaging simulation of targets in wireless sensor network is taken as a typical application and carried out in Section III. The results depict a good agreement with the theoretical expectation and it thus verifies the improvement stated above. Section IV concludes the paper.
where denotes the electric-electric dyadic Green’s function between the field position and the source position . The formulae lead to the incident electromagnetic fields expressed in terms of the driven currents on the transmitter dipoles as follows: (2a) (2b) where stands for the permeability of background medium, . Then, they could while be converted into a matrix form as follows: (3) and , and two matrices and , on where the two vectors, the left- and right-hand sides are explicitly defined respectively as
(4a) (4b)
II. THEORETICAL FORMULATIONS and A. Multistatic Response and Time Reversal Matrix The analysis configuration of the physical model for the forward propagation, as shown in Fig. 1, is composed by a transmitter array, some desired targets, and a receiver array in homogenous background media, say, free space for most of the practical cases. The transmitter array and the receiver array, which were both assumed to be linear or planar in literature, are antenna elnow assumed to be general in distribution, where ements are located respectively at , while antenna elements are located at , , respectively. Each of the elements consists of three dipoles oriented in (with the -, - and -directions with lengths of , , and , ). Assume that the source at the th element can be , written as , , and stand for the driving currents at the where three-direction oriented dipoles of the th antenna element. Meanwhile, the scattering targets (which are assumed to be , anisotropic spheres with radii of , permittivity tensors of , respectively) are located at and permeability tensors of . the positions , where
(5a) (5b) At the same time, the sub-matrices in (5b),
and
, are defined in (6), where their elements are determined by the dyadic Green’s function at different locations. See (6), shown at the bottom of the next page. The derivation is carried out for anisotropic scatterers without any loss of generality. For completeness, the permittivity and permeability tensors are necessarily provided as in [19], [20] (7a)
(7b)
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where (or ) represents the permittivity (or permeability) element aligned to the th electric (or magnetic) principal axis of the th scatterer, while (where , ) denotes the rotation transforming matrix and it is a function of the rotation , and . Euler angles Explicitly, it is defined that whose three respective angular contributions are described in terms of the , and by Euler angles
where
(10a)
(8a) (10b) (8b)
Rewriting (9) in matrix form, one obtains (11)
(8c)
where the matrices are defined as
By considering the multiple scattering among the targets and using the Foldy-Lax equation, the relationship between the incident fields and the total fields nearby the targets could be obtained as
(12a) (12b) (12c) In (12c), the sub-matrices, , , and , are explicitly defined in (13), shown at the bottom of the next page. Therefore, the scattered electric fields at the receiver antenna (where ) are expressed elements located at in the vectorial summation form as
(9a)
(14) or in the matrix form as (9b)
(15)
.. .
.. .
..
.
.. .
(6a)
.. .
.. .
..
.
.. .
(6b)
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where
(16a) (16b) Then, the voltages induced on the antenna dipoles can be obtained in a vector form defined as follows: (17) where
(18a) (18b)
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B. Eigenvalue Systems and Pseudospectrum Definition It was shown in literature that the DORT imaging can be performed using the back-propagation of the singular vectors associated to nonzero singular values of the and matrices. But it is not an effective-enough solution because this method requires that the targets are sufficiently far separated from each other such that they can be resolved in imaging. In addition, the relationship between the individual target and the nonzero singular value is in an one-to-one manner in acoustics area. In electromagnetic applications, the relationship becomes more complicated due to polarizations, array configurations, shapes, electromagnetic characteristics of targets, and so on. Therefore, using the DORT method is inadequate for the high quality electromagnetic imaging. The TR-MUSIC algorithm is an enhanced solution for the electromagnetic detection and imaging. It is developed also based on the singular value decomposition of the matrix, which has the so-called signal subspace spanned by the background Green’s function vectors evaluated at the target , locations. by considering the singular system it can be written in the following form:
At last, as a consequence of combining (3), (11), (15), and (17), one arrives at
(22a) (22b)
(19) Hence, the operator matrix (20) is referred to as the multistatic response matrix. Furthermore, the time reversal matrix is written as
denotes the th singular value, while and stand where for the th column vectors of the orthonormal matrices and , respectively. Consequently, the so-called transmitter and receiver time reand , have the versal matrices, following eigenvalue system: (23a) (23b)
(21) where the operation
and , The transmitter and receiver spaces are spanned by respectively. They can be both subdivided into signal space
denotes the conjugate transpose.
