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Corner reflector tag with RCS frequency coding by dielectric resonators

2021; Institution of Engineering and Technology; Volume: 15; Issue: 6 Linguagem: Inglês

10.1049/mia2.12067

1751-8733

Ali Alhaj Abbas, Mohammed El‐Absi, Ashraf Abuelhaija, Klaus Solbach, Thomas Kaiser,

Antenna Design and Analysis

IET Microwaves, Antennas & PropagationVolume 15, Issue 6 p. 560-570 ORIGINAL RESEARCH PAPEROpen Access Corner reflector tag with RCS frequency coding by dielectric resonators Ali Alhaj Abbas, Corresponding Author ali.alhaj-abbas@uni-due.de Department of Electrical Engineering and Information Technology, Institute of Digital Signal Processing, University of Duisburg-Essen, Duisburg, Germany Correspondence A. Alhaj Abbas, Institute of Digital Signal Processing, University of Duisburg-Essen, Bismarckstr. 81 (BB), 47057, Duisburg, Germany. Email: ali.alhaj-abbas@uni-due.deSearch for more papers by this authorMohammed El-Absi, Department of Electrical Engineering and Information Technology, Institute of Digital Signal Processing, University of Duisburg-Essen, Duisburg, GermanySearch for more papers by this authorAshraf Abuelhaija, Department of Electrical Engineering, Applied Science Private University, Amman, JordanSearch for more papers by this authorKlaus Solbach, Department of Electrical Engineering and Information Technology, Institute of Digital Signal Processing, University of Duisburg-Essen, Duisburg, GermanySearch for more papers by this authorThomas Kaiser, Department of Electrical Engineering and Information Technology, Institute of Digital Signal Processing, University of Duisburg-Essen, Duisburg, GermanySearch for more papers by this author Ali Alhaj Abbas, Corresponding Author ali.alhaj-abbas@uni-due.de Department of Electrical Engineering and Information Technology, Institute of Digital Signal Processing, University of Duisburg-Essen, Duisburg, Germany Correspondence A. Alhaj Abbas, Institute of Digital Signal Processing, University of Duisburg-Essen, Bismarckstr. 81 (BB), 47057, Duisburg, Germany. Email: ali.alhaj-abbas@uni-due.deSearch for more papers by this authorMohammed El-Absi, Department of Electrical Engineering and Information Technology, Institute of Digital Signal Processing, University of Duisburg-Essen, Duisburg, GermanySearch for more papers by this authorAshraf Abuelhaija, Department of Electrical Engineering, Applied Science Private University, Amman, JordanSearch for more papers by this authorKlaus Solbach, Department of Electrical Engineering and Information Technology, Institute of Digital Signal Processing, University of Duisburg-Essen, Duisburg, GermanySearch for more papers by this authorThomas Kaiser, Department of Electrical Engineering and Information Technology, Institute of Digital Signal Processing, University of Duisburg-Essen, Duisburg, GermanySearch for more papers by this author First published: 16 March 2021 https://doi.org/10.1049/mia2.12067Citations: 3AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat Abstract For a novel indoor-localization system, chipless tags with high retro-directive radar cross-section (RCS) under wide-angle incidence are required as fixed landmarks. Tags based on dielectric resonators (DRs) were proposed to provide identification by resonance frequency coding. To achieve a satisfactory read range for the localization system, the low RCS levels of these tags require a major boost. A solution was found by adopting the metallic corner reflector which is known for high RCS levels over a wide bandwidth and over a wide angle of incidence. The study presents a novel corner reflector design where notches in the RCS spectral signature are created by the attachment of arrays of dielectric resonators to the metallic surfaces of corner reflectors. It is shown that notches appear due to the increased scattering of the resonators at resonance and by the power loss due to grating lobes formed in addition to the specular reflection from the arrays and from the metallic surfaces. Results from electromagnetic simulations are verified by measurements of an example dihedral corner reflector of 100 × 100 mm2 plate size with two arrays of 3 × 3 DRs producing a notch signature at about 7 GHz. 1 INTRODUCTION Automation in logistics and industrial processes increasingly requires highly precise self-localization of, for example, robots in an indoor environment. While outdoor localization and positioning systems are dominated by satellite-based radio technology (GPS etc.), modern indoor positioning systems tend to employ existing wireless infrastructure, like Bluetooth and WiFi [1]. These systems employ the lower microwave spectrum and thus are limited to localization accuracies in the cm-range; even the high microwave frequencies in 5G systems will not provide below-cm accuracies [2]. For many applications, the lowest overall system cost