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Study on Two-Dimensional Sparse MIMO UWB Arrays for High Resolution Near-Field Imaging Xiaodong Zhuge and Alexander G. Yarovoy
Abstract—A novel generic topology for two-dimensional (2-D) sparse multiple-input–multiple-output (MIMO) ultrawideband (UWB) arrays is suggested. Based on the proposed topology, a 2-D MIMO UWB array for high-resolution short-range imaging is developed. The focusing properties of this array are studied both theoretically and experimentally and are shown to be superior to those of arrays with a similar number of antennas and based on known topologies such as Mills Cross, rectangular, and spiral configurations. Decisive impact of a large operational bandwidth and short focusing distance on MIMO array performance is shown. Imaging capabilities of the proposed array are experimentally demonstrated for distributed targets. Index Terms—Multiple-input–multiple-output (MIMO), nearfield, sparse array, two-dimensional transducer array, ultrawideband (UWB), volumetric imaging.
I. INTRODUCTION
T
WO-DIMENSIONAL (2-D) array-based ultrawideband (UWB) microwave imaging systems offer great potential in various short-range applications, such as free-space surveillance, airport security, through-wall or rubble imaging and rescue, and medical diagnosis. By use of digital beamforming, such systems have the capability to deliver instant high resolution in three-dimensions. A real-time three-dimensional (3-D) volumetric imaging system that provides high-resolution images remains the ideal device for microwave imaging. Early examples of array-based UWB microwave systems can be found in [1]–[4]. For their operation, such systems require 2-D arrays that operate over an ultrawide frequency band, fine cross-range resolution (narrow mainlobe), low sidelobe level (sidelobe level limits the dynamic range and contrast of the resulting image), scanning capability over a wide field of view, etc. The major problem facing the development of 2-D arrays for imaging is the complexity arising from the large number of elements required in such systems. Under monochromatic condition, element spacing must be no further than one-half of a wavelength (and in the near-field even quarter of wavelength) in order to prevent unwanted grating lobes. To achieve fine Manuscript received December 06, 2010; revised March 16, 2012; accepted April 02, 2012. Date of publication July 03, 2012; date of current version August 30, 2012. This work was supported in part by the EU within the framework of FP6 Project RADIOTECT COOP-CT-2006-032744. X. Zhuge was with the International Research Centre for Telecommunications and Radar, Delft University of Technology, 2628 CD Delft, The Netherlands. He is now with FEI Electron Optics, 5651 GG Eindhoven, The Netherlands (e-mail:
[email protected]) A. G. Yarovoy is with the International Research Centre for Telecommunications and Radar, Delft University of Technology, 2628 CD Delft, The Netherlands (e-mail:
[email protected]). Digital Object Identifier 10.1109/TAP.2012.2207031
cross-range resolution, a large array aperture (in terms of the wavelength at the center frequency) is required. For example, to achieve a 1-cm resolution at 1-m range, an array aperture needs to be at least 100 wavelengths along both horizontal and vertical directions [5]. In order to satisfy the above mentioned spatial sampling criteria, this 2-D array has to be filled with over 201 201 (40 401) elements. The cost of a fully populated high-resolution planar array that maintains half-wavelength element spacing in the two-array directions is almost prohibitive for any commercial application at this moment. To circumvent these difficulties, significant efforts have been made to investigate the capabilities of sparse 2-D arrays. A representative approach to avoid the appearance of grating lobes is through periodicity reduction by either randomly or nonuniformly arranging the array elements [6]–[9]. Although aperiodic arrays do not produce grating lobes, high-level pedestal sidelobes are quite often found due to the drastic thinning process [5]. Furthermore, an increase in the average sidelobe level results in a transducer gain reduction associated with sparse arrays [7]. Some opportunities for sparse array thinning might be introduced by using signals with large bandwidth. Von Ramm and Smith pointed out in [10] that the level of grating lobes can be reduced for pulse echo phased-array imaging systems that transmit acoustic pulses a few cycles in duration. They explained the amplitude lowering by arguing that, in a pulsed transducer array, grating lobes are formed by signals from far fewer elements than the mainlobe. Anderson further expressed the idea that the resolution of a wideband array may be increased by simply moving the elements apart without incurring grating lobe problems [11]. A quasi-closed-form beam pattern definition for beamforming with a rectangular pulse was presented in [12] by placing special emphasis on the invariance of grating lobe level to the interelement spacing. Schwartz and Steinberg thoroughly described the wideband array behavior in terms of interception of pulses and defined sparse array as the condition where the average interelement spacing is much greater than the pulse length (pulse duration multiplied with propagation speed) [13]. Additional opportunity for array thinning lies in use of multiple-input–multiple-output (MIMO) imaging approach. The term MIMO array refers to an array that employs multiple, spatially distributed transmitters and receivers. In 1975, Von Ramm et al. [14] suggested to use different element spacings for transmit and receive arrays so that grating lobes raised from transmit and receive arrays can be moved to different spatial locations in the complete two-way radiation pattern. Synthetic focusing using partial datasets from the complete two-way transducer array was suggested by Cooley and Robinson in [15]. Lockwood et al. [16] proposed a framework for sparse
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2-D array design by selecting different element spacing for transmit and receive elements. Smith et al. [17] investigated several representative 2-D array configurations under far-field conditions using fast Fourier transform methods. More recently, Ahmed et al. [18] investigated different MIMO geometries for short-range UWB imaging and noted differences between far-field and short-range performances of MIMO arrays. Synthesis of MIMO array is to some extent similar to synthesis of antenna arrays in radio-astronomy: While the performance of the radio-astronomy array is determined by the auto-convolution function of its topology (see, e.g., [19]), the MIMO array performance in the far-field is determined by the cross-convolution of transmit and receive subarray topologies [16]. Another commonality between both arrays is their sparsity over the whole operational bandwidth. A few approaches have been reported in the literature for the -density radio-telescope arrays: simulated annealing [20], optimization [21], genetic algorithms [22], [23], and minimization of the highest sidelobe [19]. All these approaches start the design/optimization procedure from a predefined topology, which are typically Mills Cross [24], Y-shape (Very Large Array [25]), and logarithmic spiral (LOFAR, SKA [26]). Performance requirements for antenna arrays for MIMO imaging are, however, essentially different from those from radio-telescopes for the following reasons. 