Corner reflector tag with RCS frequency coding by dielectric resonators

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 mm 2 plate size with two arrays of 3 � 3 DRs producing a


| 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, printedcircuit-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.
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 retrodirective 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 (a) (b) F I G U R E 1 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 ALHAJ ABBAS ET AL.
-561 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 dBm 2 . 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.

| 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.
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.
The first notch at around 7.2 GHz is connected to the excitation of a HE 11 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 TE 01 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 TE 01 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).
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 F I G U R E 2 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 F I G U R E 3 Wave scattering contributions from the linear array of DRs on a PEC plate. DR, dielectric resonator; PEC, perfect metallic conductor 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 F I G U R E 4 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 F I G U R E 5 HE 11 mode (left) and TE 01 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 TA B L E 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) -563 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 xz-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: 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. 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 TE 01 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 HE 11 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 TE 01 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 HE 11 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 HE 11 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 TE 01 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 HE 11 mode. Five other observations are worth reporting: a) The notch signature of the TE 01 mode is much narrower than the signature of the HE 11 mode which is due to the higher radiation Q-factor of the TE 01 mode. More narrow notch signatures, especially of the HE 11 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 HE 11 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 HE 11 mode and the TE 01 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 halfspherical 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 HE 11 mode frequency (e.g. to 7.4 GHz at film thickness F = 0.04 mm), and slightly reduces the TE 01 mode frequency (to 9.28 GHz in the example). d) The HE 11 mode can be excited by yand x-polarized incident waves under any angle of incidence. However, the TE 01 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.

| 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°o ff 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.
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°i n 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.
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 mm 2 spacing along the xand 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 F I G U R E 7 Geometry and indication of incident and reflected partial waves in a corner reflector TA B L E 2 Incident wave angle θ inc at the plates of a corner reflector which generates retro-directive scatter lobes due to the HE 11 mode at 7.2 GHz and TE 01 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) θ inc @7.2 GHz θ c @7.2 GHz θ inc @9. 31  -565 adhesive. Since the chosen spacing of DRs generates retrodirective scattering of the HE 11 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 retrodirective 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 HE 11 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  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. 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°t o 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 increasing angle of incidence. We also see some variation in the notch depth and a shift of the notch bottom frequency for the HE 11 mode with variation of the incidence angle. Much more than in the case of a single plate, notch depth and notch bottom frequency vary due to superposition effects of specular lobes and GLs plus side lobes and edge diffraction lobes: We find the notch variation of depth between 12 and 20 dB and variation of notch bottom frequency between 7.19 and 7.325 GHz. As can be expected due to a higher Q-factor, the TE 01 mode notch appears with less variation in frequency between 9.29 and 9.31 GHz, but notch depth varies between 5 and 25 dB up to θ c = 35°while the notch completely vanishes at an incident angle of 45°due to the mode rotational symmetry.

