Waveguide Antenna Topologies for Distributed High-Frequency Near-Field Communication and Localization

High-frequency (HF) near-field communication (NFC) is an inherently short-range technology. However, the total capture volume can be increased with traveling-wave antennas. Here, we report on the analysis, design, and measurements of flexible waveguide antennas and discuss their performance for NFC and localization. The antennas comprise sections of coaxial transmission lines loaded periodically with field-generating inductive networks. Several topologies were compared to each other theoretically, and the best-performing candidate was selected to fabricate antennas between 5 and 48 m long, each containing 15 read nodes. Waveguiding properties of the antennas were measured and agreement with the theory was demonstrated. Afterward, each antenna was integrated with a custom NFC reader and shown to be capable of communication with and localization of commercial off-the-shelf transponders compliant with ISO/IEC 14443 Type A protocol. The transverse detection range was 10 cm with 1 W input RF power. Both 1-D and quasi-2-D configurations were tested. The proposed antennas are flexible, scalable, have low loss, and could be used for NFC, identification, and tracking of distributed and mobile tags.


Waveguide Antenna Topologies for Distributed
High-Frequency Near-Field Communication and Localization

I. INTRODUCTION
H IGH-FREQUENCY (HF) near-field communication (NFC) is a wireless technology that operates in the 13.56 MHz band and is used widely for asset management, access control, and secure payments [1]. A common embodiment contains an active reader that uses a magnetic near field to power and communicates with a passive transponder. Because near fields decay rapidly away from the reader and tag antennas, communication is inherently short-range. Range extension has been achieved with active transponders [2] or with higher-power readers [3], [4], but both methods are restricted by scaling laws.
The capture volume of loop antennas can be enhanced through geometry optimization [5], and further gains can be achieved by antenna arrays [6], albeit with additional hardware overhead. Arrangements allowing arbitrary tag orientations Manuscript [7], [8], and arrays with null zone compensation [9] have been demonstrated. Traveling-wave antennas have also been used for lateral increase of capture volume at no overhead cost to hardware complexity. The system presented in [10] was able to read off-the-shelf proximity tags compliant with ISO 14443 protocol along a 2.3-m-long antenna. The antenna was a section of magneto-inductive waveguide that comprised magnetically coupled resonant circuits [11], [12]. The read range perpendicular to the antenna was 50 cm with 10 W RF power. Further examples are magneto-inductive systems proposed for body-area networks [13], [14].
In addition to communicating with tags, large antenna systems may need to locate and track them. Potential applications include automated inventory management such as tracking of library books and warehouse contents, livestock monitoring, mobile robot pathfinding, and personnel or document tracking. The HF regime, however, offers limited possibilities for localization compared to ultra high frequency (UHF) radio-frequency identification (RFID) [15], [16], [17], which relies on radiative fields. Most research on HF positioning addresses the converse problem of localization of mobile objects within reference transponder grids. Such an object has often been a robot equipped with a single [18], [19] or multiple readers [20], [21], [22], [23], while the transponder distribution could be uniform or sparse [24]. Similar methods have been applied to identify the location and orientation of furniture [25]. When tag position was unknown, the localization methods have mostly been limited to scanning with moving antennas [26], [27], or multiplexed antenna arrays [28], [29], [30], [31]. One- [32] and 2-D [33] magnetic metamaterials have also been used to locate metallic resonators and wireless power devices.
Syms et al. [34] offered an alternative approach to localization, which relied on low group velocity in a magneto-inductive wave antenna. A signal generated by a transponder propagates in two opposite directions along the antenna. Receivers placed at both antenna ends detect the signals with a measurable delay, and the transponder position along the antenna can be estimated from the time-of-arrival (TOA) difference. This system can be upscaled by adding more elements to the waveguide antenna, without increasing the hardware overhead.
Unfortunately, magneto-inductive waveguides suffer from relatively high propagation loss and from layout restrictions imposed by the need to achieve high coupling strengths between resonant elements [35]. Both aspects limit potential  [36], [37] or electrically small resonators [38]. Therefore, waveguides that both support slow waves at HF and comprise inductors that couple to NFC transponders have potential as antennas. The aim of this article is to explore candidate waveguide antennas and demonstrate their use in NFC communication and localization. Table I compares existing solutions with the one proposed in this work.
Section II analyzes transmission lines made of coaxial cables loaded periodically with two-port inductive networks, discusses design criteria and tradeoffs, and selects a suitable antenna topology. Section III discusses measurements of antenna parameters and compares them to theoretical models. Sections IV and V present experimental results for NFC communication and localization using 1-D and quasi-2-D antennas. Section VI discusses system scalability. Section VII draws a conclusion.

