A Review of Chipless RFID Measurement Methods, Response Detection Approaches, and Decoding Techniques

Chipless RFID systems can be considered as a special case of passive RFID systems, where the tag contains no power source and no electronics. Instead, the tag’s information is stored in its structure and accessed through its electromagnetic (EM) scattering response. However, robust response detection, which is primarily a function of the measurement method, measurement equipment, and processing method used, is still a major challenge in the chipless RFID field. The consequences of not properly capturing a tag response include, incorrectly assigning an ID or incorrectly reporting a sensing parameter. Due to the criticality of these challenges, this review seeks to provide an overview of the current measurement methods, equipment architectures, and processing methods as they relate to chipless RFID tag response detection and decoding. Since chipless RFID started gaining popularity around 2005, the developments in this area have been focused on three major categories: time-domain, frequency-domain, and spatial-domain systems. Frequency-domain systems have emerged as the most popular among these three categories, and thus, this review focuses on techniques used for these systems.


I. INTRODUCTION
R ADIO frequency identification (RFID) systems consist primarily of a reader with at least one reader antenna and a tag. Depending on how the tag operates, the systems can be primarily classified as either active or passive. Tags in active RFID systems have their own power source (e.g., a battery) that helps them broadcast their information back to the reader, while tags in passive RFID systems are powered by the electromagnetic wave that interrogates them. Both types of tags contain electronics, including ICs, that allow them to interpret reader requests and send back information, such as their ID or connected sensor data [1], [2], [3].
Chipless RFID tags hold their information in their structure (e.g., the resonators, antennas, microstrip lines, etc. that make up the tag) and scatter this information to the reader when they are interrogated with an electromagnetic (EM) wave. Chipless RFID can be considered as either a subset of passive RFID or as its own category.
Chipless RFID systems can be classified based on how the tag's response is viewed as time-domain, frequency-domain, or spatial-domain [4], [5], [6], [7], [8]. Frequency-domain based systems are the most common since they tend to provide for the highest coding capacity, and therefore they are the focus of this review [4], [9], [10], [11].
In comparing and contrasting the different types of RFID systems, the absence of electronics and a power source distinguishes chipless RFID tags from active and passive tags. Another difference between active and passive tags and chipless tags, is that active and passive tags use their ICs to modulate their response to the reader (i.e., transfer stored information). This provides natural isolation of the tag response from its background environment [1]. However, chipless tags do not have this capability, which leads to various measurement challenges, such as limited read range and interference from reflections due to the background environment [1], [12], [13]. These challenges are further exacerbated by the regulatory limits on the allowed transmit power for ultrawideband (UWB) interrogation of chipless tags and the relatively small size of tags at microwave frequencies, both of which limit the scattered power detected by the reader [14], [15]. All of these measurement challenges can result in not properly capturing a tag's response, which can then lead to incorrectly assigning an ID or incorrectly reporting a sensing parameter [16], [17], [18], [19].
Attempts to address these chipless RFID measurement and response detection challenges have been made both on the tag side and the reader side. However, robust response detection, which is primarily a function of the measurement method, measurement equipment, tag, environment in which the tag is, and processing method used, is still a major challenge in the chipless RFID field. Tag/reader misalignment can additionally intensify these issues and cause further challenges [19], [20], [21], [22], [23], [24], [25], [26], [27]. Due to the criticality of these challenges, this review seeks to provide an overview of the current measurement methods, equipment architectures, and processing methods as they relate to chipless RFID tag response detection and decoding for frequency-domain tags. This is done in one place and in a comprehensive manner so that interested readers can be fully informed of these issues and challenges, as well as of the variety of proposed solutions at their disposal. To this end, Section II discusses the quantities, namely radar cross-section (RCS) and S-parameters, that are commonly measured and considered as the chipless RFID tag response, while Section III discusses the roles polarization, desired reading distance, monostatic vs bistatic setups, and calibration techniques play in how the tag response is measured. Section IV provides an overview of the hardware, both off-the-shelf and custom, that has been used to measure and, in some cases, decode the tag response. Section V examines the techniques used to pre-process, detect response features of interest, analyze, and decode the tag response. Lastly, Section VI provides a comparison of some measurements that have been reported in the literature and showcases the diversity of chipless RFID measurement methods and response detection/decoding approaches.

II. MEASUREMENT QUANTITY SELECTION
When it comes to measuring a frequency-domain chipless RFID tag, there is a choice to be made primarily between measuring the S-parameter(s) (e.g., the complex reflection coefficient, S 11 , or the complex transmission coefficient, S 21 ) of the tag or its radar cross-section (RCS) and whether to measure them in a monostatic or a bistatic configuration. RCS can be thought of as a target's equivalent area that would be seen by a radar, and it is proportional to the ratio of the power scattered by the target to the power that was incident on the target. As such, RCS is a scalar quantity (i.e., it does not contain phase information) and the units of RCS are m 2 or dB square meter (dBsm) [28], [29]. S-parameters are ratios of reflected and received waves to the transmitted wave. S-parameters are complex (i.e., have a real and imaginary component) and are unitless. Both the RCS and S-parameters are functions of the polarization, frequency, and incidence angle of the interrogating wave [28], [29], [30].
While there are similarities between RCS and S-parameter, there are also differences. The former is a far-field distance independent quantity while the latter is distance dependent. Another difference between RCS and S-parameters is that while S-parameters can be directly measured by a vector network analyzer (VNA), the RCS cannot. Instead, the RCS is calculated from measured quantities like received power or S-parameters in conjunction with some type of a calibration procedure [4], [29], [31]. Thus, determining RCS through measurement can be performed in several different ways [4]. Fig. 1 is provided to illustrate the relationship between RCS and S-parameters. Fig. 1 shows simulated S 11 and RCS responses of a tag with eight circular slot resonators, which was presented in more detail in [32], [33]. The responses were simulated using CST Studio Suite R in a couple of different ways. The first response was simulated using a waveguide port and by setting the boundary conditions such that plane-wave interrogation was performed and the complex reflection coefficient, S 11 , response was generated. Next, a waveguide with an engineered flange was used to interrogate the tag at three different reading distances, namely: 0 mm, 10 mm, and 20 mm [34]. The setup for this simulation case is shown in Fig. 1b. Lastly, plane-wave interrogation was used with a RCS probe placed at a distance of 100 mm to extract the RCS vs. frequency response of the tag. In comparing the responses in Fig. 1c, the distance dependence of the S 11 responses and the similarities in terms of number of notches between the S 11 and RCS responses can be seen. These notches, as well as other response features, could be used to assign a binary code or determine a sensing parameter (i.e., decode the response) depending on the application. The response feature detection and decoding mechanisms used in the chipless RFID field are discussed in more depth in Section V. It should also be noted that the difference in magnitude between the S 11 and RCS responses is due to a difference in quantity definitions (voltage vs. power) and units (dB vs dBsm), rather than reading distance.
One approach to determining the RCS is to measure the received power (P r ) and use the radar range equation to solve for the RCS (σ ) of a tag as [14], [31], [35]: In this equation P r and P t represent the received and transmitted powers, respectively, while R represents the distance to the target (i.e., tag), λ represents the operating wavelength, and G r and G r represent the gain of the transmit and receive antennas (i.e., reader antenna) that are used to interrogate the target. This approach requires the careful measurement of power, gain, and distance in order to accurately determine the RCS [14], [31], [35]. It should also be noted that this is a simplified version of the radar range equation that does not take into account parameters like receiver noise, polarization losses, and required SNR for detection [15], [36].
A second method relies on the relationship between S-parameters and RCS and again employs the radar range equation. Assuming that the gain of the transmit and receive antennas are equal (G), this relationship can be expressed for S 21 (the complex transmission coefficient/the S-parameter measured at port 2 when a signal is transmitted from port 1) as follows [29], [37], [38], [39], [40], [41]: This approach can also be done with a S 11 (the complex reflection coefficient/the S-parameter measured at port 1 when a signal is transmitted from port 1) measurement using the following equation: Equations (3) and (4) reveal that while it is possible to determine RCS from a complex S 21 or S 11 measurement, it is not possible to determine the complex S 21 or S 11 from RCS (i.e., only the magnitude of S 21 or S 11 can be determined) [29], [37], [38], [39], [40], [41]. Similar to the previous method, this approach is contingent upon the accurate knowledge of antenna gain and target distance and also relies on accurate measurement of the target's S 21 or S 11 response [29], [31], [37], [42]. Another method combines S 21 measurements of a target and a calibration standard with the radar range equation. In this approach, the calibration standard, such as a metal plate or sphere, is used to help achieve more accurate RCS measurement results [35]. The S 21 response of a target can be related to the power as follows: In equation (5), P target is the power received from the target and S 21 is measured in dB. By combining equations (5) and (1) and using the following relationship, the RCS of the target can be expressed in terms of the RCS of the calibration standard and the S 21 measurements of the target and the calibration standard: In equation (7), both S 21 measurements are in units of dB [35]. The RCS of the selected calibration standard (σ std ) should be well-defined analytically so that it can be used in equation (7) [35], [36], [43]. One challenge of this approach is ensuring that the target and calibration standard are measured at the exact same location so that when their S 21 responses are subtracted coherently there is no unwanted constructive or destructive interference.
A fourth method that was derived in [44] and discussed in [45] utilizes S 21 measurements of a reference target and of its background environment in conjunction with an S 21 measurement of the tag to determine its RCS. This method can be expressed analytically as: In equation (8), S support 21 refers to the S 21 response of the background/tag measurement setup (e.g., the anechoic chamber with a stand to hold the tag during measurements) without the tag. The assumption is that the reference standard is measured with the same setup as the tag [44], [45]. It should be noted that in both the numerator and denominator of equation (8), coherent subtraction is performed with the linear form of the S-parameters (not dB). Implementing this method results in a complex RCS, which differentiates this method from the others. This approach has gained popularity in the chipless RFID field and has also been modified for monostatic rather than bistatic measurement setups [4], [9], [46], [47], [48], [49], [50], [51].
A fifth method was designed specifically for monostatic setups and again combines S-parameter measurements to obtain the RCS, as [50]: In equation (9), S 11 Tx/Rx is the S 11 of the reader antenna in free-space. Just as in the previous approach, this approach also requires that coherent subtraction be performed with the S-parameters in linear form [50].
A sixth method was proposed for cross-polar tags (i.e., tags that produce a response with polarization that is orthogonal to that of the interrogating wave). This method, which is very similar to the previous one, uses a background reference measurement to subtract out the effects of the background environment, but does not account for the antenna effects (e.g., coupling and aperture reflections) like the previous method [52]: Equation (10) assumes that a dual-polarized reader antenna is used in the measurements so that the transmit and receive gain are the same (G) [52]. The methods depicted above demonstrate the relative complexity of measuring the RCS of a tag as compared to measuring its S-parameters. As was pointed out, inaccuracy in the measurement of any of the measured parameters is propagated into the calculation of the RCS [42], [53]. Additionally, the reference measurements are distance specific so if a tag were to be measured at a different distance, the reference measurements would also need to be repeated. It should also be noted that many of these methods are not feasible outside of a laboratory setting, especially in sensing applications. For example, a tag couldn't be replaced with a calibration target to determine its RCS in an embedded materials characterization scenario [4], [32], [54], [55], [56], [57]. Due to the relationship between RCS and S-parameters, which has also been depicted in Fig. 1c, both are frequently used in the design and measurement of chipless RFID tags [4], [58], [59].
While S-parameters and RCS are the most commonly used chipless RFID measurement quantities, others such as power, voltage, and electric field have also been measured. This is especially done when custom readers, radars, or software defined radios are used to make the measurements rather than VNAs [60], [61], [62], [63], [64], [65].