requires an active reader on the device to be localized and passive, chipless tags as landmarks fixed to the environment. Chipless tags are well known as candidates for radio-frequency identification (RFID) and sensor applications [3]; however, read ranges are limited on the order of 10 cm to 1 m using microwave frequencies up to about 10 GHz. By extending this application scope, printed-circuit-based chipless tags have also been demonstrated in 2D- [4, 5] and 3D-localization [6] systems at cm- to mm-accuracies at such short distances. To achieve high localization accuracies at several metre read range, we proposed a novel self-localization system [7] which is intended to work at high mm-wave frequencies. This system employs passive, chipless tags as landmarks fixed to the infrastructure and a wide-band frequency-modulated continuous-wave Radar as the reader. Inspired by the potential of dielectric resonators (DRs) as RFID tags and sensors [8], in our original proposal, the tags are based on DRs. These tags provide retro-directive mono-static radar cross-section (RCS) with peak levels at the DR resonance frequencies, thereby allowing discrimination of each tag by its frequency signature. Figure 1(a) gives a sketch of the considered system, where a Radar reader transmits a swept frequency signal and scans its environment by the antenna beam. The room is equipped with retro-directive chipless tags functioning as landmarks with precisely known positions (x Tm, y Tm). After the reader has detected, identified (by resonant frequency) and ranged the tags in their environment, its own position coordinates (x Reader, y Reader) can be calculated from the ranges to the tags and the knowledge of the landmark positions. In a practical system, a reader may interrogate a landmark tag at large distance and under arbitrary incidence angle. Therefore, the tags should exhibit high-level wide-angle retro-directive RCS to be detectable by the reader. FIGURE 1Open in figure viewerPowerPoint Self-localization system design and components. (a) Sketch of self-localization system considered in [7]. (b) Comparison of representative spectral signatures caused by dielectric resonators (single or in a planar array) in free space and in an array placed on the surface of a metal corner reflector Since RCS levels of single DRs are very low [9], especially at millimetre-wave frequencies, we boost the RCS levels by combining DRs with spherical lenses [10, 11] or 2D-lenses [12] and even realize tags with angle-of-arrival sensing [13]. However, the increase in RCS is limited to about 30 dB by the structural reflections from the 3D dielectric lenses and the metallic part of the 2D-lenses except for the spherical Luneberg lenses. Unfortunately, these cannot be produced easily with dimensions suited to millimetre-wave frequencies. As an alternative method to produce high retro-directive scattering levels, arrays of DRs can be used [15, 14]. The spectral signatures shown in Figure 1(b) for a single DR and a planar array of 7 × 5 DRs demonstrate the boost in RCS by a planar array. However, linear and planar arrays exhibit high retro-directive RCS only close to the normal direction of incidence. We, therefore, investigated arrays of DRs arranged in two planes under 90° angle in order to exploit the wide-angle high retro-directive RCS known from corner reflectors [16, 17]. For normal incidence, planar arrays of DRs exhibit high reflection magnitude at the DR resonance frequency close to that of flat metallic surfaces. However, at an oblique incidence, reflection properties tend to degrade as we see a strong variation of the mono-static RCS spectral signature versus incidence angle in a corner reflector arrangement of DRs. Even, if such degradations could be reduced, it is difficult to support the elements of such DR arrays in an electrically large corner arrangement with a minimum of structural reflecting material shaped to avoid superseding of the resonant frequency signature. To solve the mechanical problem, instead of placing arrays of DRs in free space, in an experiment, we used a double-sided adhesive film to fix arrays of DRs to the metallic plates of a corner reflector. As a result, we found an inverse spectral signature of the retro-directive RCS: Instead of high scatter levels only at the DR resonance frequencies, the metallic corner reflector arrangement produced high retro-directive RCS levels over a broad frequency band with deep notches at resonance frequencies of the DRs. For illustration, in Figure 1(b), the spectral signatures of a single DR and a planar array of DRs (peak RCS at the DR resonance frequency) are compared to the notched signature of a dihedral metal corner reflector with DR arrays on its surface. Corner reflectors mostly made up of three metal plates joined under 90° angles (trihedral) have widespread application as retro-reflector buoys for navigational