II. DESIGN OF LTLS
This section provides a theoretical analysis of waveguide antennas formed by sections of transmission lines (such as coaxial cables) loaded periodically with lumped-element networks. The networks must contain inductors that generate a magnetic near field and can couple to an NFC device placed in their vicinity. We will refer to these networks as sensors and to the entire waveguides as loaded transmission lines (LTLs). In this article, we derive characteristic equations of LTLs and discuss how their properties can be optimized for HF near-field transponder localization.

A. Two-Port Cascades
First, we briefly state known properties of a periodic cascade of two-port networks shown in Fig. 1(a) [39]. The networks can be modeled by a 2 × 2 transmission matrix P = [A, B; C, D]. A current I n at an angular frequency ω flows into the nth network that has a voltage V n across its left-side terminals. The voltages and currents on either side of the two-port are related by This periodic structure can support waves, with voltages and currents satisfying relationships V n+1 = V n e − jks and I n+1 = I n e − jks , where k is the propagation constant, and s is the length of a network. Nontrivial solutions of (1) exist when Equation (2) is the dispersion relation for the two-port cascade. If P is reciprocal, then det P = 1, and (2) can be simplified as The propagation constant is generally complex and frequency dependent. However, if P is lossless, A and D are real, while B and C are imaginary. Propagation may only occur in passbands for which | cos(ks)| < 1, so that ℑ(k) = 0. Propagation is forbidden in stopbands, where k is purely imaginary. If a network contains lossy components, attenuated out-of-band propagation is allowed. The voltages and currents at any plane of the cascade are related by a characteristic impedance defined as The values of Z P are different for forward-and backwardwave propagation. In lossless symmetrical networks, Z P is real in the passband and imaginary in the stopbands.