III. CHIPLESS RFID MEASUREMENT APPROACHES
The choice of technique used to measure the quantity of interest is influenced by the tag design, the desired application, and the available equipment [4]. When it comes to the tag design, how the tag is designed to interact with the polarization of the interrogating wave is a major measurement approach determinant. In terms of their polarization response, tags can be categorized as co-polarizing or cross-polarizing. Co-polar tags are designed so that their response has the same polarization as the interrogating wave, while cross-polar tags are designed to have their response in the polarization orthogonal to that of the interrogating wave. In general, co-polar tags have a higher RCS and data capacity than cross-polar tags, but cross-polar tags tend to perform better in real (i.e., non-anechoic) environments. This is because background objects generally reflect with the same polarization as the interrogating wave, while a cross-polar tag produces a cross-polar response, providing for natural isolation of the cross-polar tag response from the background environment [66], [67]. Both co-polar and cross-polar tags can be categorized as Tx/Rx tags or backscatter/RF encoding particle (REP) tags. Tx/Rx generally consist of two patch antennas connected by a microstrip line loaded with resonators, while backscatter tags consist just of resonating elements [68].
Co-polar tags can further be delineated as either linearly-polarized or orientation insensitive tags, where linearly-polarized tags require precise polarization alignment between the tag and the reader antenna, while orientation insensitive tags do not [20], [27], [40], [45], [69], [70], [71], [72], [73], [74]. There are also dual-polarized tags that are a special case of co-polar tags; they are designed to be read in two orthogonal polarizations that are co-polar with the polarization of the reader antenna. In the case of dual-polarized tags, the reader antenna is typically either dual-polarized, or the orientation of the reader antenna relative to the tag is changed to measure the tag in the two polarizations [69], [72], [75], [76], [77], [78]. Fig. 2 shows models of the different types of co-polar and cross-polar tags discussed above. A reference for each tag model is provided which gives more details on the dimensions, substrate material, response, frequency of operation, etc. of each tag [32], [58], [69], [76], [79].
There are numerous configurations with which co-polar and cross-polar tags can be interrogated. These include the following: • A single linearly-polarized antenna (i.e., a monostatic setup), such as a horn or open-ended waveguide, used to interrogate a co-polar tag. • A bistatic configuration of linearly co-polarized antennas used to interrogate a co-polar tag. • A single dual linearly-polarized antenna used to interrogate a co-polar, cross-polar, or dual-polarized tag. This is the case of having a bistatic reader with a monostatic reader antenna. • A bistatic configuration of linearly cross-polarized antennas used to interrogate a cross-polar tag. From the list above, it can be seen that having a crosspolar or dual-polarized tag does necessarily imply a bistatic setup because of the use of dual-polarized antennas, such as dual-polarized horn antennas or specialized patch antenna arrays [15], [67], [69], [75], [80], [81]. In general, a monostatic configuration is limited by the directivity of the reader antenna. Using a bistatic configuration helps overcome this and improves the signal-to-noise ratio (SNR) of the received signal. However, bistatic configurations can suffer from misalignment issues and coupling between the two reader antennas [45], [69], [78], [82], [83], [84], [85], [86], [87]. Fig. 3 shows schematics of some of the measurement configurations that have been discussed in this section. This figure is not comprehensive due to the breadth of possibilities, and instead provides illustrative examples from which the mechanics of other setups can be extrapolated. In Fig. 3, the polarization of the reader antenna and the tag are indicated with red arrows and the polarization of the transmitted and received wave are described with text. In the case of the cross-polarized tag, the tag polarization is represented by two orthogonal red arrows with a yellow arrow between them to represent the polarization conversion performed by the tag. In the case of monostatic dual-polarized measurement, two lines are used to connect the reader to the antenna to represent that this is a two-port measurement (i.e., a bistatic reader with monostatic measurement setup). While a horn antenna is used in the schematics of Fig. 3 for illustrative purposes, there are many different types of reader antennas that are used for making measurements of chipless RFID tags. The reader antenna landscape will be discussed in more detail in Section IV-B.
Co-polar and cross-polar tags can also be interrogated with a circularly-polarized wave [69], [85], [88], [89]. When a circularly-polarized wave impinges on a surface and is reflected, the polarization sense changes (i.e., righthand polarized becomes left-hand polarized and vice versa). In general, a reader antenna that is circularly-polarized can only send and receive with a single sense [90], [91]. This means that if tags can produce a circularly-polarized response with the same polarization sense as the reader, then the tag response becomes naturally isolated from the environment. This is similar to the concept of crosspolar tags, but it does not require precise alignment between the polarization of the tag and the reader. In other words, by using circular polarization to interrogate a tag, orientation independence can be achieved along with potential background isolation assuming appropriate tag design [69], [81], [89], [92], [93], [94], [95]. It should be noted that while circular polarization can help overcome sensitivity to roll-based rotations, it does not necessarily help with pitch-and yaw-based rotations [20], [62], [93], [96]. The reader setups used to implement circularly-polarized orientation insensitive reading can be either bistatic or monostatic and vary in complexity [85], [89], [93]. Additionally, some of these circular polarization reading setups require specifically-designed tags while others are able to read tags with any of the polarization schemes discussed above [69], [85]. Relatedly, measurement setups that achieve orientation independence with linearly-polarized antennas have also been proposed [23], [97], [98].

