Path Loss Modeling of RFID Backscatter Channels With Reconfigurable Intelligent Surface: Experimental Validation

In the realm of radio frequency identification (RFID) technology, the integration of reconfigurable intelligent surfaces (RISs) has opened up new possibilities for real-time remote data capturing and seamless connectivity. By manipulating the electromagnetic properties of the environment, RIS enables the control of electromagnetic wave propagation and allows for virtual line-of-sight (LOS) in cases where physical LOS is blocked. This has tremendous implications for the future of RFID applications, particularly with the emergence of chipless RFID technology. In this regard, this paper develops free-space path loss models for RIS-assisted RFID wireless communications. The proposed models in this study have taken into account several crucial physical factors, including tag radar cross-section (RCS), the physical properties of the RIS, and the radiative near-field/far-field effects of the RIS. To further validate the theoretical findings, we have conducted experimental measurements using a fabricated RIS. Numerical simulations were also utilized to validate the models and verify our findings. The channel measurements have demonstrated good agreement with the proposed path loss models, further bolstering the potential of RIS-assisted RFID wireless communications.


I. INTRODUCTION
The increasing demand for wireless connectivity in emerging systems such as industrial equipment, cars, and healthcare applications has resulted in the rapid development of wireless systems.This demand for real-time wireless connections requires simple and low-cost solutions to be available anywhere and anytime [1].However, emerging wireless The associate editor coordinating the review of this manuscript and approving it for publication was Olutayo O. Oyerinde .systems require higher performance metrics, including datademanding, delay-sensitive, and millimeter-precision sensing and localization [2].To meet these demands, the research community has turned to millimeter-wave (mmWave) and terahertz (THz) frequency bands for the next-generation wireless systems, which offer ultra-broad bandwidth and submillimeter wavelength [3].
Chipless radio frequency identification (RFID) has emerged as a promising enabling technology for keepconnected and real-time remote data capturing utilized in various emerging applications such as indoor localization and automated identification [4], [5].With their extreme reduction of costs and complexity, chipless RFID infrastructures have the potential to act as indoor infrastructure [6], [7], [8], [9], [10], [11], [12], [13].Unlike network infrastructures such as Wi-Fi, chipless RFID infrastructure does not require time and data synchronizations.The main concept of chipless RFID technology is that the reader communicates with tags through backscattered signals, where the reader interrogates the tags in the forward link, and the backscattered signal from the tag conveys the information from the tag to the reader in the backward link [6].
Real-time data capturing at any time and location requires continuous connectivity between the smart object and the chipless RFID infrastructure [14].However, the increased operating frequency required for such real-time data capturing comes at a price of severe path loss, sensitivity to blockages, and limited coverage [15], [16].These limitations are more severe in RFID systems than in conventional communication systems due to the presence of two distinct links: the forward link and backscatter link [9], [14].
Recently, reconfigurable intelligent surfaces (RISs) have emerged as a promising technology to circumvent propagation issues in wireless systems.RISs can assist wireless systems by intelligently controlling impinging signals to focus, steer, and enhance signal power in the desired direction [17], [18], [19].RISs are planar structures consisting of a large number of passive and low-cost reflecting elements that can be installed on large flat surfaces such as walls or ceilings of indoor environments.RISs provide a potential solution for the critical coverage challenge by offering an alternative virtual line-of-sight (LoS) radio path when the direct link to reference tags is blocked.Moreover, RISs can play a vital role in several applications such as sensing and positioning [20].
Developing RIS-assisted path loss models is essential for optimizing the configuration and deployment of RISs and conducting link budget analysis.Several theoretical and experimental studies have been conducted to derive path loss models for RIS-assisted communications as in [21], [22], and [23] and the references therein.RIS Path loss models have been derived in [21] and then refined in [22] for different application scenarios with the aid of channel measurements.Both models consider the radiation patterns of the transmit antenna, receive antenna, and the unit-cells of the RIS, where the path loss models have been validated experimentally.In [23], a physical model for the path loss of an RIS-assisted link is proposed by using antenna theory, which confirms the main findings in [21].
To the best of our knowledge, there exists no established path loss model for RIS-assisted RFID systems, even in the simplistic free-space propagation environment.Therefore, we present in this work a novel contribution to the field of RFID technology by proposing free-space path loss models for RIS-assisted RFID wireless backscattering communica-tions.The proposed models incorporate the physical and electromagnetic properties of RISs, including tag radar crosssection (RCS), RIS size, and the radiative near-field/farfield effects of the RISs.To validate the models, we have utilized numerical simulations.Furthermore, experimental measurements have been conducted using a fabricated RIS to confirm the theoretical findings.Specifically, our contributions can be summarized as follows: 1) We present a system model and general free-space path loss model for RIS-assisted RFID backscattering link, grounded on electromagnetic theory and considering important physical factors such as tag properties and the physical dimension and properties of the RISs.2) Radiative near-field and far-field free-space path loss approximations are introduced based on the derived general formula.3) We provide the first experimental results for RIS-assisted RFID backscattering link that validate the proposed path loss models.
This paper is organized as follows: The path loss of RIS-assisted RFID link is modeled in Section II.Numerical simulations are used to validate the models in Section III.Section IV shows the experimental validation for the proposed models.We conclude our work in Section V.