1) The final image is formed using a bandwidth from several gigahertz up to several dozens of gigahertz (as opposed to 100–400 MHz instantaneous bandwidth for radio-telescopes) resulting in spatial averaging (spreading) of the sidelobes in azimuth and elevation planes. 2) The image is formed in the near zone of the array aperture, where radiation patterns are not yet formed and the focusing in the azimuth-elevation plane changes with the range. 3) The point spread function (PSF) is essentially three-dimensional, and its range behavior is also important. While linear (1-D) MIMO UWB array topologies are reasonably well studied (see, e.g., [13] and [27]–[29]), only a few 2-D MIMO array topologies for short-range imaging have been investigated so far: Mills Cross [17], [30], rectangular [18], [31], and expanded 1-D MIMO [32]. All these topologies were derived based on mutual orthogonality of far-field radiation patterns of transmit and receive arrays. Unfortunately, such properties of orthogonality deteriorate in the near-field, and these designs suffer from relatively high shadowing, resulting in strong sidelobes along two orthogonal planes of the principal symmetry. In this paper, we propose a new class of array configurations with lower shadowing, which is the main problem in previously known regular configurations. By arranging element distributions of both transmit/receive arrays according to curvilinear geometries, the element shadowing effect that is common with periodic arrays has been reduced, resulting in a decreased grating/sidelobe level in the near-field. This paper is organized as follows. The new generic MIMO array topology is introduced in Section II, and particular MIMO arrays (one designed using the novel topology, one designed based on -plane uniform coverage, and two other ones designed based on Mills Cross and rectangular geometries) with the same total number of antennas are described in Section III.
Using these arrays as examples, importance of the virtual aperture uniformity along with -plane coverage, the influence of element shadowing, the short-range focusing capabilities, and the effect of bandwidth on the focusing performance of sparse arrays are studied theoretically in Section IV and experimentally in Section V. As simulation and experimental results have been found in excellent agreement with each other, for each particular analysis, either theoretical or experimental results are shown for the sake of brevity. In Section VI, impact of the array sidelobes on the extended target imaging capabilities is demonstrated experimentally. Finally, Section VII summarizes the results and concludes this paper. The experimental setup is described in the Appendix. II. GENERIC MIMO TOPOLOGY According to the formulation introduced in [33], the PSF of a UWB MIMO array can be expressed as
(1) where denotes convolution in the time dimension, is the and position of the target, denotes the focusing point, and represent the location of the transmit and receive elements, respectively. The aperture functions and define the distributions of antenna elements within the transmit and receive apertures, respectively, and (2) and are derived to steer the Both focusing functions beam throughout the 3-D image space. As one can see from (1), the PSF of the complete MIMO aperture (and at a large distance from it) is determined by the crossconvolution between the transmit and receive apertures. The cross-convolution of aperture functions results in the so-called virtual aperture [16]—a collection of midpoints in all transmit/ receive pairs, which are called virtual elements. In the far-field, the virtual element has the exactly the same elementary Green’s function as the associated transmit/receive pair. In the near-field of the array, such a relation is approximate, with the phase front of the virtual element remaining spherical while the real antenna pair turns to ellipsoidal. Although such an approximation results in a moderate deviation of beam pattern in the near-field between the MIMO array and its virtual aperture, the similarity between the two is still prominent, allowing the virtual aperture to be applied as a design tool [15], [31]. For an array with transmit and receive antennas, the maximum number of virtual elements is equal to the product of . Array the numbers of transmit and receive antennas redundancy exists when two virtual elements from collinear Tx–Rx pairs overlap spatially within the resulting 2-D virtual aperture, causing the total number of virtual elements to be less than . Although repeating a baseline can increase
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the signal-to-noise ratio (SNR) and allow tolerance for element failure, it is still better to have a uniform spread of baselines (or uniform virtual aperture coverage) especially for array with a small number of elements. According to the projection slice theory [34], the projection of array elements onto a rotated axis at a certain angle within the array plane determines the pattern of the planar array at that particular angular cut. The case when more than three elements overlap along one spatial direction is called shadowing. In three-dimensional space, the spatial interception of pulses radiated from two elements will be an arc instead of a point (as in the 2-D case). This arc will be located along the orthogonal plane to the line that connects the corresponding two virtual elements. Since any two virtual elements will be aligned along a certain direction, it is the third possible colliding element that should be carefully avoided. Hence, in order to realize the best scanning capabilities, the virtual aperture should possess the lowest shadowing. From this point of view, any periodic topology (e.g., rectilinear uniform [18], [28] or multiple rings [19]) is not desirable. On the other hand, it is known that a virtual aperture uniformly covering the -plane will result in the lowest sidelobes [25] due to the lowest redundancy. Thus, both uniformity of the virtual aperture and its -plane coverage are needed in order to achieve good MIMO array performance. From the shadowing point of view, a circle is an ideal geometry in terms of rotational properties: For any radiation direction, the circle always has the same projection function. However, a single circle topology does not uniformly cover the whole -plane, and any projection of a single circle tends to be over sampled at the edges of the projection in comparison to its center area, causing unwanted weighting function to the aperture. To overcome these unwanted properties, curvilinear geometries, such as the multiple rings and spiral, which are able to maintain a uniform structure over the rotational angle and minimize element shadowing, have been proposed [19], [26], [35]. Their geometric properties allow the array to maintain as much control freedom as possible in every projected axis over the 2-D space. Although the density function is similar between the multiple ring and spiral, the latter is superior in terms of its uniform distribution over the 2-D aperture plane and lack of transitional periodicity. To achieve a virtual aperture with both uniform distribution and angular properties, we propose to distribute the transmit elements on the ring structure plus one element in the center, as in (3) shown at the bottom of the page, while arranging the