A. DESIRED READING DISTANCE
Interrogation with the polarization schemes described above has been performed in both the near-field and far-field of a reader antenna. The far-field is typically defined as starting at a distance of 2D 2 /λ away from the antenna, where D is the primary dimension of the antenna. It should be noted that near-field chipless RFID measurements are typically done in a monostatic configuration. The exception to this is transmission line-based near-field readers where the tag is placed between two waveguides or on a microstrip line [33], [69], [99], [100], [101], [102], [103], [104]. The desired reading distance, and consequently whether the tag is read in the near-field or far-field, is dictated by the application and plays a role in determining the optimal measurement approach. As such, the reading distance has not necessarily increased over the evolution of chipless RFID systems. This is demonstrated in Fig. 4a where the reported reading distance is plotted against the year published for 172 different reported works, which have compiled in the dataset available in [105]. The different symbols represent whether the measurement was done with a monostatic or bistatic setup and the different colors represent whether a co-polar or crosspolar tag was measured. In works where multiple reading distances were reported, the highest one at which the tag was successfully read according to the authors of that work is reported in Fig. 4a. Furthermore, it should be noted that "success" is somewhat subjective and the criteria for success are often not provided. Therefore, some caution needs to be taken when comparing reading distances. From Fig. 4a it can also be seen that the reading distance is typically below 1 m.
There is also a relationship between the operational frequency range of the tag and the reading distance. This is illustrated in Fig. 4b. In Fig. 4b, the colors are used to help distinguish the 172 cases reported in [105] from each other (i.e., each case is represented by one vertical line) and illustrate the frequency ranges that have been used in chipless RFID measurements in the literature. Fig. 4b shows that the higher reading distances tend to be for tags operating at lower frequencies. Note the concentration of data along the bottom of the plot between reading distances of 30 cm and 100 cm. The intuition behind this is that as the frequency decreases, the tag tends to get larger, which is associated with a larger RCS. Relatedly, increasing the RCS has been demonstrated to be necessary for increasing the read range [15], [106]. One way to increase the RCS of a tag is by creating an array of tags [47], [106]. Additionally, at lower frequencies there is less path loss, which results in a larger tag response magnitude relative to that of tags that operate at higher frequencies [15]. Fig. 4b also shows that there is a concentration of designed and measured tags in the 3.1-10.6 GHz range (i.e., 35 of the 172 cases considered fall in this range and 131 of the 172 cases considered were measured at frequencies less than 10.6 GHz). This is largely due to Federal Communications Commission (FCC) and European Telecommunications Standards Institute (ETSI) requirements for ultrawideband (UWB) applications which restrict the equivalent isotropic radiated power (EIRP) [61], [67], [235], [236]. An exception to both the frequency range and reading distance trends is reported in [157], where a combination of a 24 GHz Van Atta Array cross-polar tag, bistatic measurement setup, and a high gain transmit antenna with beam scanning capabilities is used to achieve a reading distance of 58 m. Table 1 breaks down the number of each type of tag and type of measurement setup considered across the 172 cases in [105] and also shows the average reading distance for the different tag/reader configurations considered in Fig. 4a. From Table 1 it can be seen that cross-polar tags and bistatic reading setups, on average, tend to have higher reading distances. However, if the 58 m reading distance case from [157] is removed from the data set, the average cross-polar tag reading distance drops to 30.0 cm, the average bistatic reading distance drops to 44.8 cm, and the average bistatic cross-polar reading distance drops to 34.8 cm. This means that while cross-polar tags can be theoretically read at larger distances than co-polar tags, practitioners are not always leveraging this advantage to its fullest potential [15], [237].
Read range is defined as the largest possible distance at which a tag can be read. While the reading distance is typically shorter than the read range, they can be the same. Read range is often measured or defined based on specific conditions (e.g., measuring in an anechoic chamber or with an antenna with a specific gain). In practice, the reliable reading distance is typically degraded from the read range due to a number of factors, such as polarization mismatch between the tag and reader antenna, reflections from the background environment of the tag, dynamic range of the receiver, and reader antenna performance (e.g., gain, beamwidth/reading zone, and bandwidth) [12], [15], [61], [85], [188], [237]. In order to increase the read range, the RCS of the tag relative to the background must increase, as simply increasing the transmit power also increases the scattering from the background environment [9], [15], [16], [82].

B. CALIBRATION PROCEDURES
Calibration procedures can help in isolating the tag response, which can also impact the achievable read range and reliable reading distance. Here, calibration procedures describe those that require specific steps be taken during the measurement process. Signal processing procedures that are implemented post measurement will be described in Section V. Based on this convention, there are a number of primary ways by which calibration is performed. The first, involves measuring the background response in the absence of the tag and then coherently subtracting this response from that of the tag [29], [32], [238], [239]. While this helps remove "clutter" (i.e., response due to the background environment) from the measurement, it does not help remove the effect of the reader antenna. Additionally, it has been shown that background subtraction is most effective for large reading distance measurements with there being miniscule effects for small reading distance measurements [234]. In order to remove the effect of the reader antenna, a reference target, typically a large metal plate, is often used. The reference target is measured at the same location as the tag is to be measured and then is used to calibrate the response. This is done either through the procedures described for RCS measurement in the previous section or by dividing the result of subtracting the background response from that of the tag by the Fourier transform of the time-gated metal plate response [35], [38], [45], [123], [134]. By using a reference target in this manner, the calibration procedure becomes distance specific (i.e., it only allows for tags to be measured at the specific distance at which the reference target was measured) [240]. While these approaches can be effective in static environments where the background is not changing significantly from one measurement to the next, they do not work as effectively when the environment becomes dynamic (e.g., the tag and other objects in the scene are moving) [241].
Another calibration approach that suffers from the same distance-specific limitation, is the use of calibration tags. For this approach, a calibration tag, which is typically a tag with the same form factor as the tag of interest and all the resonators removed or shorted, is measured at the same distance as the tag of interest. The responses of the tag of interest and the calibration tag are coherently subtracted and this magnitude difference is examined. In dynamic systems (e.g., sensing applications where the response is changing over time), a measurement from a specified increment of time in the past can be used as the calibration tag/reference measurement and subtracted from the current response. The responses measured from calibration tags can also be used to create a threshold of detection for the response. Furthermore, the use of a calibration tag can also be combined with background environment response subtraction and time gating [65], [100], [121], [129], [142], [160], [222].
Time gating has also been used by itself as a calibration procedure to help reduce the effects of multi-path and isolate the tag's antenna mode from its structural mode. A more detailed explanation of antenna and structural modes is provided in Part A of Section V. Time gating can be implemented directly on some VNAs, which are frequently used to read frequency-domain chipless RFID tags, or in post processing [39], [57], [94], [124]. Similarly, averaging can also be implemented on a VNA to help increase the fidelity of the tag response [51], [137]. Another approach, is to calibrate a VNA either up to the connectors or up to the aperture of the antenna, which can be done with port extension or with calibration standards when standardized antennas like waveguides are used as the reader antenna [54], [58], [69], [119], [120], [194].
Another approach geared towards systems with dualpolarized or cross-polar tags involves measuring a tag and/or the background in multiple orthogonal polarizations. The background environment responses can either be individually subtracted from their associated tag response or they can be combined with each other. For example, by subtracting the two background measurements made with orthogonal polarizations, an estimate of the mutual coupling between the two orthogonally-polarized ports of the reader antenna can be obtained [52], [142]. Just as with some of the calibration procedures discussed previously, this multiple polarization approach can also be combined with time gating. As an example, in [75] a dual-polarized tag and the background responses were both measured in orthogonal polarizations and then the associated background response was subtracted from each tag response. These background-subtracted responses were then individually time-gated and then subtracted from each other in the frequency domain [75].
An approach which is not distance specific has also been developed [240]. This approach involves performing a measurement of the background environment and of a large metal plate at a known distance. The metal plate response is then subtracted from the background response and the result is inverse Fourier transformed into the time-domain so it can be time windowed. From this time-domain response the time of arrival from the metal plate can be computed. Subsequently, the tag response is measured and the background response is subtracted from it. This background-subtracted response is also inverse Fourier transformed for time windowing purposes and from it the time of arrival of the tag response is computed. From the time of arrival of the tag and metal plate responses and the known distance at which the plate was measured, the distance at which the tag is measured can be computed. Consequently, by knowing all of these parameters the tag transfer function can be estimated. This process is described and demonstrated in more detail in [240]. The benefit of this process is that only one set of calibration measurements is necessary in order to measure tag response at any distance from the reader.
In general, the number of measurements required to measure a tag, including those associated with the calibration process, can be used as a metric to indicate practicality when comparing measurement approaches. Additionally, some measurement approaches with associated post processing procedures have been developed that explicitly do not require calibration [241], [242], [243], [244], [245]. In [193], a table (Table 1) is provided which shows whether one or two measurements are needed in the measurement approach. In Section VI of this work, the number of required measurements for a given approach is implied by the calibration technique and measurement parameter.