(13a) .. .
.. .
.. .
.. .
.. .
..
.. .
.
(13b)
.. .
.. .
.. .
..
.. .
.. .
.
..
.
.. .
(13c)
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and noise space, respectively spanned by singular vectors corresponding to nonzero singular values and zero singular values. It is formulated as follows:
mode configuration to investigate the performance of the separated pseudo-spectrums corresponding to transmitter space and the receiver space, respectively. They are denoted by and , and expressed below
(24a) (24b)
(28a)
(24c) Meanwhile, the background medium Green’s function vectors are the orthonormal bases of the signal space. Concretely, the Green’s function vectors between locations of the transmitter array and the targets are bases of transmitter space, and the ones between locations of the targets and receiver array are bases of the receiver space. Therefore, the inner product of the background Green’s function vectors of the target locations and singular vectors in noise space theoretically equals to zero, that is
(25a) (25b) where
(28b) and It is notable that to locate all the targets, the values of must be larger than six times of the number of the targets since one target can be associated to at most six nonzero singular values [21]–[23], so that there exist zero singular values in the multistatic response matrix to perform the TR-MUSIC searching. In practice, the system requires more antenna elements, however, to achieve good performance due to the loss and noise. In addition, since the DORT method has the analysis processes similar to those of the TR-MUSIC method, it can be also extended to Maxwell equations. Therefore, in the subsequent numerical studies, the electromagnetic transmitting-mode DORT is also considered as a reference method.
III. NUMERICAL VALIDATION AND EVALUATIONS (26a)
.. .
.. .
(26b)
and and (where , 2, 3) denote the th column vectors of and (where ), respectively. of the transNow, one defines the pseudo-spectrum mitting-mode TR-MUSIC algorithm as follows:
(27)
In this section, we first carry out a simulation of electromagnetic imaging in the wireless sensor network so as to verify the feasibility and applicability of the proposed electromagnetic transmitting-mode TR-MUSIC algorithm. Then, the performance comparison between the traditional DORT method and the proposed algorithm is made by performing the second numerical simulation to show the improvement in terms of resolution. The last simulation example deals with the far-field detection where an obstacle comes up due to the multiple scatterers overlapped in the vertical direction of the transmitter aperture. The physical configuration of simulation model is shown in Fig. 1 where a 2-D imaging plane and a 3-D imaging domain are respectively set up for the 2-D and 3-D numerical examples in Section III-A. In addition, the additive white Gaussian noise is considered in all the simulations. This is done by contaminating the multistatic response matrix with the noise generated at certain level of signal to noise ratio (SNR), which was defined in [13], so will be not repeated herewith. A. Electromagnetic Transmitting-Mode TR-MUSIC Imaging
, the location and imaging of By checking the peaks of the targets can be obtained numerically without any back propagation of the signals which is required in the time reversal mirror imaging. Furthermore, we define the transmitter pseudospectrum and the receiver pseudo-spectrum in this transmitting-
The 16 transmitter array elements and 32 receiver array elements are employed the analysis. The coordinates of the elements are denoted by where , with or 32 for the transmitter array and the receiver array,
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= 40
Fig. 2. Two-dimensional detection and imaging results when SNR dB. (a) The geometrical distribution of the two scatterers on the imaging plane. (b) The transmitter pseudospectrum in (28a) of the transmitting-mode TR-MUSIC detection is utilized. (c) The receiver pseudospectrum shown in (28b) of the transmitting-mode TR-MUSIC detection is considered. (d) The transmitting-mode pseudospectrum shown in (27) for the transmitting-mode TR-MUSIC algorithm is implemented.