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receive elements along a single branch of Fermat’s spiral according to the law in (4), shown at the bottom of the page, where represents the golden ratio. Such topology of the receive array results in a uniform distribution of the receive array elements without shadowing [36]. Parameter , which is of the circular transmit expressed in terms of the radius array as (5) is defined in the way resulting in the creation of a quasi-uniform element distribution within the virtual aperture. An example of array following the definitions in (3)–(5) is shown in Fig. 1(a). III. MIMO ARRAY DEMONSTRATORS To analyze performances of the proposed generic topology, we apply it to the design of an UWB MIMO array for application to concealed weapon detection (CWD) [4], [34] and evaluate its performance theoretically and experimentally. The CWD system should provide 3-D images at a range up to 1 m with an imaging area at least 0.5 0.5 m and a dynamic range of the image better than 15 dB for a distributed target, a down-range resolution of at least 5 cm, a cross-range resolution of at least 2 cm, and have a size of no more than 0.5 0.5 m . From the hardware point of view, to limit the complexity and costs, the system should not include more than 25 antennas within the aperture. Based on the system requirements, the following specifications for the antenna array has been drawn: center frequency of 11 GHz, operational bandwidth of at least 3 GHz, sidelobe level within PSF is better than 20 dB within the scanning area of 1 1 m . An array design following the topology defined by (3)–(5) is shown in Fig. 1(a). The positions of the antennas are indicated in terms of the wavelength at the center frequency , which is 2.7 cm at 11 GHz. The proposed curvilinear MIMO array (Array I) has 25 antenna elements within its aperture with 9 transmit and 16 receive elements. The transmit array is arranged on a ring structure, while the receive array is distributed on a spiral. For comparison, we have used two widely used MIMO topologies in references, namely the Equivalent uniform rectangular (Array II) and the Mills Cross (Array III) array, and an array designed purely based on uniformity of uv-plane coverage of transmit and receive arrays separately—the spiral array (Array IV). All the arrays consist of 25 antenna elements within their aperture (Fig. 1).
(3)
(4)
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Fig. 1. MIMO array topologies and virtual apertures. (a) Curvilinear structure composed array (array I). (b) Equivalent uniform rectangular array (array II). (c) Mills Cross array (array III). (d) Spiral array (array IV).
IV. THEORETICAL STUDY Both in the simulations and experiments, the array performance has been evaluated via the PSF. In simulations, the PSF has been determined in the following way. Hertzian dipoles are used as transmit and receive antennas. A 1-cm-diameter metal sphere is used as the point scatterer and located in front of the
array center at a certain distance. The scattered electromagnetic field is computed by the applied electromagnetic simulation tool FEKO, which utilizes the method of moment (MoM) to solve the integral equations. The simulated signal is obtained in the frequency domain over the specified frequency band. It is further transferred into the time domain by the fast Fourier transform (FFT). The data from all transceiver pairs are then focused within the near-field of the array aperture using the modified Kirchhoff migration [37]. The two-dimensional PSF is then generated over the cross-range and range. The maximum value along its range dimension is selected to represent the “focusing pattern” of the array in the near-field. We start the analysis with a comparison of the virtual apertures of the four arrays. All arrays have a virtual aperture occupying approximately the same area, thus resulting in similar width of the PSF main lobe. Both arrays II and III have a uniformly distributed spatial aperture, which however exhibits very high periodicity and thus shadowing along certain directions. The proposed array (array I) and the array IV, on the contrary, have nonregular virtual aperture without any periodicity. This improves the array performance due to the reduction of element shadowing effect. Hence, arrays I and IV will exhibit better angular properties. On the other hand, the distribution of elements in the virtual array for the arrays I and IV are less uniform over the 2-D surface. Some of the virtual elements within the virtual aperture of the arrays I and IV are located very closely to each other. When the element spacing is much less than the distance corresponding to the pulse length, the closely spaced elements would be regarded as redundancy. Therefore, one expects that the MIMO array I will suffer from a certain level of degradation in terms of mainlobe focus compared to arrays II and III, but not as much as array IV, which exhibits the lowest uniformity in the virtual aperture. Among the proposed strategies, the curvilinear array I will provide the lowest grating/sidelobe level due to its well-distributed control freedom over angular directions. With the same physical size, the equivalent uniform rectangular array design results in the largest virtual aperture, therefore the highest angular resolution. Array IV will have the lowest angular resolution due to its heavy weighting at the center of the virtual aperture. The next step is the focusing pattern analysis. The pattern is estimated by first producing a 3-D image, then maximum projection along the range dimension, then maximum projection along the angular dimension (over 360 rotation). This is why only half of the pattern is shown in Fig. 2. The array focusing patterns depend both on operational bandwidth and on focusing range. For a proper comparison, the focusing patterns are shown for 10% and 150% of fractional bandwidth and for ranges varying from 20 to 60 wavelengths at the center frequency. As the focusing ranges are comparable to the aperture size, there is no sense in using radiation angles; the patterns are presented as functions of Cartesian coordinates along the horizontal and vertical directions. It can be seen in the case with 10% bandwidth that, at the long ranges (above 50 wavelengths), well-defined nulls and clear sidelobes appear in the patterns, while at short ranges (20–30 wavelengths) only the main lobe is clearly seen above the pedestal level. For small operational bandwidth, the sidelobes (and zeros between them) are clearly defined, while for the large operational bandwidth, the sidelobes are spread over
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TABLE I WIDTH OF INTERFERENCE REGION OF 2-D SPARSE MIMO UWB ARRAYS
Fig. 2. Focusing patterns of four MIMO arrays at various focusing distances to ) under different fractional bandwidths. (a) Array I under (from 10% fractional bandwidth. (b) Array I under 150% fractional bandwidth. (c) Array II under 10% fractional bandwidth. (d) Array II under 150% fractional bandwidth. (e) Array III under 10% fractional bandwidth. (f) Array III under 150% fractional bandwidth. (g) Array IV under 10% fractional bandwidth. (h) Array IV under 150% fractional bandwidth. The center frequency is 11 GHz.