B. Loaded Transmission Lines
We now consider the LTL shown schematically in Fig. 1(b). A unit cell is formed by a section of a coaxial cable of length d, followed by a reciprocal two-port network S = [A S , B S ; C S , D S ] of length a. Together they correspond to the earlier P.
The cable can be described as a lossy transmission line with an inductance per unit length L T and capacitance per unit length C T . The cable transmission matrix T is of the form where Z T is the cable characteristic impedance. The cable propagation constant is complex, γ = β − jα, with β ≈ ω √ L T C T . The unit cell of the LTL has a transmission matrix P = T S and a length s = d + a. Using (3) and (4), we obtain an LTL dispersion relation in the form The characteristic impedance of the LTL can be rewritten as C. Sensor Network Topologies Equations (6) and (7) model generic LTL waveguides, and candidate networks S should now be identified that are suitable for HF NFC, identification, and localization. Requirements are set by communication protocols, and we will use the common ISO 14443 standards for proximity cards [40]. The reader carrier frequency is f c = 13.56 MHz. In Type A systems, signals are transmitted from the reader to a transponder by amplitude modulation of the carrier using on-off-keying at a bit rate of f c /128 bit/s. The transponder responds by loadmodulation using sub-carriers separated from f c by f s = f c /16 at the same bit rate. The minimum bandwidth is BW = 2 f s + f c /32 = 5 f c /32 = 2.12 MHz, where the first term is the subcarrier separation, and the second is the approximate bandwidth required for Manchester encoded data transmission. If a waveguide antenna is used, its dispersion should be minimized to prevent signal distortion. On the other hand, the localization method of [34] relies on being able to detect the difference in arrival times of transponder signals. To maximize this difference, the group velocity of the waveguide should be minimized.   Sensor network candidates that include series/shunt impedances (i) and (ii), pi-sections (iii) and (iv), and t-sections (v) and (vi). be calculated from the idealized dispersion characteristic as where the numerator is in meters. The characteristic impedance over the passband must be real and equal to Z T , independently of the cable length used [ Fig. 2(b)]. Fig. 2 shows characteristics of a right-handed waveguide, but the arguments apply also to a left-handed one.
Such characteristics are unattainable in practice but can serve to assess practical sensor implementations. Possibilities are shown in Fig. 3, in the order of increasing complexity. The simplest LTL topologies comprise a shunt or a series impedance Z . The impedance itself can be either (i) a series or (ii) a parallel LC resonator. Topologies (iii) and (v) are, respectively, the standard lumped-element pi-and t-sections of right-and left-handed transmission lines. Topologies (iv) and (vi) are constructed from (iii) and (v) by adding another capacitor K . Analytical calculations presented in this section will assume lossless wave propagation; effects of loss will be considered in Section III.
For LTLs made of coaxial cables loaded with impedances Z in a series or a shunt configuration, we have A S = D S = 1. Cable sections of non-zero length are required for wave propagation. Equation (6) can be simplified as where r = Z /Z T for the series and r = Z T /Z for the shunt configurations. Fig. 4(a) shows the real part of the propagation constant and Fig. 4(b) shows the slow-wave factor for (i) series and (ii) parallel LC resonators connected in series and shunt configurations, respectively, with C T = 92 pF/m, L T = 230 nH/m, and Z T = 50 . In both cases, L = 2 µH, and the value of C is chosen to place the resonant frequency at 13.56 MHz. The cable length d is 4 m. Both cases exhibit a For both configurations, increasing the cable length narrows the passband and shifts it down in frequency. The effect is more pronounced at higher frequencies. For the series configuration, a larger value of L reduces the upper cut-off frequency but has little effect on the lower cut-off. Conversely, a larger value of L increases the upper cut-off frequency for the shunt configuration. The characteristic impedance Z 0 = Z T at f c for both configurations. Series loading with (i) favors high values of L, while shunt loading with (ii) requires impractically small L to achieve a similar SWF. Series (ii) and shunt (i) loads are not considered as they cannot have Z 0 = Z T within their passband at any frequency.
The LTL becomes a ladder network with cable interconnects when the sensors are formed by a pi-or a t-section shown in Fig. 3(iii)-(vi). Denoting k 0 as the propagation constant for a cascade of sensors with no cables, we can express the LTL propagation constant, k, in terms of k 0 , and the cable propagation constant, β. For a symmetric pi-or t-section, cos(k 0 a) = A S according to (3), and the characteristic impedance is Z S = B S /[ j sin(k 0 a)] according to (4), while C S = (A S D S − 1)/B S owing to reciprocity. Equation (6) can then be rewritten as Equation (9) shows that k ≈ k 0 for short cables, but long cables affect the value of k owing to the second term on the right-hand side of (9). The impedances Z S and Z T can always be made equal at a single frequency, for example, f c . Fig. 5 shows the dispersion curves and the slow-wave factor for cable sections of length d = 2 m. The pi-section (iii) has a low-pass response while the t-section (v) has a high-pass one. The presence of cable sections lowers the cut-off frequencies for both topologies. It also converts the high-pass response of a CL section (v) into a bandpass one. Topology (iii) offers good linearity if the cut-off frequency is sufficiently higher than the upper sideband frequency, but higher slow-wave factors may be achievable with (v) owing to its bandpass characteristic. The maximum inductor values of both (iii) and (v) are restricted by the simultaneous need to keep the sideband frequencies within the LTL passband and to match the impedances at f c .
All sensor topologies considered approximate to a different degree the ideal characteristics shown in Fig. 2. Series loading with (i) offers a bandpass response with good linearity and high SWF. However, this topology leaves little freedom for dispersion engineering since the value of C is restricted by matching requirements. The value of d can be restricted by the geometry of a specific application, and the value of L may be constrained by the need to generate magnetic fields. Topologies (iv) and (vi) have an additional degree of freedom offered by the capacitance K . Both topologies (iv) and (vi) have a bandpass response; topology (vi) supports backward waves and topology (iv) forward waves. Topology (iv), however, favors higher values of L.

D. Resonant LC Pi-Section
Of all the topologies considered, the pi-section (iv) in Fig. 3 is the closest match for the communication and localization requirements of Fig. 2, and it offers the largest design freedom. Fig. 6 shows calculated frequency variations of (a) dispersion, (b) slow-wave factor, and (c) and (d) real and imaginary parts of the characteristic impedance for several values of cable length d. The LTL is perfectly matched to Z S = Z T = 50 at f c independently of d. The matching condition is given by where ω c = 2π f c . Capacitance K introduces an additional degree of freedom, allowing L and C to be set independently to tailor dispersion while retaining matching at f c if (10) is satisfied. The cable length affects the cut-off frequencies and the group velocity. Because longer cables reduce the original passband and shift it to lower frequencies, practical cable lengths are limited by the need to accommodate the NFC frequencies inside the passband. If Z T = Z S at f c , then ks = βd + k 0 a according to (9), and expressions for the group velocity and SWF at f c can be derived as Equations (11) and (12) suggest that in a matched antenna the total slow-wave effect is the sum of individual contributions from the cables and the sensors.