| EXPERIMENTAL VERIFICATION
The simulation example of Figure 9 with 3 � 3 DR arrays and element spacing of 30 mm was chosen as our demonstrator, Figure 10. The PEC corner reflector was manufactured from a 2-mm thick aluminium sheet of 200 � 100 mm 2 which was bent into a 90°angle; thus, due to a rounded corner from the sheet bending process, the total inner length of each plate was reduced by 2 mm. Dielectric resonators of 6.4 mm dia. and 3 mm height produced by T-Ceram, s.r.o., of Cech Republic were bonded to the plates using a polyvinylacetat-based synthetic resin adhesive (trademark 'UHU'). However, by dipping a DR into the adhesive and stamping it onto a plate with high pressure, the layer thickness could not be well controlled: We realized an average thickness of 0.02 mm with a random variation in thickness within about ±0.01 mm. Also, manual positioning of the DRs on the corner plates showed a random variation within ±2 mm in xand y-directions. A measurement of the dielectric permittivity of the adhesive was performed using a coaxial specimen holder [30] realized by a 2 mm long section of an open-circuited air-filled coaxial line which was filled with the fluid adhesive. After curing and solidification, we evaluated the reflection coefficient to represent a relative dielectric constant of about 2.5 with a high loss tangent between 0.1 and 0.05.
The measurement setup uses a broadband double ridge horn antenna (type HF906 from Rohde & Schwarz, Germany) which is encapsulated in an absorber box to suppress stray radiation. The antenna is connected to a vector network analyzer (VNA) (type Hewlett Packard HP8510, USA) to measure the reflection coefficient generated by the device under test (DUT). The DUT is placed on top of a Styrofoam block on the turn table at 1.5 m distance between the horn aperture and the apex of the corner reflector and is surrounded by pyramidal absorbers. With the VNA calibrated at the coaxial connector to the horn antenna, the reflection coefficient S11 of the horn antenna was measured. Since the antenna mismatch return is much larger than the returns from the target and the environment, the first measurement was without the DUT ('empty room') and afterwards with the DUT in place. By subtraction of the stored 'empty room' data from later measurement data for a corner reflector, the reflection coefficient of the corner reflector was gained. Under perfect far-field conditions, from [31], the relationship between this reflection coefficient and the sought for RCS of the DUT is explained by Equation (2): For an ideally matched antenna, the reflection coefficient square is proportional to σ, the RCS of the DUT as: where G is the antenna gain, λ is the wavelength and R is the distance between the antenna and the target. Using Equation (2), we calculated the RCS which resulted from an S11 level of −45 dB at 8 GHz as about + 3.5 dBm 2 . Since the DUT is not quite in far-field distance and the precise antenna gain is uncertain due to the loading by the absorber encapsulation, we made one additional measurement of a corner reflector of same size but without DRs. For this DUT, we calculated the theoretical RCS at normal incidence which, similar as in [32], was then used as a reference value for the translation of measured S11 into RCS magnitudes as: where the index CRDR stands for the corner reflector with DR arrays and the index CR for the reference corner reflector without DRs and the index Empty stands for the 'empty room' measurement. Using this normalization to the reference measurement, the S11 level of −45 dB at 8 GHz was found to represent about + 2.5 dBm 2 which is still close to the result from Equation (2). In the following, we use this transfer factor to rescale the plots of the measured reflection coefficient to represent the measured mono-static RCS magnitude.
In Figure 11(a) we show the measured RCS of the corner reflector at normal incidence (θ c = 0°) with and without DR array. We clearly see the notch of the HE 11 mode at around 7.3 GHz and of the TE 01 mode at about 9.3 GHz. Between the notches, the RCS magnitudes of both cases track very well, which shows that the DR array causes only little loss outside the resonance range. Close to 6.5 GHz and above 9 GHz, we notice that the measured RCS magnitude tends to decrease with increasing frequency which is due to the absorber loaded horn antenna transfer characteristic. The small ripples are due to a standing wave effect between the horn antenna and the corner reflector. Comparing the measured responses to the simulated responses, we recognize the antenna gain variation with frequency due to the absorber encapsulation. Apart from this, the simulated response from Figure 8 (array centre offset S = 0 mm) is found to predict a more narrow notch at 7.3 GHz compared to the measured notch. However, considering the above remarks, the overall agreement with the measured signature is satisfactory.
In Figure 11(b), we plot the measured reflection coefficient for incidence angles of 0°, 10°, 20°, 40°and 45°. We see a variation of the position of the HE 11 mode notch between 7.15 and 7.3 GHz and of the notch depth between 10 and 20 dB. On the other hand, the TE 01 mode notch shows little frequency variation but also considerable variation in depth. With a view to the non-ideal bonding of the DRs, agreement with simulations is satisfactory. The RCS magnitude between the two notches compares well, the notch depth variation of the HE 11 is found similar as in simulations, while the notch bottom frequency positions are found shifted by only about 0.05 GHz.