the whole area. Degradation of the focusing due to the short focusing distance is much more severe for the small operational bandwidth and is less pronounced for the large operational one. This can be explained from the spatial interference of UWB pulses. Under large bandwidth, the emitted signals exhibit only a short pulse duration and only interact with each other around the focusing point. This area of interference is referred as the interference region (IR). Outside the IR, grating lobes caused by array sparseness cannot be formed due to the absence of interference. The width of the IR around the focusing point depends on the topology of the array, the focusing distance,
and the duration of the pulse. The IR widths for the four arrays are listed in Table I, which explains the significant reduction of grating lobes caused by high fractional bandwidth. Comparing curvilinear with both rectangular and Mills Cross arrays, the curvilinear design is superior in the near-field in both narrowband and UWB cases. In the narrowband case, the degradation of the focusing pattern of the two arrays is worse than for the curvilinear design. This is due to the different design methods: Both array II and III rely on the orthogonality between the Tx and Rx array, which is only valid in far-field condition. When the distance becomes shorter, the orthogonality becomes worse and the pattern is less controllable. On the contrary, the curvilinear design relies on the spreading of grating lobes, which remain at the same level with focusing distance. In the UWB case, degradations by decreasing distance of both arrays are similar. However, because the orthogonality gets worse (this is a narrowband property that influences the interference region around the main lobe), the pattern of the reference arrays within the interference region get worse than that for the curvilinear design. Comparing the curvilinear array with the spiral array, the curvilinear design performs similarly under narrowband condition and exhibits lower grating lobe level under the UWB condition. This is mainly due to the less uniform virtual aperture from the spiral array, which causes less lowering of the grating lobes under UWB conditions than for the proposed array. This comparison confirms importance of the virtual aperture uniformity in the MIMO UWB array design and demonstrates that uniform coverage of the -plane alone is not sufficient for a good MIMO UWB array performance. The sidelobe level for the broadside focusing is of about 23.7 dB for the curvilinear array, while it is about 3–5 dB higher for the reference arrays. For the offset imaging, the sidelobe level increases in all four arrays, however in the curvilinear one it remains the lowest. The array performance analysis continues in the next section with experimental studies. V. EXPERIMENTAL STUDY A. Tx/Rx Coupling Within 2-D MIMO Array The influence of cross-coupling is prominent in narrowband phased-array systems due to the fact that directly coupled sig-
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Fig. 3. Coupling level and maximum contaminated range of all transmit/receive pairs within the measured MIMO arrays. (a) Array I. (b) Array II. (c) Array III. (d) Array IV. The maximum contaminated range is defined by the distance in the range profile where amplitude of direct coupling drops 10 dB below the range distance. response of a 1.5-cm metal sphere at
nals between transmit and receive array elements are able to affect the entire image space after the beamforming process. In contrast, ultrawideband arrays that radiate short pulses exhibit a high level of mutual coupling in a relative short duration directly after transmission. The duration of this direct coupling is determined by both the type of antenna element and their arrangement. If the coupled signals can be separated from target responses in the range profiles of each transmit/receive pairs within the array, the mutual coupling produces minimal influence on the resulting image of the target. On the other hand, an overlapped response of target and element coupling could significantly reduce the dynamic range of the imaging system. Subtraction of prerecorded coupling is commonly not very effective in this case due to the instability of electronics, which causes high amplitude residuals comparable to the level of a small target in the array near-field. Fig. 3 shows the coupling level and maximum contaminated ranges of all transmit/receive pairs within each tested 2-D array. We define the maximum contaminated range as the distance in the range profile where amplitude of coupling drops 10 dB below the measured amplitude of a 1.5-cm-diameter metal sphere at 0.5 m range. The polystyrene foam used for the frame of the arrays has a permittivity close to that of air, therefore with minimum effect on the coupling among the antennas. Except for the differences in terms of coupling level due to array topology, all of transmit/receive pairs within the four arrays are free of coupling influence beyond , which is fairly close to the aperture plane. The imaging results of the 2-D arrays will not be affected by direct coupling if the target appears at farther range distances. B. Focusing Patterns Focusing patterns of the four 2-D arrays when focused at center and edge positions are shown in Figs. 4 and 5. The results are obtained from measurements with a 1.5-cm-diameter
Fig. 4. Measured focusing pattern of four MIMO arrays with focal point at . (a) Array I and (b) its contour plot to show 22-dB center position beamwidth. (c) Array II and (d) its contour plot to show 22-dB beamwidth. (e) Array III and (f) its contour plot to show 22-dB beamwidth. (g) Array IV and (h) its contour plot to show 22-dB beamwidth.