radar [16] or as calibration target in satellite-based radar [18]. Such reflectors exhibit a flat spectral signature for wide-angle incidence which, however, does not allow discrimination and identification of the reflectors. To add some coding information to the response of a corner reflector, in [19], electronic switching of the reflecting surfaces was integrated to produce an amplitude modulation in the RCS signature. While this requires active switching devices and power supply, completely passive corner reflectors with coding are needed for an inexpensive self-localization system. With the availability of a wide-band Radar reader, we can take advantage of frequency-selective scattering, as in [20], where a spherical lens retro-reflector design is modified by a patch resonator reflective surface. Frequency selective RCS signatures can also be realized for metal corner reflectors, as proposed in two recent studies: Both corner reflector designs exhibit a notched spectral RCS signature for wide-angle incidence which allows identification of individual reflectors by the position of the notch in the spectral signature. One design uses a linear array of DRs placed in front of a dihedral corner reflector [21] which produces a narrow notch in the RCS signature; however, the size of the corner reflector is limited in one dimension. The other design uses a printed frequency selective surface (FSS) placed in front of a trihedral corner reflector [22]. This design can be realized for any size of corner reflector; however, the notch produced by the FSS is relatively broad and exhibits a serious degradation at normal incidence. Notched spectral signatures have also been realized in applications of printed FSS for the reduction of the RCS level of antennas over a narrow band [23] or introduce narrow-band absorption in the specular reflection characteristics of a plane structure [24]. Although such structures can provide high RCS outside the notches over wide-angle range in specular reflection, corner reflectors replacing the metal plates by FSS boards using this property have not been reported yet. Rather, printed FSS boards have been designed to realize low profile (flat) corner reflectors [25]. In another application to antenna design, printed FSS boards have been used in a dihedral corner arrangement as a reflector behind an omnidirectional monopole to increase directivity [26]. In this design, the corner reflector produces increased reflection at the FSS resonance frequency, such that the RCS exhibits a peak instead of a notch in its spectral signature. Other examples of notched RCS spectral signatures are found in the large class of chipless RFID backscatter tags, for example, [27], where notches are created at the resonant frequencies of planar printed circuit resonators. However, even if such tags can be designed to provide wide-angle retro-directivity [28], the achievable RCS levels are limited by the (small) footprint of the resonator structures. At lower microwave frequencies, we find RCS magnitudes below −20 dBm2. When scaling such tags to mm-wave frequencies, both the reduction of RCS due to the smaller size and due to the increased conductor and dielectric dissipation losses very much would limit practical operating distances to far below 1 m. In contrast, the proposed corner reflector with frequency coding by planar arrays of dielectric resonators can be realized for mm-wave frequencies with low loss. Most importantly, this design can be increased in size to achieve any required RCS level while maintaining its notched wide-angle retro-directivity. In the following sections, we investigate the frequency notch effect using electromagnetic (EM) simulations and show that the underlying mechanism is scattering rather than absorption due to DR resonant modes excited by the incident wave. Based on the analysis, design considerations are presented, and an example design is proven experimentally. Because of easier experimental demonstration, our study frequency range was scaled down to below 10 GHz and although the approach also can be applied to trihedral corner reflectors, we only study dihedral reflectors for simplicity. 