C. APPLICATION-SPECIFIC MEASUREMENT APPROACHES
Another aspect that dictates the measurement approach is the application for which a tag is designed. For example, for the purpose of assessing and mitigating the effects of tag/reader misalignment several approaches have been proposed, including: 1) characterizing the reading volume of the tag using a 3D raster scanner, 2) using a specific slot resonator tag with a reader architecture consisting of two orthogonally located linearly co-polarized antennas, and 3) employing a reader capable of tag polarization recognition [19], [62], [98], [246]. Determining the position of tags (i.e., tag localization) can also require the use of multiple reader antennas arranged at specific known locations [26], [247], [248]. Another application where a specific measurement setup may be required is sensing of environmental parameters, such as temperature, humidity or pressure. In these cases, a chamber is used to produce specific conditions and the measurement setup is adjusted to meet the constraints imposed by the chamber [159], [249], [250]. For Internet-of-Things (IoT) applications, high read range in real environments is cited as an important system requirement [251], [252].
The polarization schemes, reading distances, calibration procedures, and application specific measurement approaches discussed in this section provide some insight into the breadth and lack of standardization in the chipless RFID field. This will be further demonstrated in Section VI where an additional comparison of reported chipless RFID measurements are provided. Table 2 provides a summary of the pros and cons of the various chipless RFID measurement approach related choices that are made when determining how to measure a tag (e.g., measuring with a monostatic or bistatic setup). These choices are largely independent from each other and can be made based on the application and available equipment. As such, no one combination of measurement approach choices is inherently superior to another.

IV. MEASUREMENT HARDWARE
When it comes to the measurement hardware used to implement the measurement approaches previously discussed, there is a mix of off-the-shelf and custom solutions for both the reader itself and the reader antenna. Factors involved in selecting measurement hardware include, the operating frequency, bandwidth, dynamic range, sensitivity, cost, desired read range, and measurement speed, which can all affect the system response detection and decoding capabilities.

A. READER ARCHITECTURE SELECTION
While this work focuses on the measurement of frequencycoded tags, where the tag information is encoded and viewed in the frequency-domain, the tag response can be acquired either directly with a frequency-domain reader or indirectly with a time-domain reader, such as a ultrawideband (UWB) impulse radio (IR-UWB) system. The time-domain response can be translated to its frequencydomain response through a Fast Fourier Transform (FFT) operation [253], [254]. A brief description of the off-the-shelf and custom frequency-domain and time-domain readers and their respective limitations is provided here. Fig. 5 shows schematics of one custom frequency-domain reader and one custom time-domain reader for basic comparison purposes. However, many different architectures of frequency-domain and time-domain readers have been proposed and therefore, interested readers can refer to the block diagrams of frequency-domain and time-domain reader architectures with more in-depth descriptions of the individual components that can be found in [63], [236], [254], [255], [256].
Pertaining to frequency-domain readers, VNAs are the most common off-the-shelf option [105]. While VNAs can support UWB operation with high frequency resolution and accuracy, they can be costly and bulky which has prompted interest in the development of custom-designed and economical readers. However, it should be noted that with the current developments in the design and commercialization of microwave components, relatively low-cost and handheld VNAs have appeared in the market in recent years [110], [257]. Software defined radios, which tend to be less expensive than VNAs, and a combination of an RF signal generator and spectrum analyzer have also been used for reading chipless RFID tags [86], [187], [216], [242]. When it comes to custom-designed frequency-domain systems, scalar, homodyne, and superheterodyne architectures have also been proposed. All of these architectures have faced some common challenges, namely: balancing voltagecontrolled oscillator (VCO) performance and cost (i.e., having a VCO with a wide enough bandwidth to read the tags of interest), managing transmit power regulations, achieving a high read range, reducing read time/system latency, and mitigating self-interference due to signals from the transmitter leaking into the receiver sub-section of the reader. By the virtue of lacking phase information, scalar readers also suffer from calibration-based limitations and high receiver noise power [82], [86], [186], [254], [258], [259], [260], [261], [262], [263]. In addressing the issue of self-interference, self-interference cancellation boards [86], an UWB compensation unit based on a polyphase power divider [186], [235], a compensation unit based on wideband differential phase shifters [264], and a wideband directive filter have been proposed [260]. For the issue of noise, various techniques, such as a moving average filter, has been proposed and implemented on-board the reader [265], [266].
With respect to off-the-shelf time-domain readers, highspeed digital oscilloscopes with impulse generators and radar systems have been used [67], [170], [244], [267], [268], [269]. The main benefit of using a time-domain reader system is the spreading of the transmitted power over the frequency band of interest with a short single pulse, which provides for high peak power with a low average power. In this way, these systems effectively increase the power of the signal used to interrogate the tag while still being compliant with FCC and ETSI regulations, which theoretically increases the maximum read range of time-domain readers over that of frequency-domain readers for some types of tags [61], [82], [255], [270]. However, the amplitude of the interrogation pulse is not constant over frequency; rather, it takes a gaussian shape. Therefore, additional signal processing is often recommended to interpret and decode the tag response in the frequency-domain. One alternative to this uses a set of pulses with different center frequencies to create a more even spectrum amplitude across the overall interrogation signal [271].
There are two primary custom-designed time-domain reader architectures, namely: IR-UWB and chirped pulse Fourier transform microwave (CP-FTMW). IR-UWB readers can theoretically capture the entire tag response simultaneously in the backscattered short-duration pulse because they do not need to sweep the frequency. This makes this approach very fast, but it also means that the resulting frequency resolution will suffer after the Fourier transform due to the short duration of the pulse. CP-FTMW readers, in contrast to IR-UWB readers, use a broadband chirped pulse that is stretched in time while still generally having a shorter reader time than IR-UWB readers. This longer duration pulse provides for the transmitted power to be more evenly distributed over the frequency range of interest and provides for better frequency resolution post Fourier transform [203], [236], [254].
For both IR-UWB and CP-FTMW readers, a highperformance high-speed analog-to-digital converter (ADC) is needed to sample the signal that is scattered from the tag [61], [203], [236], [254]. To reduce the cost associated with high-performance ADCs in custom solutions, a method that uses multiple ADCs and an equivalent time approach method have been proposed [236], [272]. In the equivalent time approach, multiple UWB impulses are used to interrogate the tag and the reader incrementally samples a few points from each backscattered pulse. While cost effective, this approach can experience drawbacks as a result of sampling clock jitter. However, these issues can be mitigated with increased hardware complexity [236], [268], [273]. In practice, the pulse repetition rate can be increased and averaging can also be implemented to increase the SNR [203]. Additional recent developments of custom time-domain readers include, a fully-tunable ultra-low jitter baseband pulse generator [274], reduction in read time through FPGA implementation optimization [236], a dual-comb technique for increasing the frequency resolution while reducing the complexity of the receiver portion of the reader design [203], a combined IR-UWB transmitter/frequency translation reading method [61], and a multicarrier-based receiver with a pulse distortion decoding approach [275].
For both frequency-domain and time-domain readers, numerous techniques have been proposed in the literature for increasing performance. These include implementing features like a handshaking algorithm for detecting if a tag is present in order to reduce power consumption [276], selectively silencing the transmitter to allow for increased radiated power while interrogating the tag [235], using a fast locking phase-locked loop (PLL) to allow for higher transmitted power [186], including adaptive frequency hopping and adaptive sliding window methods to reduce read time [262], [263], and using ZF equalization to improve the tag detection rate [277]. Increasing the number of receiver antennas to increase receiver diversity, using a Selective-RAKE receiver to filter clutter, using dual signal sources to intentionally create different interrogating wave polarizations, and creating a reader that can read tags in two polarizations without changing the orientation of the reader antenna have also been proposed [98], [242], [278], [279]. Additionally, using a bank of bandpass filters in the receiver with each filter having a center frequency corresponding to a resonance frequency of the tag has been proposed. While this approach reduces the reader receiver complexity and lowers the ADC performance requirements, it also is limited in terms of the tags it can read [63].
In comparing frequency-domain and time-domain readers, frequency-domain readers tend to be more sensitive to the tag response due to their input noise bandwidth and they tend to provide higher frequency resolution. This is primarily due to the short duration of IR-UWB pulses, which determines the frequency resolution. However, IR-UWB readers tend to have a faster read time than frequency-domain readers and as discussed previously, have transmitted power advantages that result in stronger received signals and therefore greater potential reading distances [63], [82], [236], [254], [255]. It should be noted that read time is dependent on the bandwidth, number of frequency points, and reader architecture. Therefore, as a metric read time needs to be considered in the context of the application and one-to-one comparisons of read times can only be made when similar tags are read by both readers. This points to the potential benefit of the chipless RFID field agreeing on specific tag standards for testing and comparing reader performance, which do not currently exist.
The reader hardware for the 172 cases reported in [105] is compared in Fig. 6. This plot depicts the highest reported reading distance vs. the center frequency of the range over which the tag was measured for three categories of readers,  9, 11, 12, 16, 19, 20, 22, 32, 33, 37-39, 45-48, 51-54, 57, 58, 60-62, 65-67, 69, 70 namely: VNAs, non-VNA frequency-domain readers, and time-domain readers. Fig. 6 demonstrates the similar reading distances that are achieved in practice for frequency-domain and time-domain readers, despite time-domain readers theoretically providing longer read ranges [61], [255]. However, of the 172 cases considered, only six were done with timedomain readers, while 156 were done with a VNA and ten were done with other types of frequency-domain readers. This provides evidence for both the lack of prevalence of time-domain readers for frequency-domain chipless tags and the potential to better leverage the advantageous features of time-domain readers.
The evolution of the custom-designed chipless RFID reader development landscape is depicted in Table 3. Table 3 lists the readers that have been proposed and tested in the literature over time, and allows for comparison across architectures, required calibration complexity, bandwidth, and cost when possible. It should be noted that some of the entries represent incremental improvements over others and that only readers that were prototyped were included in this table. As can be seen from Table 3, most of the readers operate in the 3.1 -10.6 GHz range, which is in line with the trends shown in Figs. 4 and 6. As previously discussed, this frequency range is popular due to the desire for developed readers and tags to comply with FCC and ETSI regulations. There is also a tradeoff to consider when it comes to higher frequency tags: as tags are designed to operate at higher frequencies, they tend to become smaller and then have a smaller average RCS over frequency and smaller read range [54]. This means that in order to read a higher frequency tag, readers generally need to have a higher sensitivity to lower level signals so that they are able to detect the minimum RCS value of the tag [82].
Another point of interest in Table 3 is that there is a mix of both monostatic and bistatic setups for both frequencydomain and time-domain readers. Cost is potentially another metric across which readers can be compared. However, cost is not always discussed in the published technical literature, and when it is mentioned, the currency is not always specified and there are inconsistencies in terms of whether or not the cost of the antennas is included in the total reported price of the reader. The performance of custom readers like these in terms of measuring tags will be further demonstrated in the comparison provided in Section VI.