metal sphere placed at 50 cm range distance in front of both array center and edge, respectively. The focusing pattern is computed by taking the maximum level along the range dimension of the focused three-dimensional image (PSF). The measured focusing pattern agrees with numerical simulation. In terms of performances around the mainlobe and within the interference region that is governed by narrowband properties, the rectangular and Mills Cross arrays perform equally well due to their uniform virtual aperture function. The spiral array exhibits some sidelobes closely distributed to the main lobe. The curvilinear array has slightly wider PSF than other arrays due to the feature of its design methodology, which makes it less controllable in terms of distribution in the virtual aperture. However, it is only the curvilinear array that demonstrates absence of the sidelobes at 22-dB level in the image of the centrally located target. For the offset target, level of the sidelobes increases
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TABLE II SUMMARY OF FOCUSING PATTERN OF 2-D SPARSE MIMO UWB ARRAYS
22-dB grating/sidelobe level with only 25 antenna elements within the array aperture.
Fig. 5. Measured focusing pattern of four MIMO arrays with focal point at edge . (a) Array I and (b) its contour plot to show 22-dB position beamwidth. (c) Array II and (d) its contour plot to show 22-dB beamwidth. (e) Array III and (f) its contour plot to show 22-dB beamwidth. (g) Array IV and (h) its contour plot to show 22-dB beamwidth.
in all four arrays. The performance degradation in terms of sidelobes is especially severe when the beam is steered toward the edge position (Fig. 5). Image “pollution” by sidelobes is especially severe for the spiral-based topology, where a large number of sidelobes rises around the main lobe. This in turn could reduce its capability to reconstruct the continuous shape of distributed target. From a wideband properties point of view, the rectangular and Mills Cross arrays perform poorly due strong shadowing. In contrast, the curvilinear array is well designed to avoid element shadowing effects and shows a lower level of sidelobes. Both 3-dB pattern width and maximum grating/sidelobe level of all four arrays are summarized in Table II. The 2-D MIMO UWB array designed based on proposed generic topology (the array I) achieves experimentally 2 angular resolution and
VI. VOLUMETRIC IMAGING OF DISTRIBUTED TARGETS The potential of employing a 2-D sparse MIMO array lies in its the capability to perform real-time 3-D volumetric imaging. Differences of focusing pattern would have greater impact when the array faces targets with higher spatial dimension. This is due to the fact that the resulting image represents the integration between the array PSF and the target object space [33]. Therefore, the level of grating/sidelobe varies depending on the dimension, shape and orientation of the possible target. Two distributed targets are tested using four planar arrays as shown in Fig. 6. The first one is a pair of scissors, which is full of target features. The position of the scissors during the test is shown. They are placed at the same height in front of the array center at 50 cm distance from the aperture plane. Under such imaging geometry, resolving capabilities in both crossrange directions are provided by the real array aperture while the down-range is supported by the bandwidth of the transmitted signals. Besides their obvious cross figure, the scissors consist of two pieces of metal parts, which should be separable in the resulting image. The two circular rings (handles) at the end of each piece will give smaller reflections than the scissors’ front joints, therefore presenting a dynamic range test for the imaging array. Among the results of the four arrays, the Mills Cross array gives the highest sidelobe response distributed at angles. Such pattern corresponds to its point spread function, but appearing with higher amplitude due to the extension of the scissors in the directions. The equivalent rectangular array exhibits the second highest sidelobe level along the horizontal plane. It is not better than the Mills Cross array in the sense that the sidelobe passes directly through the center of the target. This leaves no separation between target response and energy leakage, which is definitely not wanted. The spiral array provides improved image quality, but with closely located sidelobes, which interferes with the target response. The curvilinear array gives much lower sidelobe level and size. Close comparison indicates the advantages of the curvilinear array design. Due to the lower sidelobe level, the scissors are better reconstructed by the curvilinear array than by the other three with much less artifacts in the 3-D image. The revolver under test was placed in a similar position as shown in Fig. 6. An important feature of the revolver is that it has a relatively long extension in the elevation plane along its barrel. Therefore, any array that has sidelobes distributed along the elevation direction would result in an untruthful image of the revolver. The interaction of side/grating lobes can be either
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of the revolver’s barrel gives slightly a wider response than its real shape. Although the target does not have excessive extension along the diagonal directions, the sidelobe pattern of the Mills Cross array is still quite visible. The test results from distributed targets indicate an overall advantage of the curvilinear array in terms of producing 3-D images with lower and less artifacts. However, further improvement may be necessary to reduce closely located sidelobes and further improve its imaging capabilities. One should also note that the proposed arrays may not be directly applied for high-contrast targets (e.g., medical imaging) where full inversion techniques must be considered. VII. CONCLUSION
Fig. 6. Volumetric imaging of a pair of scissors and revolver placed at distance by 2-D MIMO arrays. (a) Photograph of the targets under test. (b) 3-D images obtained by array I. (c) 3-D images obtained by array II. (d) 3-D images obtained by array III. (e) 3-D images obtained by array IV. The dynamic range of the image is set to 15 dB.