2 SCATTERING OF ARRAY OF DRs ON PEC PLATE In a first step, we investigate the scattering of a linear array of DRs placed on a perfect metallic conductor (PEC) plate. Figure 2 shows an array of cylindrical DRs at a spacing d which are bonded to a PEC plate by a thin adhesive layer. The DR material is assumed to be a lossless ceramic of ɛ r = 37, while the bonding layer is characterized by ɛ r = 2.5, typical for polymer-based adhesives. FIGURE 2Open in figure viewerPowerPoint Construction of linear DR array on a PEC plate with P = 1 mm thickness and width W = 30 mm and dielectric resonators of radius R = 3.2 mm and height H = 3 mm bonded to the plate by an adhesive layer of thickness F = 0.02 mm in a spacing d = 30 mm. DR, dielectric resonator; PEC, perfect metallic conductor Since we are interested in the application as corner reflector with PEC plates in 45° tilted from the normal incidence, we first simulate the scattering from the linear array for plane waves incident under θ inc = 45° in the x-z-plane. EM modelling of bi-static RCS characteristics employs the finite element simulator of CST Microwave Studio with plane wave excitation. For a plain PEC plate, we expect a strong specular reflection under θ 0 = −45°, as indicated in Figure 3, with RCS magnitude tending to increase with frequency. However, a plot of the bi-static RCS for the specular reflection direction, Figure 4, shows two notches in the frequency range from 6.5 to 9.5 GHz. FIGURE 3Open in figure viewerPowerPoint Wave scattering contributions from the linear array of DRs on a PEC plate. DR, dielectric resonator; PEC, perfect metallic conductor FIGURE 4Open in figure viewerPowerPoint Bi-static RCS for specular reflection at θ 0 = −45° and mono-static RCS of a linear array of eight DRs on a PEC plate as in Figure 2 with 240 mm length of plate. Resonators assumed lossless. Adhesive assumed lossless or lossy with tanδ = 0.1. DR, dielectric resonator; PEC, perfect metallic conductor; RCR, radar cross-section The first notch at around 7.2 GHz is connected to the excitation of a HE11 mode, as seen in Figure 5 (left), which produces a broad back-scattering lobe. The second notch at about 9.3 GHz appears when a TE01 mode is excited, as seen in Figure 5 (right), which produces a back-scattering pattern with a broad null in z-direction due to its rotational symmetry. It is interesting to note here that the mono-static scattering, also shown in Figure 4 for θ = 0°, only exhibits a notch at 7.2 GHz since the TE01 mode cannot be excited at its pattern null. The notch frequencies depend on the mechanical dimensions of the DRs: Table 1 shows that the frequencies increase as the height of the DR is reduced (this also applies to the reduction of the DR radius). FIGURE 5Open in figure viewerPowerPoint HE11 mode (left) and TE01 mode (right) excited at the notch frequencies by y-polarized wave. (a) Distributions of resonator electric and magnetic fields and (b) bi-static RCS patterns. RCR, radar cross-section TABLE 1. Notch frequencies of DRs of radius R = 3.2 mm and adhesive layer thickness F = 0.02 mm as a function of height H (ceramic ϵ r = 37 and adhesive ϵ r = 2.5) H (mm) f Notch (HE11) f Notch (TE01) 3.8 6.70 8.48 3.4 6.94 8.84 3.0 7.25 9.31 2.6 7.68 9.89 2.3 8.13 10.5 Abbreviation: DR, dielectric resonator. The explanation of the notch effect is based on the resonance behaviour of the DRs: At resonance, the effective RCS of each DR in the array significantly increases from the low structural RCS which is found at a far-off resonance [9]. Due to the excitation by the incident wave, the array of DRs produces a scattered beam into the same specular direction as the PEC plate, and thus we have a superposition of two contributions. However, since the reflection at the PEC surface inverts the phase, this contribution appears in anti-phase to the DR mode reflection. Therefore, we see a drop in RCS in this direction and at this frequency. We see from EM simulations that the total scattered power is nearly unchanged by the notch effect. This means that to compensate the reduced level in the specular beam, power conservation requires increased scattering into other directions. In the present example, we find a major part of this scatter power in a grating lobe (GL) in the x-z-plane: The 'electrical' spacing of DRs in the array is d/λ = 0.72 at 7.2 GHz and d/λ = 0.93 at 9.3 GHz which allows GLs when the transmit beam is scanned to 45° off the normal. From antenna theory, for example, [29], we apply a relation for scan direction and the direction of the first appearing GLs: sin θ 0 − sin θ G L = − n λ d (1)where θ 0 is the scan direction (of the specular reflection lobe), due to Snell's law assumed to be the negative incidence angle. θ GL is the direction of a GL of order n, respecting the − sign to the inverse normalized spacing λ/d of the DRs. In our example array with θ 0 = −45°, we expect single first-order GLs at 44° (7.2 GHz) and 21.6° (9.3 GHz). Far-off the resonance frequencies, due to the lower structural RCS magnitude, the GLs appear relatively low, see lobe #2 in Figure 6(a) for a frequency between the two observed resonance frequencies; the high RCS of the DRs at the mode resonances boosts the GLs while the specular lobe (lobe #1) drops, see Figure 6(b) for 7.2 GHz and Figure 6(c) for 9.3 GHz. FIGURE 6Open in figure viewerPowerPoint Bi-static RCS for 45° incidence angle of linear array of eight DRs on a PEC plate as in Figure 2 with 240 mm length of plate. The forward scattering lobe (#3) is at −135°, the specular lobe (#1) is at about −45°and GLs (#2) are at 33°, 43° and 21.5°. (a) Far-off resonance at 