B. ANTENNA SELECTION
Similar to reader hardware, the antennas used to interrogate a tag can be off-the-shelf or custom and depend on factors, such as the polarization scheme and desired read range. Additional factors for consideration include desired gain, half power beam width (HPBW), form factor, cost, and calibration potential. Notably, read range been shown to be affected by the gain, beamwidth, and polarization of the reader antenna [12], [85], [157], [280]. Ultimately, however, the driving requirement for chipless RFID reader antennas is the operational frequency range of the tags of interest. In other words, the reader antenna needs to be able to interrogate the tag over a range of frequencies that captures all of the response features of interest (e.g., all of the resonances) [63], [85].
When it comes to off-the-shelf solutions, rectangular waveguides and horn antennas are popular choices. Some benefits to using rectangular waveguides are that they can be calibrated up to their aperture with well-known standards (e.g., short, shifted short, and matched load) and are inherently wideband as compared to basic patch antennas. However, waveguides have a smaller gain than some other types of antennas, such as horn antennas, and measurements made with waveguides can suffer from flange effects. To mitigate flange effects, engineered flanges that approximate infinite flanges have been developed and used in the measurement of chipless RFID tags [20], [34], [54], [58], [103]. Horn antennas, on the other hand, have higher gains than openended waveguides and can be more wideband (e.g., ridged horns). However, there is a lot of phase variation in the nearfield of horn antennas and therefore, they are typically only used in far-field measurements [90]. Horn antennas can also be dual-polarized and are therefore often used for the interrogation of cross-polar tags when a monostatic antenna setup is desired [66], [67].
Custom options have been proposed mainly because of the larger form factors and costs of standard off-the-shelf options, such as horn antennas, that are commonly used in laboratory settings and would not necessarily be suitable for large scale commercial use [63], [236], [285]. Customdesigned antennas can be categorized by whether they are planar or nonplanar, their polarization characteristics, their operational frequency range, gain, and other pertinent parameters. Table 4 provides a comparison of antennas that have been custom-designed specifically for chipless RFID applications. It should be noted there are many other UWB antennas in the literature that could be suitable for chipless RFID applications, but all cannot be explored comprehensively within the scope of this work. Based on the custom-designed reader antennas reported in Table 4 there are a few trends that can be identified, namely: 1) custom-designed reader antennas tend to be planar (i.e., microstrip patch antennas), 2) they tend to operate in the UWB 3.1-10.6 GHz range in order to be compatible with the proposed custom-designed readers and regulations, and 3) the gain varies widely from 2.6 to 26 dBi.
A consequence of many planar custom-designed reader antennas is that they are often fabricated using printed circuit boards (PCB). However, 3D printing has also been employed for fabrication [69], [188]. Table 4 also shows that linear polarization and dual linear polarization are the dominant polarization schemes for custom reader antennas. However, since the use of circular polarization for chipless RFID applications is relatively new, more circularly-polarized reader antenna designs could be on the horizon [69], [92], [93].

V. RESPONSE PROCESSING
Detecting tag response features (e.g., notches, peaks, and phase jumps) is critical for assigning a binary code or sensing parameter. Due to factors, such as noise, misalignment, multipath, overwhelming background reflections, and tag response collisions, a number of post processing methods have been developed in order to extract the tag response from the measurement and assign binary codes and sensing parameters as appropriate. Post processing needs and requirements are driven by the choice of the parameter being measured, the environment the tag is measured in, the hardware used to make the measurements, and the calibration techniques employed [57], [290], [291], [292].
Analysis of a tag response begins with how the response is considered, which is limited by the measurement parameter (e.g., if RCS is measured then there will generally not be phase information available to examine). For example, the interpretation and analysis of a response considered in magnitude and phase form may be different than that viewed in group delay form or as the amplitude difference between the tag of interest and a reference tag. To this end, this section will examine and analyze the components of a tag response, how the resonance frequencies are determined, how binary codes and sensing parameters are assigned, the metrics used to compare post processing and decoding methods, and application specific post processing methods.