constructive or destructive. Destructive interactions are visible in the images from the equivalent rectangular array due to its energy leakage in the vertical direction. One can see that the response of the barrel is broken into two parts, which is a clear sign of target breakup phenomenon. In contrast, the interactions of sidelobe and target responses from the curvilinear array result in constructive accumulation. This is why the jointing part
In this paper, we propose a new class of MIMO array configurations with lower shadowing than all previously known regular configurations. By arranging element distributions of both transmit/receive arrays according to curvilinear geometries (resulting in curvilinear virtual topologies), the element shadowing effect, which is common for periodic arrays, is reduced, resulting in a decrease the grating/sidelobe level. In order to demonstrate the advantages of the proposed topology, four MIMO UWB antenna arrays for short-range imaging were designed. Requirements of the specific application—concealed weapon detection—were used to determine the operational frequency band and the array parameters. Two of these arrays are based on previously proposed topologies—one designed based on -plane uniform coverage, and one on the curvilinear virtual topology suggested in this paper. The proposed 2-D MIMO array achieves by 150% fractional bandwidth 2 angular resolution, and overall 22-dB grating/sidelobe level with only 25 antenna elements, while it is about 2–5 dB higher for the reference arrays. A theoretical and experimental study on focusing capabilities of these arrays as a function of the focusing distance and operational bandwidth has been performed. It has been demonstrated that the array based on the proposed generic topology keeps its focusing performance on a short distance (up to 20 wavelengths at the center frequency) from the array aperture, while the arrays based on orthogonality of transmit–receive array patterns lose their focusing abilities at a short range. This comparison demonstrates that periodic uniformity of the virtual array, the best according to [13], is in fact not optimum in the near zone and that nonperiodic uniformity with the proposed spiral lattice of the virtual array resulting from curvilinear Tx and Rx arrays much better eliminates redundancy and shadowing. The impact of element shadowing on the performances of sparse 2-D MIMO array is shown, and the applicability of the virtual-aperture-based approach for the near-field imaging is proven. The numerical comparison of the array built on the proposed generic topology with the one built based on -plane uniform coverage confirms importance of the virtual aperture uniformity in the MIMO UWB array design and demonstrates that uniform coverage of the -plane alone is not sufficient for a good MIMO UWB array performance. The importance of low sidelobe levels for imaging of distributed targets is demonstrated. The experimental results from volumetric imaging illustrate a great potential of the proposed two-dimensional sparse MIMO array-based UWB imaging system in real-time short-range applications such as surveillance, through-wall imaging, and concealed weapon detection.
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Fig. 8. Measured reflection from metal plate and small metal sphere of 1.5 cm diameter. (a) Signal waveforms. (b) Normalized power spectrum densities indicating a 10-dB bandwidth from 2.8 to 19.5 GHz.
Fig. 7. Measurement setup with four 2-D MIMO arrays connected to a network analyzer through a multiport switch in anechoic chamber. (a) Array I, curvilinear array. (b) Array II, equivalent uniform rectangular array. (c) Array III, Mills Cross array. (d) Array IV, spiral array. (e) Network analyzer with multiport test set. The array topologies are the same as those shown in Fig. 1.
APPENDIX Near-field measurements are performed to test the proposed theory and 2-D MIMO array design strategies. The setup together with four tested two-dimensional sparse MIMO arrays are illustrated in Fig. 7. Although the proposed sparse array theory has greater potential in practice in combination with impulse systems, this experiment is conducted with a network analyzer in order to demonstrate the theoretical performance. Each one of the tested 2-D arrays represents one of the design strategies introduced in the previous section with exactly the same topology shown in Fig. 1. Assuming an application for a handheld device, the aperture size of the 2-D array is limited to 0.5 0.5 m . The arrays are constructed using a low-profile antipodal Vivaldi antenna. This antenna element has an aperture size of 45 mm and exhibits consistent UWB characteristics in the frequency band from 2.7 to 26 GHz [38]. Array elements are connected to the network analyzer through a computer-controlled multiport switch. The switch operates up to 20 GHz, which influences the higher frequency band of the setup. All the antenna elements within the planar array are placed in a vertical position producing vertical polarization along the elevation plane. Full-port calibration of the network analyzer, switch, and cables are performed before the measurement. The data is collected in the frequency-domain by sweeping within the frequency band from 1 to 26 GHz and switching through all transmit/receive pairs within the MIMO array. Each obtained frequency-domain signal is then windowed and transformed to time domain by inverse Fourier transform and further focused using migration algorithms specially developed for MIMO array imaging [37]. Direct coupling between elements within each array is recorded in free space and then subtracted from all the measured data sets. This also serves as background subtraction that removes clutter from the raw data.