II. PATH LOSS MODELLING OF RIS-ASSISTED RFID CHANNEL A. SYSTEM DESCRIPTION
We consider an RIS-assisted single-input single-output (SISO) mono-static RFID backscatter channel as shown in Fig. 1, where the direct link between the RFID reader and the RFID tag is blocked.In the forward channel, the transmission is carried out from the reader to the tag via an RIS, while the transmission is carried out from the tag to the reader via an RIS in the backward channel.It is assumed that the reader is placed in [x r , y r , z r ], while the tag is placed in [x t , y t , z t ].An RIS is assumed to be placed in the x − y plane of a Cartesian coordinate system, where the center of the RIS is exactly the origin of the coordinate system, as shown in Fig. 2. The distances from the reader and the tag to the center of the RIS are d r and d t , respectively.θ r and φ r denote respectively the elevation and azimuth angles of arrival of the waves traveling from the reader to the center of RIS.θ t and φ t denote the elevation and azimuth angles of departure of the waves traveling from the center of RIS to the tag, respectively.
We assume that the real-time controlled RIS is equipped with N ×M unit-cells reconfigurable reflect elements that can be adjusted according to channel phases.These unit-cells are identical and have d x and d y dimensions, which are usually of sub-wavelength scale within the range of λ 10 and λ 2 .U n,m identifies a particular unit-cell in the n th row and the m th column of a planar array, where n ∈ [1, N ] and m ∈ [1, M ].According to [22], the maximum gain of the unit-cell is

B. PATH LOSS OF RIS-ASSISTED RFID CHANNEL
The reader directs its signals the RIS, which reflects the incoming signal to the tag direction by introducing appropriate phase shifts at the unit-cell level.The reader's antenna is assumed to have maximum gain G r and normalized power field pattern F r (θ, φ) as a function of the azimuth and elevation angles θ and φ from the antenna to a certain point direction, respectively.
Accordingly, the power incident on U n,m at the forward channel is expressed as where P x is the transmitted power from the reader, and d r n,m is the distance between the reader and U n,m unit-cell.θ r n,m and φ r n,m denote respectively the elevation and azimuth angles of departure of the waves traveling from the reader to U n,m .F u (θ u r n,m , φ u r n,m ) is the normalized power field pattern of U n,m unit-cell, where θ u r n,m and φ u r n,m denote respectively the elevation and azimuth angles of arrival of the waves traveling from the reader to U n,m .
Since U n,m reflects the incident signal from the reader towards the tag, the reflected power is given by F n,m is the reflection coefficient of the U n,m unit-cell at the forward channel and given by where A F n,m and ψ F n,m are the controllable amplitude and phase shift of U n,m , respectively, that are optimized to direct the reader signal towards the tag via U n,m .
As the considered chipless tag can be modeled as an antenna with a short circuit termination, the tag has maximum gain G t and normalized power field pattern expressed as [9] Tag gain in ( 4) is a function of the tag RCS σ t (θ t n,m , φ t n,m ) and the wavelength of the carrier frequency λ o , where θ t n,m and φ t n,m denote the elevation and azimuth angles of arrival of the waves traveling from the U n,m to the tag, respectively.Consequentially, the power impinging on the tag from U n,m at the forward link is [9] where F n,m is the overall normalized pattern related to U n,m and given by d t n,m is the distance between the tag and U n,m , and θ u t n,m and φ u t n,m denote respectively the elevation and azimuth angles of departure of the waves traveling from the U n,m unit-cell to the tag.Consequently, the electric field of the received signal received by the tag from the reader via U n,m can be presented as [24] Ēn,m = where is the effective aperture of the tag, and η expresses the characteristic impedance of the air.The term n,m represents the phase shift introduced by the signal propagation at the forward channel, the forward reflection coefficients of U n,m , and the delay caused by the tag response, i.e. δ t [9].
The total electric field resulting from the signals received from all the unit-cells at the tag is the superposition of the individual electric fields from each unit-cell.This can be formulated as Accordingly, the total received power at the tag from the reader through RIS at the forward channel is given by where Accordingly, the backscattered power from the tag to U n,m at the backward channel is given by Similar to (1), the incident backscattered power from the tag on the U n,m unit-cell at the backward channel is It can be concluded that the received power at the reader from the tag via U n,m is n,m and ψ B n,m are respectively the controllable amplitude and phase shift, to direct the backscattered signal from the tag towards the reader at the backward channel.
Similar to (7) and ( 8), the total electric field resulting from the backscattered signals from all the unit-cells at the reader is the superposition of the individual electric fields from each unit-cell.This can be formulated as Accordingly, the total received backscattered power at the reader from the tag through RIS is given by where As ( 15) is in the form of the Friis transmission equation, the path loss is given by The model in ( 17) is a general free-space path loss model for RIS-assisted RFID link, which can be applied in the radiative near-and far-field regions.This model is proportional to the eighth power of the operating frequency, since d x d y is inversely proportional to the square of the operating frequency.Moreover, this model shows the parameters that affect the path loss model such as: the distance between the reader/tag and the RIS unit-cells, the gain of the reader antennas, the RCS of the tag, the gain and size of RIS unitcells, the angles of arrival and departures from the reader/tag and RIS unit-cells, and the reflection coefficients of the RIS unit-cells.
The RIS-assisted chipless RFID link is considered in order to provide an alternative virtual LoS path in the case of LoS blockage between the reader and the tag.Therefore, the received backscattered power at the reader through RIS should be maximized depending on the design of the reflection coefficients of the unit-cells, i.e.Next, the model in (17) will be further discussed for the radiative near-field and far-field cases.