respectively. In this simulation, we have assumed: for transmitters
[13] for ease of validation and comparison. The Euler angles are set to be
and for receivers
The position is randomly chosen while is also assumed. The three-direction oriented dipoles all have the same length of . Two anisotropic scatterers are and . They both have placed, respectively, at . The principle elements of the permittivity and a radius of permeability tensors are assumed to follow the same setup as in
Meanwhile, the operation frequency is chosen to be at 100 MHz and the SNR is set to be 40 dB. Fig. 2 presents the detection and imaging results from simulations in 2-D view. Fig. 2(b)–(d) employ the detection pseudospectrum defined in (28a) and (28b) and (27), respectively. It is shown that all of them can be used to accurately locate the scatterers even when the noise levels are high. The receiver pseudospectrum is found achieving relatively higher resolution since its focusing spot is much smaller than the transmitter pseudospectrum. This is due to the larger number of the antenna elements of the receiver array. If the scatterers are not on the as indicated in Fig. 1, one needs to imaging plane at perform the 3-D detection at the imaging domain to locate the
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= 40
Fig. 3. Three-dimensional detection and imaging results when SNR dB. (a) The geometrical distribution of the two scatterers in the imaging domain. (b) The transmitter pseudospectrum shown in (28a) of the transmitting-mode TR-MUSIC detection. (c) The receiver pseudospectrum shown in (28b) of the transmittingmode TR-MUSIC detection. (d) The transmitting-mode pseudospectrum shown in (27) for the transmitting-mode TR-MUSIC algorithm.
scatterers. Fig. 3 presents the scatterers’ distribution and the detection results in 3-D view. In the 3-D simulations, three different definitions made in (28a) and (b) and (27), respectively are also considered. It is clearly seen that the scatterers are located with a good accuracy. Thus, it proves a good feasibility of the proposed transmitting-mode TR-MUSIC algorithm. Meanwhile, according to the different occasions and requirements of various applications, one can choose different algorithms to perform the detection and imaging. This actually demonstrates that the TR-MUSIC method is more flexible and practical.
B. Investigation on the Enhanced Resolution In our second simulation, the performance comparison of the existing time reversal imaging methods and the proposed method is made. The emphasis is made on the resolution of the imaging and the ability of locating the closely positioned targets. As mentioned in previous sections, one of the popular time reversal imaging methods is called DORT. Here, we also discuss its two modes, i.e., echo mode and transmitting-mode. Actually, the transmitting-mode DORT has not been reported elsewhere so far. It can be easily derived from the discussion in Section II due to the resemblance between DORT and TR-MUSIC. So the four algorithm in solving the Maxwell equations problems: echo-mode DORT, transmitting-mode DORT, echo-mode TR-MUSIC, and transmitting-mode TR-MUSIC, will be investigated in the following simulation. In the analysis using the transmitting-mode methods, 16 elements of the transmitter array and 16 elements of the receiver
array are assumed. Similar to the previous setup, the coordinates of the elements are
while the
and
coordinates are randomly chosen so that for transmitter elements and for receiver elements. All the three-direction oriented dipoles . For comparison, the above also have the same length of transmitter elements with duplex function are assumed in the echo-mode methods. In addition, the frequency is also chosen at 100 MHz but the SNR is changed to a lower value dB. Fig. 4 presents the imaging results of of SNR one anisotropic sphere, which is located at with a . It is shown that all the four methods correctly radius of locate the target sphere. The proposed transmitting-mode TR-MUSIC algorithm provides, however, the best resolution of the imaging, which can be judged by checking the cross-range of the focusing spots. Meanwhile, it can be seen that the transmitting-mode methods work is better than the echo-mode methods for both the DORT and TR-MUSIC. When the number of targets increases, these methods are all effective only in the cases where the scatterers are adequately well-separated. But if the distance between two adjacent targets are not large enough, the DORT method may firstly become invalid. This can be seen in Fig. 5 where three targets are included , and , and the locations are at respectively. Both the echo-mode TR-MUSIC method and transmitting-mode TR-MUSIC method are still working, but
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Fig. 4. Detection and imaging results for a scatterer located at (0; 3; 0) when SNR = 20 dB and at f = 100 MHz. (a) The echo-mode DORT algorithm. (b) The transmitting-mode DORT algorithm. (c) The echo-mode TR-MUSIC algorithm. (d) The transmitting-mode TR-MUSIC algorithm shown in (27).