A. ANALYSIS AND PRE-PROCESSING OF THE BACKSCATTERED RESPONSE
When a tag is measured in a real environment (i.e., not in an anechoic chamber environment), the response often contains interfering signals, such as noise and unwanted reflections from background objects. Additionally, as the reading distance increases, so does the path loss. This results in weaker signals that can be more easily overwhelmed by the aforementioned interfering signals (i.e., clutter) and is prohibitive to increasing the quantity of information coded in the tag (i.e., it is unproductive to increase the number of notches in a response if they cannot be detected and decoded). Consequently, pre-processing is often necessary to enhance the signal quality prior to detecting response features for the purpose of decoding (i.e., assigning a binary code or a sensing parameter) [240], [293], [294]. Additionally, sometimes pre-processing is needed to get the measured response into a desired format (e.g., using the Hilbert transform to get the amplitude and phase responses from a custom reader without the need for a calibration tag) [240], [258], [295]. Some popular approaches to pre-processing include, analysis of the backscattered signal components in the time-domain (reader mode, structural mode, and tag mode), channel estimation, and general filtering.
The response of a tag can be broken down into three general components in the time-domain: the reader mode (also referred to as the rejection mode), the structural mode, and the tag mode (also referred to as the antenna mode). The reader mode occurs first temporally and captures the aperture reflections and coupling of the reader antenna(s). This is usually the largest mode and contains most of the signal's energy. The structural mode occurs second temporally and consists of the immediate reflections from the tag structure (e.g., the substrate and the metallic resonators). In these reflections, the frequency content of the interrogating wave is not altered. In other words, the spectrum of the structural mode is effectively the same as that of the interrogating pulse. Additionally, in the case of cross-polar tags, the structural mode is greatly reduced with respect to that of co-polar tags [11], [216], [241], [245], [271], [294], [296], [297]. The tag mode occurs third and consists of information related to the tag's resonances. It is considered to be the late time, source-free portion of the response according to complex natural resonance (CNR) theory [298], [299]. The tag mode usually lasts for tens of nanoseconds while decaying exponentially and is smaller in amplitude than both the reader mode and the structural mode. There can also be additional components in the response, such as reflections from background objects and multipath reflections. Therefore, various filtering, subtraction, and time gating procedures have been proposed for isolating the tag mode, which can then be transformed to the frequency-domain for decoding [216], [241], [271], [296], [297]. Fig. 7 provides an example of the three different modes of a tag response and the process of extracting the tag mode. For this, the process outlined in [216] was followed. For Fig. 7, the eight circular slot tag shown in Fig. 1 was simulated in front of a horn antenna at a distance of 30 cm. Fig. 7a, shows the time-domain response of the tag that was obtained through an inverse FFT (IFFT) with the reader mode (y r ), structural mode (y s ), and tag mode (y t ) are designated. The horn antenna was then simulated without the tag and its response was also transformed to the time domain. The two signals were then subtracted to obtain the response shown in Fig. 7b, which was then time-gated using a rectangular window to extract the tag mode. The time window start and stop times were determined through trial-and-error. The FFT was taken of the structural mode and the extracted tag mode to obtain the spectrums shown in Fig. 7c. In Fig. 7c, the three peaks in the tag mode correspond to the three resonances of the tag that occur in the considered frequency range (see Fig. 1c).
One challenge when trying to isolate the tag mode from the structural mode is determining at what time the tag mode begins, assuming the tag mode and structural mode are not completely overlapped with each other or the reader mode [241], [298]. Additionally, the performance of time gating to isolate the tag mode is reduced for higher frequency resonators [15]. For this reason, isolating the antenna mode is only really possible when the tag is being measured at a large distance from the reader antenna (i.e., at least 15 cm according to [300]) and the tag is operating at sufficiently low frequencies [241]. Approaches previously proposed for determining the start time of the tag mode include, trial and error [297], having a Tx/Rx tag with a meandering transmission line between the tag antennas to create enough temporal separation to distinguish between the structural and tag modes easily [296], using the reading distance and system parameters like the cable lengths to estimate the starting time of the tag mode [57], examining the spectral norm of the impulse response data matrix over a sliding window [301], using the half Fourier transform [302], and examining the time-frequency plot after employing the short-time matrix pencil method (STMPM) [134], [303], [304]. Another challenge is making sure that the window isn't too long since this can introduce unwanted noise into the response. Methods, such as using knowledge of the lowest frequency pole or estimating it from the dimensions of the tag, have been proposed for this purpose [245], [304].
After determining the start and stop times of the window for isolating the tag mode, a variety of different types of windows can be used to extract the tag mode. For example, raised cosine window was used in [216] and [270], a Hamming window was used in [245], and a Tukey window was used in [304], while the example in Fig. 7 used a rectangular window. It should also be noted, that windowing can be applied to a background-subtracted response to further reduce the effects of noise or it can be combined with the use of a narrow beam antenna to achieve volume gating [266], [300]. Once the tag mode is "windowed" out, a Fourier transform can be performed to view the response in the frequency-domain and perform further processing and decoding [241].
Beyond analyzing the tag backscattered response, the wireless channel can be estimated and analyzed. This estimation can take into account many different factors, including the angles of arrival and departure of the interrogating wave and the spatial gain of the tag [25], whether the tag is being read in the near-field or the far-field with varying levels of noise [305], multipath components [57], fading [277], calibration accuracy [306], polarization dependence [293], and estimation of the residual environment [15]. In order to mitigate channel effects, zero forcing (ZF) equalizers have been proposed [277], [293].
While denoising and decluttering techniques, like moving average filters, have been implemented in hardware, they can also be implemented on a computer in the pre-processing stage [265], [266], [281], [307]. Other examples of improving the tag response signal quality include, the use of a prolate spheroidal wave function-based filter in [308], using a general matched filter [309], using a continuous wavelet transform as a matched filter in [244], using the least mean square error algorithm to do adaptive direct path cancellation [310], and detrending the response followed by denoising with a discrete wavelet transform [311].

B. DETECTION OF RESPONSE FEATURES AND RESPONSE DECODING
The first step in decoding the tag response is to identify the features of interest in the response. These features of interest are often notches or peaks in the magnitude vs. frequency response of the measured quantity (e.g., S 21 or RCS). These features are created by the designed resonant properties of the tag, but they can vary depending on the reader architecture, how the response is viewed, and the decoding method being used. For example, while the RCS magnitude or the magnitude or phase of S-parameters are typically directly examined for decoding, in [56] and [77] the tag is measured in two orthogonal polarizations and the two responses are subtracted which creates sharp amplitude changes that can be used to identify the resonance frequencies and assign a binary code. Other examples of unique response viewing approaches include, determining the zeros in the derivative of the group delay which is itself the derivative of the phase vs. frequency response [308] and examining the pulse distortion in the response of an IR-UWB reader [275]. Decoding can then be performed either onboard the reader, as in [65], or in post processing on a computer. The common methods used for decoding in chipless RFID applications are detailed below.
Some of the proposed methods for binary code assignment, which is primarily done for identification applications but has also been done for sensing applications, include the following: 1) Method 1: Specified response features (e.g., a peak or a notch) are 0's. Removing an instance of the specified response feature results in a 1 in the code [110]. 2) Method 2: Specified response features are 1s.
Removing an instance of the specified response feature results in a 0 in the code [46]. 3) Method 3: Specified response features are 1s and removing an instance shortens the code [312]. 4) Method 4: Encoding multiple bits per resonator state in conjunction with encoding the phase deviation and frequency position in a frequency channel [116], [117]. 5) Method 5: Frequency shift coding. The bandwidth is divided into sections and the sections are divided into sub-sections. Each sub-section represents a possible position of a resonance and has a different binary bit sequence. In this way, each resonance is encoded by multiple bits [67], [135]. 6) Method 6: Concatenating the codes generated using Method 2 when the tag is measured in two different polarizations [139]. 7) Method 7: Concatenating the codes generated by Method 4 when the tag is measured in two different polarizations [144]. [128]. 9) Method 9: Division into windows and assigning 1's where the response is primarily above the threshold (determined via integration) and assigning 0's where the response is primarily below the threshold [32], [194].