8 GHz, (b) at resonance frequency of HE11 (7.2 GHz), and (c) at resonance frequency of TE01 (9.3 GHz). DR, dielectric resonator ; RCR, radar cross-section For other angles of incidence, the same principal behaviour of scattering is found: The coupling of the DR modes to the incident wave depends on the angle of incidence and the mode pattern (for normal incidence, the TE01 mode is not excited due to its field distribution rotational symmetry, as seen in Figure 5). Therefore, the magnitude of the scatter lobes from the DR array can vary and thus the notch depth and the GL strength. Also, the specular reflection from the PEC plate and from the DR array both superimpose with the edge diffraction lobes of the PEC plate and with the sidelobes of the GL. In particular, the notch depth of the HE11 mode is found to vary seemingly in a random manner between 15 and 20 dB for incidence angle from 65° to 25°. At the same time, the notch bottom frequency varies by ±0.05 GHz around 7.2 GHz. However, due to the modal field distribution, the notch depth of the TE01 mode varies in a systematic manner from 0 dB at 0° and 6 dB at 25° to 13 dB at 65°. while the variation of notch bottom frequency is one order of magnitude lower than for the HE11 mode. The assumption of lossless material used up to now may be well justified in the case of the usual high-Q ceramic dielectric material of the resonators. Note that RF quality ceramics are characterized by a loss tangent of better than 10−4. However, the adhesive layer may need a realistic model since many types of adhesives are highly lossy dielectric materials. We, therefore, evaluated variations of loss factors for the adhesive layer. Major changes in the GL magnitude, notch depth and notch width of the HE11 mode were found when the loss tangent went below 0.01 in the adhesive material due to its strong electric field normal to the PEC plane. On the other hand, the TE01 mode is much less sensitive to loss in the thin adhesive layer due to vanishing electric field strength in this region. To illustrate the effect, in Figure 4, we also show the response for the case of lossy adhesive that leads to a more shallow, broadened notch at the HE11 mode. Five other observations are worth reporting: a) The notch signature of the TE01 mode is much narrower than the signature of the HE11 mode which is due to the higher radiation Q-factor of the TE01 mode. More narrow notch signatures, especially of the HE11 mode, could be realized by using dielectric material of higher permittivity. For example, DRs with ɛ r = 78 reduce the 3-dB width of notches to less than 50% of the width using ɛ r = 37. b) The magnitude of GLs and the notch depth of specular lobes reduces as we reduce the number of DRs per plate area by setting spacings considerably larger than the width of the effective receiving area of a DR mode. Based on the directivity of the HE11 mode as used in the simulations above, this area has an approximate diameter of 20 mm at 7.2 GHz. c) The ratio of the resonant frequencies of the HE11 mode and the TE01 mode depends on the geometry of the DRs and the thickness of the adhesive layer. For example, the frequency ratio of about 1.31 for the flat cylindrical DR (R/H = 1.07) used above can be increased by using a half-spherical DR to 1.41 and can be reduced by a tall, thin cylindrical shape to 1.17 (R/H = 0.38). Increasing the adhesive layer thickness increases the HE11 mode frequency (e.g. to 7.4 GHz at film thickness F = 0.04 mm), and slightly reduces the TE01 mode frequency (to 9.28 GHz in the example). d) The HE11 mode can be excited by y- and x-polarized incident waves under any angle of incidence. However, the TE01 mode can only be excited by the y-polarized wave and only under oblique incidence in the x-z-plane due to its particular field symmetry. e) Even when a narrower DR spacing does not allow GL creation, notches at the DR resonance frequencies may appear when the scattering pattern of the excited DR modes are broader than the pattern of the plate. This becomes most relevant, when we employ a one-dimensional DR array on a strip reflector plate, and it loses significance for a two-dimensional array on a strip reflector plate of electrically large dimensions. 