the transmitting-mode has advantage of the higher resolution. Meanwhile, the resolution is also related to the number of the array elements. The imaging performance can be improved if the number of elements increases. It is, therefore, proved in this subsection that the enhanced resolution has been achieved for applications, and it is especially true for wireless sensor network using the proposed transmitting-mode TR-MUSIC method. C. Scenario of Limited Effective Array Aperture In the third numerical example, we perform a far field EM detection and imaging to verify the advantage of the electromagnetic transmitting-mode TR-MUSIC over the echo-mode method in dealing with the special problem where one target is atop another one in the upright direction of the transceiver antenna array aperture even they are well-separated. The 60 elements of transmitter array and 60 elements of receiver array are placed in the far-field zone in a similar fashion to the above examples except that the coordinates are randomly chosen for the transmitter elements; and within for the receiver elements. To increase difficulty of the problem, the imaging plane shown in Fig. 1 is meanwhile rotated clockwise with respect to the -axis by 90 to the -plane. Four targets are considered in this numerical and example. Two of them are centered at , respectively. The other two scatters are overlapped in the direction and in the perpendicular direction of the approximate array aperture. Concretely, their locations are and , respectively. Their electric
and magnetic parameters are all set to be the same as those of the first scatterer in Section II-A. This further increases the resemblance of the overlapped scatterers. The operation frequency MHz and the signal noise ratio is set to be is chosen as 50 dB. Fig. 6 depicts the imaging results of the echo-mode TR-MUSIC method, where the four scatterers are not readily detected due to the overlapping (in -direction) by two of these four scatterers, the decreased array aperture, and the smaller distance between the scatterers. Oppositely, the transmitting-mode method leads to precise true locations of all the four scatterers as shown in the Fig. 7. The problem that the echo-mode method encounters is effectively solved because of the increase in the equivalent array aperture by using the bistatic transmitter and receiver configurations. This is a common problem and it frequently appears in the wireless sensor network and also other applications. Therefore, this is seen as a remarkable improvement made by the proposed transmitting-mode TR-MUSIC algorithm. IV. CONCLUSIONS In this paper, the transmitting-mode TR-MUSIC algorithm is applied to Maxwell equations for electromagnetic detection and imaging problems. Taking the advantage of the released requirement of the sensor distributions, the proposed method is found to be very suitable for applications to wireless sensor network, where the antenna elements (or sensors) are randomly located and the arrays are nonlinear and/or planar. Besides this, the electromagnetic transmitting-mode TR-MUSIC is verified to have higher resolution imaging and to lead to more accurate location.
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Fig. 5. Detection and imaging results for three scatterers located at (0; 4; 0), (; 2; 0) and ( ; 2; 0) respectively when SNR = 20 dB and at f = 100 MHz. (a) The echo-mode DORT algorithm. (b) The transmitting-mode DORT algorithm. (c) The echo-mode TR-MUSIC algorithm. (d) The transmitting-mode TR-MUSIC algorithm shown in (27).
Fig. 6. Echo-mode TR-MUSIC algorithm for far field detection and imaging of four scatterers located at ( 0:45; 0; 0:5), (0:45; 0; 0:5), (0; 0; 0:95) and (0; 0; 0:05) respectively when SNR = 50 dB, and at f = 100 MHz.
0
0
0
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0
At meanwhile, more flexible and practical configuration is believed to be very potential for many other EM applications. In addition, it effectively overcomes the problem the echo-mode encountered when one target is atop another one in the upright direction of the transceiver antenna array. The theoretical discussion is presented in detail from the view point of electromagnetic scattering and inverse scattering, by considering the multiple scattering among the targets. Then, the pseudo-spectrum for imaging using the proposed method is built up. The numerical studies convincingly justify our statements one by one in Section III. In practice, the multistatic response matrix is
Fig. 7. Transmitting-mode TR-MUSIC algorithm for far field detection and imaging of four scatterers located at ( 0:45; 0; 0:5), (0:45; 0; 0:5), (0; 0; 0:95) and (0; 0; 0:05) respectively when SNR = 50 dB, and at f = 100 MHz.