| DISCUSSION AND CONCLUSION
We have shown that a metal dihedral corner reflector can be modified by the addition of DR arrays on its surface to exhibit notches in its spectral signature of the RCS. These notches are characteristic over a wide-angle range of the incident wave while the high RCS outside the DR resonant regions is maintained. In our design, the notches were shown to be the result of increased scattering by the DRs due to resonance and the generation of GLs from the DR arrays. The two lowest frequency modes of cylindrical DRs have been identified as the HE 11 mode and the TE 01 mode, where the TE-mode couples less with the incident wave and shows smaller notch depth with more narrow width. For one example realization, GLs radiating into the direction of the incident wave at θ c = 0°have been shown to be able to fill the notch, but proper shift of the DR array relative to the corner reflector apex was demonstrated to avoid the problem. Corner reflectors with arrays of larger electrical spacings of DRs have also been simulated and experimentally checked. Here, retrodirective GLs appear at other directions of the incident wave (θ c ≠ 0°) but the unwanted filling of the resonant notch can be avoided equally by shifting the array centre suitably.
When we use the presented corner reflector tag design for the landmarks in the self-localization system of Figure 1(a), the read range can profit: Due to the mentioned limitations in achievable RCS, the tag designs proposed in [7] have been shown by simulation and in a system test bed [33] to seriously limit read range. This problem can be solved by the corner (a) (b) F I G U R E 1 1 Mono-static RCS signatures, (a) simulated and measured for corner reflector with and without DRs at zero incidence angle and (b) measured for corner reflector with DR arrays at various incidence angles. DR, dielectric resonator; RCR, radar cross-section reflector tag, since it can be scaled to realize any required RCS level without losing its characteristic spectral signature. On the other hand, the ranging accuracy will profit because the time domain impulse response of the reflector is dominated by the (potentially large) sweep bandwidth of the reader and not by the narrow resonant bandwidth of the DRs. As an illustration, in Figure 12, we show the pulse shape for both the corner reflector with DR arrays and the corner reflector without DRs; both are based on the measurement of the mono-static RCS shown in Figure 11(a). The −3 dB pulse width of the reflector without DRs is inversely proportional to the sweep bandwidth and is only slightly smaller than the pulse width for the reflector with DRs. Therefore, in a range processing based on the pulse peak position, nearly the same (high) accuracy can be expected. Note that the intended system application is at high mm-wave frequencies (e.g. W-band). This allows larger sweep bandwidth such that both pulse width and ringing time constant reduce by the frequency ratios. By this, interfering reflections are placed in time domain behind the corner reflection main pulse and ringing response, if the corner reflector is spaced at least a few centimetres in front of interfering objects, like flat walls and wall edges. On the other hand, the two reflectors can be discriminated by detecting either the notches in spectral domain (as in Figure 11) or detecting the ringing tail in time domain, as in Figure 12. In contrast, ranging of DR tags which exhibit a resonant peak (instead of a notch) in the RCS signature is based on a much wider time-domain pulse due to the narrow resonant bandwidth [7]. In our example, this gives about 10 times larger pulse width and thus lower range accuracy.
Corner reflectors with different size DRs can be accurately discriminated by their individual HE 11 mode notch frequency as long as the notch depth is at least 6-10 dB. Based on the notch width and notch bottom frequency variation found in our example design, resonant frequencies should be spaced by about 6% of the centre frequency. This allows about five different tag frequencies to be evaluated by the reader with 30% relative bandwidth. For example, the DR dimensions presented in Table 1 would fit for a frequency sweep range of 6.5-8.5 GHz. The TE 01 mode would allow much narrower spacing, however, its polarization sensitivity limits the usefulness of this mode.
We can also show the advantage of the corner reflector with DR arrays over the planar DR array and the single DR of Figure 1(b) by looking at the read range of our test setup: From the variation of the mono-static RCS magnitudes of the corner reflector with the incidence angle we can derive the variation of the read range with incidence angle by solving Equation (2) for the range R. Given the wavelength at the notch frequency and the antenna gain of our test setup, we set the reflection coefficient S11 to −80 dB as threshold for the reader (as seen in Figure 12, this leaves about 20 dB dynamic range). The read range based on this approach is compared in Figure 13 to that of the DR planar array and the single DR from Figure 1(b). The corner reflector exhibits a broad 'wideangle' behaviour with a minimum of around 35°and a second peak at 40-45°, which is quite typical for a dihedral corner reflector [17]. In contrast to this, the DR planar array exhibits a narrow main beam with a first sidelobe useful only up to about 17°off broadside from where on the resonance signature degenerates. For the single DR, we see a perfect omnidirectional retro-directive pattern, however, at much lower range due to the very low RCS magnitude of the single DR.
Instead of using the cylindrical DR design, spherical resonators have also been found useful as elements in the DR array: When the resonators are elevated from the PEC surface so that the HE 11 mode can freely align to the incident wave without mode splitting, we observe single-mode operation over a broader frequency range than that found for the cylindrical DR design investigated in this work.
Compared to the DR-based tags reported in [7,10,11], in principle, the corner reflector dimension can be increased without limit and thus may produce much higher RCS levels. Up to about 100 GHz, this was found practical by manual placement of many individual DRs of close to millimetre size on the metal plates of a large corner reflector. In experimental designs for 64-100 GHz notch frequency, we employed an intermediate foam layer between the PEC plate and the spherical DRs to fix and carry the resonators of 0.8-0.5 mm diameter [34]. However, with a view to a system realization at low THz frequencies [7], the manufacturing of plate-DR assemblies with DR dimensions on the order of 100 μm require new technologies which are just evolving. Here, the new F I G U R E 1 2 Measured reflection coefficient in time domain for corner reflector with and without DR at zero incidence angle over the band (6.5-9 GHz) which contains only the first resonance frequency of HE 11 mode. DR, dielectric resonator ceramic 3D additive manufacturing technology, for example, [35], can be a solution; in our cooperative research project, where we employ Lithography-based ceramic manufacturing technology of Lithoz GmbH, Viena, Austria.
The trihedral corner reflector can be looked at as an extension of the dihedral corner reflector with three mutually orthogonally placed metallic plates. However, the combination of three reflecting surfaces creates more angle and polarization dependencies which were found to be best solved by using spherical DRs, but this needs further investigations. In one other modification which has been experimentally proven, a single corner reflector may be equipped with arrays of DRs of different dimensions to produce tags with two notches offset by a frequency as 2-bit coding (dihedral corner reflector) [34] or with three notches as 3-bit coding (trihedral corner reflector).
Finally, the corner reflector with arrays of DRs on its metal surfaces has been presented as a tag solution for a self-localization system. This puts it into the class of chipless RFID tags. Its special RFID characteristics are a rel. low number of bits useful only in a broadband RF system but exhibiting high RCS for large range. Therefore, in particular, ultra-wide-band RFID applications may profit from extended range by the use of corner reflector tags. Apart from this, any Radar-based navigational or metrological application may profit from a simple coding capacity provided by the DRs fixed to metal surfaces.