8) Method 8: Phase position modulation
Methods 6 and 7 can be considered as hybrid methods since at least two parameters are combined to create the full code [69], [313], [314].
In terms of sensing parameter assignment, a variety of methods beyond binary code assignment have also been proposed [4], [194], [315]. These include the following: 1) Correlating a resonance frequency shift to a sensing parameter [169], [315]. 2) Relating a change in response magnitude to a sensing parameter [316], [317]. 3) Associating a calculated value, such as an error estimator, with a sensing parameter [157]. 4) Matching response shapes to a sensing parameter [154]. 5) Correlating changes in tag parameters, such as gain, impedance, or max RCS with a sensing parameter [318], [319].
From the decoding methods outlined above, it can be inferred that the more response features the decoding method relies on, the more accurate the response detection process needs to be. Fig. 8 provides several illustrative examples of the IDbased decoding methods shown above. For this example, the 8 slot tag that was depicted in Fig. 1 is used along with a 7 slot version (Fig. 8b) where the innermost slot resonator has been removed. The responses for both tags are shown in Fig. 8c along with the binary code assignment for Methods 2 and 3 using the notches as the "specified response feature". This demonstrates how the code can be manipulated through intentional changes of the tag structure in order to assign different IDs. Fig. 8c shows how the response of the 8 slot tag can be decoded using Method 9. This method was designed for use in sensing applications and thus can capture various types of changes in the tag response as it changes with changes in the tag environment. However, as mentioned previously, this intensifies the measurement accuracy requirements since more response features are relied on for decoding.
In terms of the extraction of resonance frequencies in a response, a number of methods have been proposed. The methods tend to vary based on whether or not there is a set of expected resonance frequencies and/or a set of potential codes to compare against [305], [320], [321]. For example, in some ID applications the expected code is known and this informs the detection and decoding procedure, while in sensing applications there is not an expected response since changes in the response are being used to determine an unknown sensing parameter [4], [194]. One of the simplest decoding methods is finding the local minima or maxima in a response and comparing their amplitudes to some preset thresholds. These thresholds can be set by reference tags, which have codes that consist of either all 1's or all 0's, or by analyzing the responses at multiple expected reading distances and selecting a threshold accordingly [65], [135], [258], [281]. This approach works well if the reading distance is known and will stay consistent or within a certain range. However, this is not always the case for practical systems. Reading distance changes can result in response amplitude variations, which could cause bits to be misread [292]. To mitigate this, using the normalized amplitude of the derivative with respect to frequency of the tag mode response for decoding with thresholds has been proposed. This is part of a method to estimates the range to solve the chipless RFID "inverse problem" [241]. However, misalignments can also cause amplitude changes and resonance frequency shifts, which are not necessarily taken care of by this method [4]. Another alternative that has been proposed is the adaptive energy detection (AED) method. The AED method divides the response into windows and performs an energy calculation in each window to determine where to set the decoding threshold. As a result, this approach both takes into account channel effects and tends to have a lower probability of error than the traditional threshold setting method, especially for low SNRs [322]. While these threshold setting methods are applicable for ID applications, they are not suitable for sensing applications.
Alternative response decoding methods for ID applications that can be used when all possible codes are known include, the Maximum Likelihood (ML) and the Signal Space Representation (SSR) methods [240], [294], [307]. In the ML method, the measured response is compared against a set of stored potential responses to calculate the ML values. The response is then decoded as the comparison that produces the highest ML value. This approach is computationally resource-intensive particularly when the code length and set of potential codes increases [292], [323], [324]. In implementations of the ML method, multiple tag readings have been performed and results averaged to mitigate potential interferences [323], the statistical properties of the channel state have been integrated into the calculations [305], the Euclidian distance between codes has been increased through the binary code assignment method which also allows Euclidean distance itself to be used to decode tag measurements [155], [325], [326], and the channel/tag combinations with the highest probability of occurrence has been determined [327]. Additionally, bit-by-bit reading has been proposed to help improve the scalability of this approach for use with higher bit density tags [305], [321].
In the SSR approach each possible tag response, of which there are 2 b where b is the number of notches in the response, is collected and fully described by a linear combination of orthonormal basis functions which are determined through singular value decomposition (SVD). These possible responses are represented as constellation points against which measured responses are compared using a minimum distance calculation. In the end, the response is decoded based on which constellation point it is closest to. The advantages of this approach are that it allows for the response to be more comprehensively considered during decoding (i.e., taking into account the Q-factor of notches rather than just comparing to a threshold) and it has an improved detection error rate (DER) over the threshold method. However, it can be very computationally resource intensive, especially for tags with high bit densities, and the DER tends to increase as the number of notches in the response increases [240], [292], [320], [322].
Improvements to the traditional SSR method have been proposed, namely: the logarithmic SSR (LSSR) and the window based SVD (WB-SVD). In the LSSR method, the basis functions are derived without the use of SVD and decoding is done by testing the tag response against the constellation one bit at a time. These two changes greatly reduce the computational resource requirements with an increase in the number of tag notches, but come with the tradeoff of increased probability of error with respect to the traditional SSR method [240]. In the WB-SVD method (also referred to as Smart-SVD (SSVD)), fewer points are used than the traditional SSR method which helps to reduce complexity and processing time. Unlike the traditional SSR method, the WB-SVD approach also takes into account channel effects, which results in a lower probability of error. Furthermore, WB-SVD allows for notch bandwidths to be estimated, which is necessary for certain decoding methods (e.g., Method 5 above) [309], [322], [328].
Another method that is similar to the ML and SSR methods, is the dynamic time warping (DTW) method, which compares the tag response to a dataset and computes cost matrices to decode the response. By considering the tag response more comprehensively, the DTW method allows for similar response shapes to be matched even if they are shifted in time or frequency or distorted. The downside to this approach is that it is very computationally intensive. However, it has shown better probability of detection than the WB-SVD method [309]. These methods that compare responses to a set of possible known codes are also mainly suited for ID applications over sensing applications, just like the threshold methods.
Another approach is to extract the complex natural resonances (CNRs) of tags, which are considered to be aspect independent (i.e., they do not change location due to angle of arrival of the interrogating wave or the observation point) [118], [134], [329], [330], [331]. It should be noted that CNRs are sensitive to changes in tag's substrate permittivity and structure effective permittivity, which makes the following discussed CNR extraction methods suitable for sensing, as well as identification, applications [332], [333]. CNRs can be extracted by using methods like the singularity expansion method (SEM), matrix pencil method (MPM), short time matrix pencil method (STMPM), and spectrogram method [19], [245], [304], [329], [333]. The latter three can be considered as more optimized methods to estimate and extract the poles described by SEM theory, of which there is a detailed explanation provided in [299] and [334]. The MPM involves solving a generalized eigenvalue problem in order to find the poles of the response. In order to employ the MPM, the response is transformed to the time-domain (if needed) and then processed. In the case of processing chipless RFID tag responses, the additional steps of background subtraction and deconvolving the background-subtracted tag response with the response of a time windowed large metal plate are taken. The deconvolved response is inverse Fourier transformed to the time-domain and time windowed before the MPM is applied. This means that three measurements are needed, the results are distance dependent, and the challenges with selecting the time window beginning and length discussed previously are relevant here [118], [134], [271]. Another challenge facing the MPM approach is that it cannot separate the reflections from background objects from that of the tag. In an attempt to overcome this, separating the poles based on their time and direction of arrival has been proposed [298]. The MPM inherently includes singular value decomposition (SVD), unlike other CNR extraction methods like Prony's method or Cauchy's method, which helps reduce the effects of noise. Additionally, an autocorrelation function approach and a time-domain averaging approach have been proposed to help further reduce the effects of noise when employing the MPM [330], [334], [335], [336].
An alternative approach that harness the benefits of MPM while helping to overcome some of its challenges is the short time matrix pencil method (STMPM). The STMPM uses a sliding time window and applies MPM at each window location to get a time-frequency plot. By examining the convergence in this plot, one can identify the approximate start time of the tag mode and can find the average resonance frequencies over time, which makes this approach even less susceptible to noise than the MPM while also calculating the CNRs more accurately. One of the limitations of the STMPM, though, is that it has fixed resolution in time and frequency [290], [292], [304], [334]. Improvements to the STMPM method have also been proposed, including a k-nearest neighbor algorithm in order to create decision boundaries and decode the tag response [220].
The Short Time Fourier Transform (STFT) method (also referred to as the spectrogram method) is similar to the STMPM method in that it uses a sliding window over the time domain response to determine the tag response from the tag mode. One of the differences is the data presentation format, namely, the STFT method presents the data in a spectrogram format. Additionally, the STFT method like STMPM and MPM traditionally requires multiple measurements to isolate the tag mode before extracting the poles [19], [245], [334]. However, the temporal separation method has been proposed for the purpose of performing the STFT method with only a single measurement and no calibration process [245]. Averaging of the spectrogram over a window of time is also used to enhance the dynamic range and robustness of the tag response detection. Although, there are still limitations with the STFT method, including fixed resolution in time and frequency, sensitivity to the window length, and limited performance in terms of distinguishing resonant frequencies when they are densely packed in the operational frequency band of the tag [334]. Overall, the STFT method has been shown to be more accurate, require fewer measurements, and require less computation time than the STMPM and MPM methods while still being able to extract the resonant frequency information in an aspect independent fashion [19], [193], [245], [329].
The STMPM and STFT methods can be classified as timefrequency approaches based on how their outputs are viewed and interpreted. Wavelet-based methods are another type of time-frequency approach. By employing the continuous wavelet transform (CWT) for a set of scaling factors and time translations a time-frequency plot with variable resolution in one domain and multi-resolution in another domain can be generated. This time-frequency plot, just like the ones for the other time-frequency approaches, gives information about the turn-on times and resonant frequencies. Similar to the MPM, this approach has the benefit of denoising the tag response since the CWT acts like a matched filter, but it can still struggle with the detection of densely-packed resonant frequencies due to its limited frequency resolution [244], [294], [295], [334]. In order to help with this, an adaptive wavelet method has been proposed that provides better resolution for high-frequency resonant frequencies while also helping to detect tags when they are attached to highly scattering objects [190], [292], [337]. While wavelet methods have been primarily applied for response detection and decoding in identification applications, they could also potentially be used for sensing applications.
While many methods are focused on determining resonance frequencies, there are additional methods that either consider the tag response more comprehensively or aim to extract other response features than the resonance frequencies in the RCS or S-parameter response. One such example is [308], where the goal is to find the zeros in the falling edge of the derivative with respect to frequency of the group delay. Another example is the use of Principle Component Analysis (PCA), which considers the full response of a tag under different conditions with multiple measurements taken under each condition. The data is then processed using SVD and principle components are generated. The principle components can be associated with different conditions [311], [325]. In [311], for example, PCA was used to detect and characterize cracks in metal samples. Machine learning based techniques have also been considered, including in [338] and [339] where quantile regression is used, in [325] where linear discriminant analysis is used, [43] that sends tag response data to a cloud database where various pattern recognition algorithms are applied for supervised learning purposes, and in [223] the Support Vector Machine approach is found to have the best performance among four machine learning approaches tested, to give just a few examples [207], [340], [341].