0
0
0
0
0
obtained from the time-domain or frequency-domain measurement. The signal measurement could be carried out at one frequency point within a wide band or within an even ultra-wide band. If it is implemented in the latter case, the algorithm can be performed using multistatic response matrices of multiple frequency points. This will improve the performance of the algorithm in a complex environment. Because different targets with different electromagnetic characteristics show various responses, weaker or stronger, at different frequency points, this wide or ultra-wide band process can collect the responses at all frequencies and compensate them for all the targets to provide a better imaging. After the location of the targets is known, one
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can employ a noniterative method based on the least squares method reported in [24] to retrieve the polarization strength tensors of the targets, where an efficient and stable estimation is shown. To sum up, the proposed electromagnetic transmitting-mode TR-MUSIC method is highly recommended to the superresolution imaging due to the flexible configuration and the enhanced performance in many potential EM applications, especially in wireless sensors network, which is the primary objective of this paper.
ACKNOWLEDGMENT
X. F. Liu would like to thank the Department of Electrical and Computer Engineering at National University of Singapore (NUS), Singapore 117576 for hosting his visiting research engineer position at the NUS for one year.
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[14] X. Chen and K. Agarwal, “MUSIC algorithm for two-dimensional inverse problems with special characteristics of cylinders,” IEEE Trans. Antennas Propagat., vol. 56, no. 6, pp. 1808–1812, Jun. 2008. [15] E. Iakovleva, S. Gdoura, D. Lesselier, and G. Perrusson, “Multistatic response matrix of a 3-D inclusion in half space and music imaging,” IEEE Trans. Antennas Propagat., vol. 55, no. 9, pp. 2598–2609, Sep. 2007. [16] X. F. Liu, B. Z. Wang, and L. W. Li, “Trade off of transmitted power in time reversed impulse radio ultra-wideband communications,” IEEE Antennas Wireless Propagat. Lett., vol. 8, pp. 1426–1429, 2009. [17] X. F. Liu, B. Z. Wang, S. Xiao, and S. Lai, “Post-time-reversed MIMO ultrawideband transmission scheme,” IEEE Trans. Antennas Propagat., vol. 58, no. 5, pp. 1731–1738, May 2010. [18] E. A. Marengo and F. K. Gruber, “Subspace-based localization and inverse scattering of multiply scattering point targets,” EURASIP J. Adv. Signal Process., vol. 2007, no. Article ID 17342, pp. 16–16, 2007. [19] C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles. Hoboken, NJ: Wiley, 1998. [20] G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 5th ed. San Diego, CA: Harcourt/Academic, 2001. [21] D. H. Chambers and J. G. Berryman, “Analysis of the time-reversal operator for a small spherical scatterer in an electromagnetic field,” IEEE Trans. Antennas Propagat., vol. 52, no. 7, pp. 1729–1738, Jul. 2004. [22] X. Chen, “Time-reversal operator for a small sphere in electromagnetic fields,” J. Electromagn. Waves Appl., vol. 21, pp. 1219–1230, 2007. [23] D. H. Chambers and J. G. Berryman, “Time-reversal analysis for scatterer characterization,” Phys. Rev. Lett., vol. 92, no. 2,023902, 2004. [24] X. Chen and Y. Zhong, “A robust noniterative method for obtaining scattering strengths of multiply scattering point targets,” J. Acoust. Soc. Amer., vol. 122, pp. 1325–1327, 2007.