3 SCATTERING BY DIHEDRAL CORNER REFLECTOR In a conventional two-plate corner reflector, two PEC plates are joined under a 90° angle, and high retro-directive RCS is generated when the incident wave hits the plates under 15–75° off their normal direction [16]. The generated specular reflection lobes are directed towards the other plate where a second reflection turns the waves back into retro-direction, as indicated in Figure 7. The incidence angles of partial waves W1 and W2 to the two plates are related to the corner reflector incidence angle by θ inc1 = θ c + 45° and θ inc2 = 45° − θ c. At wave incidence along the centre line of the corner reflector, θ c = 0°, the incidence angle is 45° to both plates, producing the least spill-over at the plate edges and we experience maximum RCS magnitude. FIGURE 7Open in figure viewerPowerPoint Geometry and indication of incident and reflected partial waves in a corner reflector As we add two DR arrays to the plates, the retro-directed scattering from the corner reflector is the result of two consecutive specular reflections, where each reflection carries a notch at the DR mode frequencies; since both reflections add a notch, under perfect symmetry, we should find the effective notch depth in the spectral signature enhanced over the notch depth of a specular beam of a single plate. However, certain combinations of incident angle θ inc1 or θ inc2 and DR spacing can produce GLs from one of the plates which are retro-directive to the respective incident wave. For example, this is seen in Figure 6(b) where the DR array scatters back into the direction of the incident wave. Such reflections superimpose the reflections of the corner reflector which are produced by the specular reflections from the two PEC plates and potentially may fill the notch in the spectral signature. Using Equation (1) with n = 1 and various DR spacings, in Table 2, we present the direction of incident wave θ inc at one of the two plates which generates a retro-directive scatter lobe such that θ inc = θ GL. With respect to the angular offset of 45° in the corner configuration, the table also presents the incident angle θ c corresponding to the appearance of a retro-directive scatter lobe from one of the two corner surfaces. At 7.1 GHz and for a DR spacing of d = 30 mm we find the retro-directive GL close to θ inc = 45° incidence angle which would mean at about θ c = 0° in the corner reflector. Second-order GLs may also appear for DR spacings above 35 mm but will be neglected in the discussion due to minor effects in the corner reflector spectral signature. TABLE 2. Incident wave angle θ inc at the plates of a corner reflector which generates retro-directive scatter lobes due to the HE11 mode at 7.2 GHz and TE01 mode at 9.3 GHz as function of the grid spacing d of the DR array together with the corresponding corner reflector incidence angles θ c d (mm) θinc@7.2 GHz θc@7.2 GHz θinc@9.31 GHz θc@9.31 GHz 25 56.4° 11.4° 40.1° 4.9° 30 44° 1° 32.5° 12.5° 35 36.5° 8.5° 27.4° 17.6° 40 31.4° 13.6° 23.8° 21.2° To demonstrate the effect of retro-directive GLs, in Figure 8(a), we present an example corner reflector with planar arrays of DRs of 30 × 30 mm2 spacing along the x- and the y-axis on plates of L = 100 mm width and length using DRs and adhesive layer as in Section 2, but with tanδ = 0.1 for the adhesive. Since the chosen spacing of DRs generates retro-directive scattering of the HE11 mode close to 7.2 GHz in the corner configuration, this radiation superimposes the scattering from the PEC corner reflector. However, the phase centre of the DR array (centre of array) is distant from the phase centre of the PEC corner reflector (the apex), see insert in Figure 8(b). Due to the path length difference, a phase difference is generated between the specular reflections (of the PEC corner reflector and of the DR arrays) and the retro-directive scattering by the DR array GLs. Figure 8(b) shows that a shift of the array can lead to major variations of the spectral signature around the HE11 mode frequency from a filled notch to a deep notch and with some shifting of the notch bottom frequency: With the DR arrays offset from the centre of the plates by S = 7.5 mm, the retro-directive GLs fill the notch produced by the specular reflections from both DR arrays (analogous to Figure 4) and a rather flat RCS signature appears around 7–7.5 GHz. However, an offset of about 2.5 mm produces a deep notch which can be attributed to a destructive interference of the contributions from the specular lobes and the GLs. On the other hand, Table 2 shows that at 9.3 GHz, the DR array does not generate retro-directive scattering at 0° incidence. Here, we do not have a superposition of the scattering from the PEC corner reflector so that the deep notch is maintained over all offset cases. FIGURE 8Open in figure viewerPowerPoint Corner reflector design. Reflector plates 100 mm × 100 mm with three rows of linear arrays of three DRs at spacings d = 30 mm and with row spacing of 30 mm. Array centre offset S from −2.5 mm to +7.5 mm. (a) Simulation model of the corner reflector. (b) Frequency signature of the corner reflector RCS for incidence angle θc = 0°. DR, dielectric resonator; RCR, radar cross-section Choosing S = 0 mm for the array centre, a notch spectral signature around 7.2 and 9.3 GHz is maintained over all angle of incidence to the corner reflector, from 0° to 45°, see Figure 9. As expected from an electrically small metal corner reflector, the RCS slightly varies over frequency but shows a clear tendency to reduce with in