C. DECODING METRICS
As evidenced by this section, there are many different approaches for detecting and decoding chipless RFID tag responses. While some comparisons of the different methods have been attempted, they are not often one-to-one comparable due to factors, such as difference in reader hardware, tag design, reading distance, measurement environment (e.g., anechoic chamber vs. "real" environment and whether or not the tag is attached to a highly scattering object), and the design of validation experiments (i.e., the number of trials/measurements, whether misalignments and noise are considered, etc.). Additionally, many of the comparisons use subjective measurement metrics, such as ranking the complexity of a method on a low-medium-high scale, without providing definitions of these classifiers [19], [77], [292], [295], [313].
In terms of quantitative decoding performance metrics, the two most common ones are detection error rate (DER) and throughput. These are related to the number of successful response decodings [65], [305], [308], [322], [342]. However, what constitutes "success" tends to vary from one work to the next, and is not always explicitly stated. Thus, while in some cases a specific threshold, such as resonant depth of at least 5 dB, is used to define which bit a notch is coded with, in others a small fluctuation in the response could be considered a notch. This means that the same response could be decoded differently by different users and therefore, the frequency of success could vary between users [20]. Additionally, similar to other chipless RFID metrics (e.g., bit density, spectral density, coding capacity, etc.) successful decoding can also be dependent on the coding method or sensing parameter assignment method used [58].
DER, also referred to as the probability of error, is expressed as follows: In equation 11, N Failures represents the number of failed decodings while N Total represents the number of attempted decodings. It should be noted that DER considers whether or not the entire response is properly decoded, while probability of error can be used to describe both the probability of the whole response being decoded properly or individual bits being decoded properly. Throughput, also referred to as probability of detection, reading accuracy, success rate, and reliability, is the inverse of the DER. As such, throughput can be expressed as follows: DER and throughput can be evaluated as a function of reading distance and SNR, with a higher SNR corresponding to a higher throughput and therefore lower DER [77], [295], [305], [342]. An example of this is provided in Fig. 9 where probability of detection (i.e., the inverse of DER), is plotted as a function of SNR. In this case, as the SNR increases so does the probability of detection. Fig. 9 also demonstrates how different decoding methods perform in relation to each other [309]. DER and throughput have also been calculated over a reading volume in front of the reader antenna. In these cases, the throughput tends to be lower because there are measurements being considered where there are large tag/reader misalignments (i.e., <15% over the total volume as compared to the reported 90%-99% in [292] where the measurements are being made at the same location) [313], [343]. This is an example of how using the same metric does not necessarily mean that a one-to-one comparison can be made. The probability of false negative and probability of false positive have also been examined as metrics related to the probability of error [344], [345].
Another quantitative metric of interest is bit error rate/bit error ratio (BER). Rather than analyzing decoding performance based on whether or not the full response is properly decoded as in DER, BER considers the decoding performance on a bit-by-bit basis. This metric, unlike bit density and spectral density, considers the RCS level of the tag and provides a measure of the detectability of the tag. This is valuable because increasing the information stored in a tag is pointless if that information cannot be properly decoded. Similar to DER, BER can be calculated as a function of the SNR or clutter level and is also affected by the tag RCS, reading distance, coding method, and measurement setup [16], [346], [347]. Table 5 provides a list of the detection and decoding comparisons that have been made in the literature. Some of the comparisons in Table 5 perform the full comparison with the same measurement setup themselves (e.g., [309], [313], [322], [343]), while others compare the method they are proposing to methods that have proposed in other works (i.e., the measurement setup, tag, etc. varies among the works compared). Another thing to note from Table 5, is that some works refer to methods like background response subtraction and time gating as decoding methods, while other works may refer to these as calibration or pre-processing methods.

VI. MEASUREMENT AND DETECTION METHOD COMPARISONS
As evidenced in the previous sections, there is significant diversity in the ways chipless RFID measurements are performed, processed, and decoded. While the different system components are often compared to each other (i.e., reader antennas are compared to other reader antennas and postprocessing methods are compared to other post-processing methods), the full systems are not often compared to each other. Since, many factors (e.g., antenna gain, calibration method, detection criteria, reader architecture, frequency range, etc.) can play a role in the achievable reading distance and other metrics, like the DER or throughput, these component level comparisons do not necessarily paint a full picture.
This section aims to provide a brief comparison of implemented measurement and detection setups across several parameters, namely: the application, tag type, reader hardware, reader antenna hardware and configuration, polarization, measurement environment, calibration procedure, measured quantity, format the measurement was examined in, measurement frequency range, reading distance, decoding method, and the year published. Table 6 provides a non-exhaustive comparison with the entries being listed in chronological publishing order. The entries were selected to showcase a variety of different measurement and detection approaches. Interested readers can see the references associated with Figs. 4 and 6 for more examples of chipless RFID tag measurements [105].
In Table 6, similar to Figs. 4 and 6, the maximum distance at which the tag was successfully measured in each reference is reported. In comparing Figs. 4 and 6 and Tables 1-6, the following statements can be made about the chipless RFID measurement and decoding landscape at the current time: 1) most tags that are currently in the literature are designed to operate below 10 GHz, 2) most tags are measured with a VNA, 3) background subtraction is one of the most common calibration methods, 4) RCS and S-parameters are the measurement quantity of choice an approximately equal amount of time, 5) reading distances tend to be below 1 m for both co-polar and cross-polar tags, and 6) tags are measured in a bistatic configuration slightly more often than in a monostatic configuration.

VII. CONCLUSION
This work provided a review of chipless RFID measurement and response detection methods. Measurement quantities namely RCS and S-parameters, were compared and an overview of measurement approaches, which vary based on the tag type, desired reading distance, and available equipment, was also given. It was shown that despite there being theoretically higher read ranges, most tags are measured at distances below 1 m at this time. Additionally, many tags are designed to operate below 10 GHz to be compliant with various transmit power regulations. As such, the custom readers and reader antennas that have been designed also tend to operate below 10 GHz. Once the tag response has been measured, there are a wide variety of techniques that have been proposed to detect specific response features and decode the response. These techniques vary in complexity from averaging of multiple measurements to machine learning and can also be application specific. In order to compare system level performance, various metrics including the DER, throughput, and BER have been proposed and some comparisons among processing methods and systems have been attempted. However, due to the breadth and diversity in chipless RFID systems, making a comprehensive comparison is an ongoing challenge. In order to address this challenge, standardization efforts, including standard tags for comparison purposes along with specific benchmark tests that clearly define the success criteria, could be undertaken.