Both antenna face-to-face transfer and reflection from the metal sphere are measured in order to define the operational bandwidth of the whole setup. The bandwidth of the complete system and its corresponding time-domain impulse are shown in Fig. 8. The pulse duration is about 0.06 ns. The operational bandwidth at 10-dB level ranges from 2.8 to 19.5 GHz with 16.7-GHz absolute bandwidth and center frequency at 11.15 GHz. In this frequency band, all four arrays are considered ultra-sparse arrays because their average element spacing within the virtual apertures are more than 2.5 times the half-wavelength at center frequency . The complete setup achieves 150% fractional bandwidth, which is sufficient to reduce the grating lobes caused by array sparseness. ACKNOWLEDGMENT The authors would like to thank Dr. A. Roederer for numerous helpful discussions on sparse arrays and his advice on paper organization, P. Aubry from Delft University of Technology for his technical support during the measurement campaign, and Dr. A. Angstenberger from the Taconic Advanced Dielectric Division for providing substrate sample for antenna manufacture as well as anonymous reviewers for their suggestions and comments. REFERENCES [1] I. J. Craddock, R. Nilavalan, J. Leendertz, A. W. Preece, and R. Benjamin, “Experimental investigation of real aperture synthetically organized radar for breast cancer detection,” in Proc. IEEE Antennas Propag. Soc. Int. Symp., July 3–8, 2005, vol. 1B, pp. 179–182. [2] A. Beeri and R. Daisy, “High-resolution through-wall imaging,” in Proc. SPIE, 2006, vol. 6201, p. 62010J. [3] A. G. Yarovoy, T. G. Savelyev, P. J. Aubry, P. E. Lys, and L. P. Ligthart, “UWB array-based sensor for near-field imaging,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 6, pp. 1288–1295, Jun. 2007. [4] S. S. Ahmed, A. Schiessl, and L.-P. Schmidt, “Novel fully electronic active real-time millimeter-wave imaging system based on a planar multistatic sparse array,” in Proc. IMS, 2011, pp. 1–4. [5] B. D. Steinberg, Principles of Aperture and Array Systems Design. New York: Wiley, 1976. [6] R. E. Davidsen, J. A. Jensen, and S. W. Smith, “Two-dimensional random arrays for real time volumetric imaging,” Ultrason. Imaging, vol. 16, pp. 143–163, 1994. [7] D. H. Turnbull and F. S. Foster, “Beam steering with pulsed two-dimensional transducer arrays,” IEEE Trans. Ultrason., Ferroelectr. Freq. Control, vol. 38, no. 4, pp. 320–333, Jul. 1991. [8] A. L. Maffett, “Array factors with non uniform spacing parameters,” IRE Trans. Antennas Propag., vol. AP-10, no. 2, pp. 131–146, Mar. 1962.
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[9] M. I. Skolnik, G. Newhauser, and J. W. Sherman, “Dynamic programming applied to unequally spaced array,” IEEE Trans. Antennas Propag., vol. AP-12, pp. 35–43, Jan. 1964. [10] O. T. Von Ramm and S. W. Smith, “Beam steering with linear arrays,” IEEE Trans Biomed. Eng., vol. BME-30, no. 8, pp. 438–452, Aug. 1983. [11] F. Anderson, W. Christensen, L. Fullerton, and B. Kortegaard, “Ultrawideband beamforming in sparse arrays,” Inst. Elect. Eng. Proc. H, vol. 138, pp. 342–346, Aug. 1991. [12] V. Murino, A. Trucco, and A. Tesei, “Beam pattern formulation and analysis for wide-band beamforming systems using sparse arrays,” Signal Process., vol. 56, pp. 177–183, 1997. [13] J. L. Schwartz and B. D. Steinberg, “Ultrasparse, ultrawideband arrays,” IEEE Trans. Ultrason., Ferroelectr. Freq. Control, vol. 45, no. 2, pp. 376–393, Mar. 1998. [14] O. T. Von Ramm, S. W. Smith, and F. L. Thurstone, “Grey scale imaging with complex TGC and transducer arrays,” in Proc. Soc. Photo-Opt. Inst. Eng., Med. IV, 1975, vol. 70, pp. 266–270. [15] C. R. Cooley and B. S. Robinson, “Synthetic focus imaging using partial datasets,” in Proc. Ultrasonic Symp., 1994, vol. 3, pp. 1539–1542. [16] G. R. Lockwood and F. S. Foster, “Optimizing the radiation pattern of sparse periodic two-dimensional arrays,” IEEE Trans. Ultrason., Ferroelectr. Freq. Control, vol. 43, no. 1, pp. 15–19, Jan. 1996. [17] S. W. Smith, H. G. Pavy, Jr., and O. T. von Ramm, “High-speed ultrasound volumetric imaging system—Part I: Transducer design and beam steering,” IEEE Trans. Ultrason., Ferroelectr. Freq. Control, vol. 38, no. 2, pp. 100–108, Mar. 1991. [18] S. S. Ahmed, A. Schiessl, and L.-P. Schmidt, “Near field mm-wave imaging with multistatic sparse 2D-arrays,” in Proc. 6th Eur. Radar Conf., Rome, Italy, 2009, pp. 180–183. [19] L. Kogan, “Optimizing a large array configuration to minimize the sidelobes,” IEEE Trans. Antennas Propag., vol. 48, no. 7, pp. 1075–1078, Jul. 2000. [20] T. J. Cornwell, “A novel principle for optimization of the instantaneous Fourier plane coverage of correction arrays,” IEEE Trans. Antennas Propag., vol. 36, no. 8, pp. 1165–1167, Aug. 1988. [21] F. Boone, “Interferometric array design: Optimizing the locations of the antenna pads,” Astron. Astrophys., vol. 377, pp. 368–376, 2001. [22] J. R. Potter and M. A. Chitre, “Optimisation and beamforming of a two-dimensional sparse array,” in Proc. High Perform. Comput., Nov. 1998, vol. 1, pp. 452–459. [23] B. E. Cohanim, J. N. Hewitt, and O. de Weck, “The design of radio telescope array configurations using multi-objective optimization: Imaging performance versus cable length,” Astrophys. J. Suppl. Ser., vol. 154, pp. 705–719, Oct. 