C. RADIATIVE NEAR-FIELD RIS-ASSISTED CHIPLESS RFID LINK
When the reader and/or the tag are in the radiative near-field of the RIS, the reflected signal can be focused towards the tag in the forward channel and towards the reader in the backward channel by properly designing F n,m and B n,m , respectively.Assuming the amplitudes of the reflection coefficients of the unit-cells are identical, and by setting , the received power at the reader at any desired location in the radiative near-field is maximized.At this case, the path loss of RIS-assisted RFID link can be formulated as Given that ψ F n,m = ψ B n,m , the system is reciprocal.Thus, the design of the unit cells for the forward link is also valid for the backward link.

D. FAR-FIELD RIS-ASSISTED CHIPLESS RFID LINK
Transmission between the reader/tag and the RIS is considered to occur in the far-field when the distance between the reader/tag and the RIS exceeds the Fraunhofer array distance [25].In the far-field region, the signal wavefront can be reliably approximated as planar.Consequently, the direction from all RIS unit-cells to the reader/tag antennas is approximately the same.
Accordingly, when the reader and tag are in the farfield region, the traveling/incident wave angles can be approximated to have the same angular directions to different unit-cells, i.e. θ r n,m = θ r , φ r n,m = φ r , θ t n,m = θ t and φ t n,m = φ t ∀n, m.Similarly, the traveling/incident wave angles from the RIS unit-cells can be approximated to have the same angular directions to the reader/tag, i.e. θ u r n,m = θ u r , φ u r n,m = φ u r , θ u r n,m = θ u r and φ u r n,m = φ u r ∀n, m.Assuming the peak radiation of the reader directs towards the center of the RIS, F r (θ r n,m , φ r n,m ) can be approximated to one in the farfield.Hence, the overall normalized pattern in (6) becomes Accordingly, the path loss of RIS-assisted RFID link can be formulated in the far-field as where d r n,m and d t n,m can be approximated as expressed in [21] as follow Assuming the amplitudes of the reflection coefficients of the unit-cells are identical, the phases of RIS can be tuned, i.e. ψ F n,m and ψ B n,m , to beamform the incident signals towards the tag in the forward channel and towards the reader in the backward channel aiming at achieving the maximum received power at the reader [21].In a special case, when the reflection coefficients of all the unit-cell s are identical, i.e.F n,m = B n,m = A exp(jψ) ∀n, m, the RIS performs specular reflection in the forward and the backward channels.Accordingly, when the received power at the reader is maximized using ψ F n,m and ψ B n,m , the path loss of RIS-assisted RFID link can be formulated in the far-field as The model in (21) shows that path loss in the far-field scenario can be reduced by increasing the geometric area of the RIS, i.e.MNd x d y .