REFERENCES [1] M. Fink and C. Prada, “Acoustic time-reversal mirrors,” Inv. Probl., vol. 17, pp. R1–R38, 2001. [2] H. C. Song, W. A. Kuperman, and W. S. Hodgkiss, “Iterative time reversal in the ocean,” J. Acoust. Soc. Amer., vol. 105, pp. 3176–3184, 1999. [3] D. Liu, G. Kang, L. Li, Y. Chen, S. Vasudevan, W. Joines, Q. H. Liu, J. Krolik, and L. Carin, “Electromagnetic time-reversal imaging of a target in a cluttered environment,” IEEE Trans. Antennas Propagat., vol. 53, no. 9, pp. 3058–3066, Sep. 2005. [4] C. Prada, J. L. Thomas, and M. Fink, “The iterative time reversal process: Analysis of the convergence,” J. Acoust. Soc. Amer., vol. 97, pp. 62–71, 1995. [5] C. Prada, S. Manneville, D. Spoliansky, and M. Fink, “Decomposition of the time reversal operator: Detection and selective focusing on two scatterers,” J. Acoust. Soc. Amer., vol. 99, pp. 2067–2076, 1996. [6] J.-L. Robert and M. Fink, “Green’s function estimation in speckle using the decomposition of the time reversal operator: Application to aberration correction in medical imaging,” J. Acoust. Soc. Amer., vol. 123, pp. 866–877, 2008. [7] G. Micolau, M. Saillard, and P. Borderies, “DORT method as applied to ultrawideband signals for detection of buried objects,” IEEE Trans. Geosci. Remote Sens., vol. 41, no. 8, pp. 1813–1820, Aug. 2003. [8] M. Davy, J.-G. Minonzio, J. de Rosny, C. Prada, and M. Fink, “Experimental study of the invariants of the time-reversal operator for a dielectric cylinder using separate transmit and receive arrays,” IEEE Trans. Antennas Propagat., vol. 58, no. 4, pp. 1349–1356, Apr. 2010. [9] E. A. Marengo, F. K. Gruber, and F. Simonetti, “Time-reversal MUSIC imaging of extended targets,” IEEE Trans. Image Process., vol. 16, pp. 1967–1983, 2007. [10] A. J. Devaney, “Time reversal imaging of obscured targets from multistatic data,” IEEE Trans. Antennas Propagat., vol. 53, no. 5, pp. 1600–1610, May 2005. [11] A. J. Devaney, E. A. Marengo, and F. K. Gruber, “Time-reversal-based imaging and inverse scattering of multiply scattering point targets,” J. Acoust. Soc. Amer., vol. 115, pp. 3129–3138, 2005. [12] H. Ammari, E. Iakovleva, D. Lesselier, and G. Perrusson, “MUSIC type electromagnetic imaging of a collection of small three-dimensional inclusions,” SIAM J. Sci. Comput., vol. 29, pp. 674–709, 2007. [13] Y. Zhong and X. Chen, “MUSIC imaging and electromagnetic inverse scattering of multiply scattering small anisotropic spheres,” IEEE Trans. Antennas Propagat., vol. 55, no. 12, pp. 3542–3549, Dec. 2007.
Xiao-Fei Liu received the B.S. degree in electrical engineering and the Ph.D. degree in radio physics from the University of Electronic Science and Technology of China (UESTC), Chengdu, in 2004 and 2010, respectively. From 2008 to 2009, he was a visiting research engineer in the Department of Electrical and Computer Engineering, National University of Singapore. Currently, he serves as a research engineer in the Nanjing Research Institute of Electronics Technology (NRIET), Nanjing, China. His research interests include antenna and active array technique, electromagnetic scattering, and ultrawide band communications.
Bing-Zhong Wang (M’06) received the Ph.D. degree in electrical engineering from University of Electronic Science and Technology of China (UESTC), Chengdu, in 1988. In 1984, he joined the UESTC, where he is currently a Professor. He was a Visiting Scholar at the University of Wisconsin, Milwaukee; a Research Fellow at the City University of Hong Kong; and a Visiting Professor in the Electromagnetic Communication Laboratory, Pennsylvania State University, University Park. His current research interests include the areas of computational electromagnetics, antenna theory and techniques, electromagnetic compatibility analysis, and computer-aided design for passive microwave integrated circuits.