2004. [24] B. Y. Mills, “Cross-type radiotelescopes,” Proc. IRE Aust., vol. 24, pp. 132–140, 1963. [25] P. J. Napier, A. R. Thompson, and R. D. Ekers, “The very large array: Design and performance of a modern synthesis radio telescope,” Proc. IEEE, vol. 71, no. 11, pp. 1295–1320, Nov. 1983. [26] J. P. Bregman, “Concept design for a low frequency array,” in Proc. SPIE, 2000, vol. 4015, pp. 19–32. [27] X. Zhuge and A. G. Yarovoy, “A sparse aperture MIMO-SAR-based UWB imaging system for concealed weapon detection,” IEEE Trans. Geosci. Remote Sens., vol. 49, no. 1, pp. 509–518, Jan. 2011. [28] T. Savelyev, X. Zhuge, P. Aubry, A. G. Yarovoy, L. Ligthart, and B. Levitas, “Comparison of 10–18 GHz SAR and MIMO-based short range imaging radars,” Int. J. Microw. Wireless Technol., vol. 2, pp. 369–377, 2010. [29] X. Zhuge and A. G. Yarovoy, “MIMO-SAR based UWB imaging for concealed weapon detection,” in Proc. EUSAR, 2010, pp. 194–197. [30] S. S. Ahmed, A. Schiessl, and L.-P. Schmidt, “Multistatic mm-wave imaging with planar 2D-arrays,” in Proc. German Microw. Conf., Mar. 16–18, 2009, pp. 1–4. [31] X. Zhuge and A. Yarovoy, “Near-field ultra-wideband imaging with two-dimensional sparse MIMO array,” in Proc. 4th EuCAP, Barcelona, Spain, Apr. 2010, pp. 1–4. [32] B. Yang, A. G. Yarovoy, P. Aubry, and X. Zhuge, “Experimental verification of 2D UWB MIMO antenna array for near-field imaging radar,” in Proc. 39th Eur. Microw. Conf., 2009, pp. 97–100. [33] X. Zhuge, “Short-range ultra-wideband imaging with multiple-input multiple-output arrays” Ph.D. dissertation, Delft Univ. Technol. (TUDelft), Delft, The Netherlands, 2010 [Online]. Available: http://repository.tudelft.nl
[34] B. D. Steinberg and H. M. Subbaram, Microwave Imaging Techniques. New York: Wiley, 1991. [35] D. W. Boeringer, “Phased array including a logarithmic spiral lattice of uniformly spaced radiating and receiver elements,” US Patent 6 433 754, May 2001. [36] H. Vogel, “A better way to construct the sunflower head,” Math. Biosci., vol. 44, pp. 179–189, 1979. [37] X. Zhuge, A. G. Yarovoy, T. G. Savelyev, and L. P. Ligthart, “Modified Kirchhoff migration for UWB MIMO array-based radar imaging,” IEEE Trans. Geosci. Remote Sens., vol. 48, no. 6, pp. 2692–2703, Jun. 2010. [38] X. Zhuge and A. Yarovoy, “Design of low profile antipodal vivaldi antenna for ultra-wideband near-field imaging,” in Proc. 4th EuCAP, Apr. 2010, pp. 1–5.
Xiaodong Zhuge was born in Beijing, China, in 1982. He received the Master of Science degree (cum laude) in telecommunication engineering and Ph.D. degree (cum laude) in the field of array-based ultrawideband imaging from Delft University of Technology (TU Delft), Delft, The Netherlands, in 2006 and 2010, respectively. After graduation, he worked as a Postdoc Researcher with the International Research Centre for Telecommunications-Transmission and Radar (IRCTR), TU Delft. In 2011, he joined the FEI Company, Eindhoven, The Netherlands, as a Scientist. His main research interests are image reconstruction, image processing, and imaging system design. Dr. Zhuge was the recipient of the 2007 European Radar Conference (EuRAD) Young Engineers Prize at the 10th European Microwave Week, Munich, Germany.
Alexander G. Yarovoy received the Diploma with honor in radiophysics and electronics and Candidate and Doctor Phys. and Math. Sci. degrees in radiophysics from Kharkov State University, Kharkiv, Ukraine, in 1984, 1987, and 1994, respectively. In 1987, he joined the Department of Radiophysics, Kharkov State University, as a Researcher and became a Professor there in 1997. From September 1994 through 1996, he was with the Technical University of Ilmenau, Ilmenau, Germany, as a Visiting Researcher. Since 1999, he has been with the International Research Centre for Telecommunications-Transmission and Radar (IRCTR), Delft University of Technology, Delft, The Netherlands. Since 2009, he leads a chair of Microwave Technology and Systems for Radar at the university. In August 2010, he was appointed as a scientific director of IRCTR. He has authored and coauthored some 250 scientific or technical papers, four patents, and 14 book chapters. His main research interests are in ultrawideband microwave technology and its applications (in particular, radars) and applied electromagnetics (in particular, UWB antennas). Prof. Yarovoy was elected a member of the Board of Directors of the European Microwave Association (EuMA) in 2008. He served as a Guest Editor of five special issues of the IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING and other journals. He served as the Chair and TPC Chair of the 5th European Radar Conference (EuRAD 2008), Amsterdam, The Netherlands, as well as the Secretary of the 1st European Radar Conference (EuRAD 2004), Amsterdam, The Netherlands. He also served as the Co-Chair and TPC Chair of the 10th International Conference on GPR (GPR 2004) in Delft, The Netherlands. He is the recipient of a 1996 International Union of Radio Science (URSI) “Young Scientists Award” and the European Microwave Week Radar Award in 2001 for the paper that best advances the state of the art in radar technology (together with L. P. Ligthart and P. van Genderen). In 2010, together with D. Caratelli, he received the best paper award of the Applied Computational Electromagnetic Society (ACES).