III. VALIDATION OF THE PATH LOSS MODELS VIA NUMERICAL SIMULATIONS
Simulations are performed using the general formula in (17) to validate both the far-field formula in (21) and the near-field formula in (18) at frequency 4 GHz.The simulations are carried out using two different RISs, one with 64 unit-cells (8 × 8) referred to as the small RIS, and the other with 256 unit-cells (16 × 16) referred to as the large RIS.The unit-cell spacing of d x = 25 mm and d y = 20 mm is assumed with The Fraunhofer boundary of the far field and the near field of the RIS is defined as [21] and [24] where D is the largest dimension of the antenna array distances.As a result, the Fraunhofer boundaries for the small and large RISs are calculated to be 0.85 m and 3.4 m, respectively.A scenario is classified as far-field when both d r and d t are larger than the Fraunhofer boundary.Otherwise, it is classified as a near-field scenario.The transmit power of the reader is assumed to be P x = 0 dBm.Moreover, the gain of the reader's antenna is assumed to be G r = 15 dBi, with F r (θ, φ) = cos 15 (θ) when θ ∈ [0, π 2 ] and F r (θ, φ) = 0 when θ ∈ ( π 2 , π].Considering a planar array tag that is discussed in [26], we assume the maximum tag RCS σ t (θ, φ) = 0 dBm 2 , with F t (θ, φ) = cos 23 (θ ) when θ ∈ [0, π 2 ] and F t (θ, φ) = 0 when θ ∈ ( π 2 , π].Fig. 3 and Fig. 4 illustrate the simulated path loss for the small and large RISs, respectively, for various distances and directions.Fig. 3a, Fig. 3b, Fig. 4a, and Fig. 4b present the path loss of the near-field case for different d t values, with d r = 0.5 m, φ r = 0, and φ t = π.The directions in Fig. 3a and Fig. 4a are θ r = π 4 and θ t = π 4 , while those in Fig. 3b and Fig. 4b are θ r = π 3 and θ t = 7π 4 .Fig. 3c and Fig. 4c show the results for different d t values when d r = 4 m and d r = 1 m, respectively, with φ r = 0 and φ t = π, where θ r = θ t = π 4 .The results presented in Fig. 3 and Fig. 4 demonstrate that the far-field formula given in ( 21) is consistent with the general formula in (17) for both the specular and intelligent reflection cases, particularly for the far-field scenarios shown in Figs.3c and 4c, where the distances d r and d t are both greater than 3.4 m and 0.85 m, respectively.It is also observed that the near-field formula in ( 18) is identical to the general formula in (17).
A comparison of Fig. 3 and Fig. 4 reveals that the power of the reflected signal in the backscattered channel is more concentrated for larger electrical sizes of the RIS.

IV. EXPERIMENTAL VALIDATION OF THE PATH LOSS MODELS
In order to experimentally validate our proposed path loss model, we designed a measurement setup as illustrated in Fig. 5.The Vector Network Analyzer (VNA) was utilized as the RFID reader, which was connected to a horn antenna with a gain of 15 dB and an operational bandwidth within the range of 3.98 GHz to 5.85 GHz.During the measurements, the RIS was placed on a Styrofoam column, which was positioned on a height-adjustable platform to control the height of the RIS.The platform was placed on a turntable to ensure that the center of the RIS was aligned with the center of the turntable.The RIS was then placed at a distance of d r from the horn antenna maintaining the maximum signal strength by adjusting the height of the RIS.In addition, a floor-line laser (Huepar S04CG) with vertical and horizontal lines was used to improve the alignment accuracy, and the maximum reflection from the RIS was measured.A movable stand equipped with absorbers was used to block the channel between the antenna and the tag, as shown in Fig. 5.The tag was placed at a distance of d t from the RIS and was maintained at the same height as the RIS and the reader antenna.