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Joshua Le-Wei Li (S’91–M’92–SM’96–F’05) received the Ph.D. degree in electrical engineering from Monash University, Melbourne, Australia, in 1992. In 1992, he was a Research Fellow with Department of Electrical and Computer Systems Engineering at Monash University, sponsored by Department of Physics at La Trobe University, Melbourne. From 1992–2010, he was with the Department of Electrical and Computer Engineering, National University of Singapore, where he was a Professor and Director of NUS Centre for Microwave and Radio Frequency. In 1999–2004, he was seconded with the High Performance Computations on Engineered Systems (HPCES) Programme of Singapore-MIT Alliance (SMA) as a SMA Faculty Fellow. In May-July 2002, he was a Visiting Scientist in the Research Laboratory of Electronics at Massachusetts Institute of Technology (MIT), Cambridge; in October 2007, an Invited Professor with University of Paris VI, France; and in January and June 2008, an Invited Visiting Professor with Institute for Transmission, Waves, and Photonics at the Swiss Federal Institute of Technology, Lausanne (EPFL). He was appointed in 2009 as a QRJH Chair Professor at the University of Electronic Science and Technology of China under the Chinese Government’s 1000-Talent Plan. His current research interests include electromagnetic theory, computational electromagnetics, radio wave propagation and scattering in various media, microwave propagation and scattering in tropical environment, and analysis and design of various antennas. In these areas, he has (co-)authored two books, namely, Spheroidal Wave Functions in Electromagnetic Theory (Wiley, 2001); Device Modeling in CMOS Integrated Circuits: Interconnects, Inductors and Transformers (Lambert Academic Publishing), 48 book chapters, over 320 international refereed journal papers, 49 regional refereed journal papers, and over 370 international conference papers. Dr. Li was a recipient of a few awards, including two best paper awards from the Chinese Institute of Communications and the Chinese Institute of Electronics, the 1996 National Award of Science and Technology of China, the 2003 IEEE AP-S Best Chapter Award when he was the IEEE Singapore MTT/AP Joint Chapter Chairman, and the 2004 University Excellent Teacher Award of National University of Singapore. He has been a Fellow of The Electromagnetics Academy since 2007 (member since 1998) and was IEICE Singapore Section Chairman between 2002–2007. As a regular reviewer of many archival journals, he was a Guest Editor of the IEICE Transactions on Electronics for ISAP2006 Special Section and the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES for APMC2009 Special Section. He is an Associate Editor of Radio Science, the International Journal of Numerical Modeling, and the International Journal of Antennas and Propagation; an Editorial Board Member of the Journal of Electromagnetic Waves and Applications (JEWA), the book series Progress In Electromagnetics Research (PIER) by EMW Publishing, the International Journal of Microwave and Optical Technology, and the Electromagnetics Journal; and an (Overseas) Editorial Board Member of the Chinese Journal of Radio Science, Frontiers of Electrical and Electronic Engineering in China, and China Science: Information Sciences. He is an Advisory Professor at the State Key Laboratory of Electromagnetic Environments, Beijing (2002-present). He is a Guest Professor at both the Harbin Institute of Technology, Harbin (2003–2011), Shanhai Jiao-Tong University (2008–2011), and Southeast University, Nanjing (2004-), and an Adjunct Professor at both Zhejiang University, Hanzhou (2004–2006) and University of Electronic Science and Technology of China, Chengdu (2006–2010). He also serves as a member of various International Advisory Committee and/or Technical Program Committee of many international conferences or workshops, in addition to serving as a General Chairman of ISAP2006, MRS09-Meta09, and iWEM series (since 2011), Vice Chairman of PIERS2010 in Marrakech, and TPC Chairman of PIERS2003, iWAT2006, PMC2009, ISAPE2010, and ISAPE2012. He is appointed as an IEEE MTT-S Commission-15 Member in 2008, IEEE AP-S Region Representative (Region 10: Asia-Pacific) in 2010, and an IEEE AP-S Distinguished Lecturer in 2011.