A. RIS CONFIGURATION
In this study, we employed two array RISs.The 8 × 8 array RIS is shown in Fig. 5a, and the 16 × 16 array RIS is shown in Fig. 5b.Each element has dimensions of 25 mm × 20 mm and is designed to operate in the 5 GHz band, based on the concept proposed in [27].Each RIS is phase-programmable with 1-bit coding, where coding 0 is applied to U n,m when A n,m = 0.9 and ψ n,m = 0 • , while coding 1 is applied to U n,m when A n,m = 0.9 and ψ n,m = 150 • .More comprehensive information about the RIS's fabrication, simulation, and characterization can be found in [28] and [29].Each RIS is composed of a rectangular patch that is connected via a  via to a ground plane, as illustrated in Fig. 6.The RIS's reconfigurable phase is achieved using a PIN When the patch is in the OFF state, it resonates at a frequency of f 0 .In contrast, the electrical length of the patch is modified in the ON state, resulting in a higher resonance frequency at f 1 .At f 1 , a phase difference of 150 • between the ON and OFF states enables one quantized bit with two combinations for each element.
In Fig. 7, we present the measured mono-static scattering coefficient (S11) of the small RIS (8 × 8) at a distance of 0.5 m as depicted in the figure.Two cases were considered: all elements ON and all elements OFF.When all elements were OFF, the RIS resonated at f 0 = 4.8 GHz, while in the all-ON case, the RIS resonated at f 1 = 5.35 GHz.In both cases, the RIS scattered high power outside the resonance frequency, which is similar to the scattering from a metal plate of the same size.However, the RIS contains resonance elements, i.e., patches in our case, that allow for configurable beam steering based on providing a specific phase pattern for the  elements.As a result, the mono-static spectrum of the RIS is not flat, causing a frequency-selective channel.In reflection mode, the RIS acts as a bandstop filter, exhibiting very low scattering levels at the resonance frequency.

B. TAG CONFIGURATION
Our chipless tag principle is based on encoding bits in the frequency domain by introducing a peak or a notch in the spectrum using resonance elements.The tag ID is defined by unique resonance frequencies in the spectrum that result from changing the dimensions of the resonance element.Therefore, a non-selective channel is preferred in our application to utilize the entire bandwidth for tag IDs.Although frequency selectivity in the RIS channel cannot be avoided, it is deterministic.Each phase pattern of the RIS provides a specific frequency spectrum that can be measured and calibrated.
In our investigation, we utilized a chipless tag with a notched spectral signature, as illustrated in Fig. 8.The tag consists of a planar array of 9 dielectric resonators (DRs)  with a vertical and horizontal element separation of S 1 and S 2 , respectively.The DR array is situated at a distance T from a metal plate of size (L × W ).
Fig. 9 shows a comparison of the simulated mono-static RCS of the DR array with and without metal backing.A resonance peak at 5.23 GHz belonging to the hybrid mode HE 11 [30], [31] is observed with only the DR array.The RCS decreases as we move away from the resonance frequency.When a metal backing is added, destructive interference occurs at the resonance frequency producing a notch.The distance T affects the interaction between the scattering from the metal and the DR array scattering, causing a variation in the notch depth.A notch depth of approximately 17 dB is obtained for a distance of 2 cm.At frequencies far from the notch, a high scattering magnitude is observed which is determined by the metal plate size.The scattering level outside the notch preferably increases as the metal plate dimensions increase.However, beyond a certain size, the scattering from the metal dominates and the notch disappears.We used a metal plate of size 19.5 × 9 cm 2 , which strikes a balance between the scattering level and the notch depth.
Besides the advantage of using a metal plate to produce the notch instead of a peak, the RCS of the tag outside the notch is flattened and boosted by the metal plate by approximately 8 dB, as seen in Fig. 9.To implement this tag configuration, we used a low permittivity Styrofoam as a support structure.Cylindrical DRs were inserted into small cylindrical holes etched in the Styrofoam, and the metal plate was then taped to the bottom of the Styrofoam, as shown in Fig. 10.

C. PATH LOSS MEASUREMENTS
The measurement setup shown in Fig. 5 was used to experimentally validate the developed path loss models of RIS-assisted RFID channel.To cancel the effect of the cables, a full TOSM (Through -Open -Short -Match) calibration is performed beforehand.To reduce the effect of reflections from the environments and the self-interference caused by the antenna mismatch, an empty room calibration was performed for each measurement.

1) SPECULAR REFLECTION VIA THE SMALL RIS
In this measurement, the tag was positioned at an angle of 90 • with respect to the reader antenna as shown in Fig. 5a, that is (θ t = θ r = 45 • ).All the unit cells of the small RIS are configured in coding state 0. Fig. 11 displays the tag ID through the small RIS when d t = 0.5 m and d r = 1 m, in which it is revealed that the tag ID can be detected through the RIS, as evident from the notch at the tag resonance frequency in the spectrum.A split in the resonance area is observed, where one resonance corresponds to the tag at around 5.28 GHz, and the other relates to the resonance frequency of the RIS when all elements are ON, at about 5.37 GHz.
Fig. 12 displays the measured path loss compared to the developed path loss formulas for two different specular reflection scenarios.In the first scenario, the near-field case is examined with d r = 0.5 m, and d t varied from 0.75 m to 3 m in steps of 0.25 m.In the second scenario, the far-field is examined with d r fixed at 1.3 m, and d t varied from 0.75 m to 3 m in steps of 0.25 m.
As seen in Fig. 12a, the measured path loss matches the proposed general path loss model given in Equation ( 17), as well as the near-field formula in Equation (18).Since this figure illustrates a near-field case, the far-field theoretical path loss approximation in ( 21) is close to the general and near-field formulas, but not identical to them, as expected.
Fig. 12b explores the far-field scenario, where the far-field theoretical path loss approximation in (21) matches the general and near-field formulas in (17) and (18), respectively, for d t values greater than 0.85 m.The measured path loss demonstrates good agreement with the theoretical formulas, with an absolute error difference of approximately 2 dB.However, it should be noted that slight deviations in the positions of the RIS, reader antenna, and tag can result in measurement discrepancies that are difficult to avoid in practical situations.Even a few degrees of RIS azimuth deviation can lead to a 2-3 dB loss in the measured path loss.

2) NON-SPECULAR REFLECTION VIA THE LARGE RIS
In this measurement, the reader position is perpendicular to the large RIS, while the tag is located at an angle of 45 • as shown in Fig. 5b, that is (θ r = 0 • and θ t = 45 • ).All unit cells of the large RIS are configured to direct the reader signal towards the tag, as discussed in [29].Literature indicates that the reflected wave divides equally between two paths 108540 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.(θ t = 45 • and θ t = −45 • ); see [21], [22], and [29] for more details.In Fig. 13, the measured path loss is compared with the developed path loss formulas for the non-specular reflection scenario.In this context, d r = 2 m, while d t varies from 1 m to 4 m in increments of 0.5 m.As anticipated, the measured path loss is greater by approximately 3 dB compared to the numerical curves.This increase in loss is expected, given that the reflected path splits evenly between the two aforementioned paths.
Based on the results reported in this section, we conclude that the measurements are in good agreement with the proposed path loss models.

V. CONCLUSION
This paper presents the development of a general free-space path loss model for RIS-assisted RFID wireless communications, considering important physical factors such as tag properties, RIS size, and near-field/far-field effects.Radiative Near-field and far-field free-space path loss approximations are derived based on the general formula.This work presents also an experimental validation of the proposed free-space path loss models for RIS-assisted wireless communications for various scenarios.The obtained results demonstrate good agreement with the proposed models, affirming their effectiveness in characterizing large-scale fading in such systems.The validated models can aid in the design and optimization of RIS-assisted RFID wireless communication systems for various applications, including IoT, smart homes, and industrial automation.

FIGURE 1 .
FIGURE 1. System description of RIS assisted RFID backscattering link.
F n,m and B n,m ∀n, m.

FIGURE 5 .
FIGURE 5. Measurements setup showing two RISs placed d r from the Tx/Rx antenna and d t from the DR tag.The path between the reader and the tag is blocked by an absorber stand.(a) Small RIS (8 × 8).(b) Large RIS (16 × 16).

FIGURE 7 .
FIGURE 7. Measured mono-static scattering coefficient of the small RIS (8 × 8) at 0.5 m distance for two cases when all elements are OFF and ON, respectively.

FIGURE 8 .
FIGURE 8. Schematic of the chipless tag used in our investigation excited by xpolarized plane wave.S 1 = 3 cm, S 2 = 2.5 cm, T = 2.0 cm, L = 19.5 cm, and W = 9.0 cm.The radius and the height of the cylindrical DR are 6.14 mm and 5.76 mm respectively.

FIGURE 9 .
FIGURE 9. Simulated mono-static of DR array with and without metal backings.

FIGURE 10 .
FIGURE 10.Three views of our chipless tag showing a DR array of 3 × 3 configuration placed on the top of a rectangular metal plate of 19.5 × 9 cm 2 size holded togheter by a rectangular styrofoam piece (ϵ r ≈ 1) of 2 cm thickness.

FIGURE 11 .
FIGURE 11.Scattering magnitude of the DR tag measured at the reader side when communicating through the small RIS (8 × 8) with a blockage of the LOS between the tag and the reader as shown in Fig.5.