III. EXPERIMENTAL CHARACTERIZATION OF LTLS
This section describes the fabrication and experimental characterization of LTL waveguides with resonant LC pi-section sensors. Three waveguides were made by cascading 15 identical sensors with coaxial cables of three different lengths, 0.3, 1.22 (4 ft), and 3 m. Fig. 7 shows a photograph of a section of an assembled LTL, together with the equipment (a PC, electronics for signal transmission, an oscilloscope for signal reception and filters for signal separation) used in communication and localization experiments described in Sections IV and V. Table II shows the component values, the equivalent sensor circuit, and the cable parameters. The inductance L was formed by a three-turn square spiral with rounded corners, made from 1/8" soft copper pipe that was bent to shape and held in place using 3-D-printed acrylonitrile butadiene styrene (ABS) mounts. The spiral had a width of W = 130 mm and a winding separation of 5 mm. The quality factor was measured as ≈250 using a vector network analyzer (Keysight E5061B) connected to two small inductive probes coupled to the assembled inductors. In these experiments, the inductors were loaded with capacitors, so that the resonant frequency was equal to f c .
A printed circuit board of a width of 30 mm was then inserted laterally into the plastic mount and served to interconnect the three inductive windings and the capacitors forming C and K , as well as to provide SMA connections to coaxial cables. Capacitance K was implemented using a symmetrical pair of 2K capacitors and a small varicap for precision impedance matching at f c . The parasitic capacitance C p was found as 4.1 pF across all inductors. The component values were chosen to optimize the LTL characteristics for a cable length of d = 1.22 m. To demonstrate that the waveguide topology offered significant design freedom, shorter and longer cables were also used, without changing the sensors. All three sets of cables had characteristic impedances of 50 , with RG-174 Telegartner used for the short (0.3 m) cables, and  The sensors were individually tuned to minimize reflectivity at f c as measured by the network analyzer. Subsequently, the cable interconnects were introduced, and the scattering parameters of the entire LTL were measured. With 15 sensors, the total waveguide lengths were 5.25, 20.0, and 48.5 m for the small, medium, and long cables, respectively. The number of elements was chosen to be large enough so that effects of dispersion and loss could be observed. Having an odd number of elements provided a convenient midpoint for the localization experiments described in Sections IV and V. Fig. 8(a) compares the theoretical propagation constant calculated using (6) (dashed lines) with measured data (crosses). Fig. 8(b) shows the measured group delay. Fig. 8(c)-(h) show the measured (solid lines) and theoretical (dashed lines) S-parameters. The results for the short cables are shown in blue, for the medium-long cables in red, and for the long cables in green. The theoretical curves were obtained by first computing the equivalent transmission matrix for each of the three antenna configurations as P N T with N = 15, followed by an S-parameter conversion. Excellent agreement is seen across the figures. The slight deviations in S 21 below the lower cut-off for short and medium cables can be attributed to cable effects and have been eliminated for long cables by placing ferrimagnetic rings to impede current flow on the outside surfaces of the cable shields. As expected, longer cables both reduce and shift the passband lower in frequency. Good matching is retained at f c regardless of the cable length. The measured group delay is flat between the two sidebands for the medium-long cables but is sloping for the short and long cables. Despite performance degradation for the short and long cables, all three cable lengths are suitable for NFC Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. applications. The loss at f c is 0.35, 0.15, and 0.12 dB/m for the short, medium-long, and long cables, respectively. The higher value for the short cables is caused by a higher relative contribution of the sensors. The same behavior can be observed for the group delay, which is dominated by the slow wave effect of the sensors. While the group delay can be improved by reducing the passband, doing so would restrict the range of possible cable lengths.

IV. NEAR-FIELD LOCALIZATION WITH 1-D ANTENNAS
This section discusses experiments on the localization of NFC transponders by TOA difference. The localization method was introduced in [34]. Fig. 9 shows a functional block diagram of the system; the previous Fig. 7 shows a photograph. An ISO/IEC 14443 Type A compliant tag was placed next to one of the sensors along the antenna. A custom reader, capable of transmitting and receiving a subset of signals according to ISO/IEC 14443 Type A protocol, injected an HF carrier at one end of the antenna using a frequency-selective filtercoupler [41]. The carrier propagated along the antenna, and the current circulating in the spiral inductors generated magnetic near fields. The other end of the antenna was connected to an identical filter-coupler.
The reader then sent a unique identifier (UID) query (in modified Miller code, using amplitude shift key carrier modulation). The tag transmitted its UID by sub-carrier load modulation (in Manchester code). The tag response propagated toward both ends of the antenna, where the filter-couplers extracted the carrier signal, and the UID response was acquired by two receivers, each applying residual carrier and out-ofband noise suppression filters followed by rectification and low-pass filtering for UID demodulation. After a pair-wise cross correlation on the baseband UID responses, the TOA difference t = t 2 − t 1 was calculated from the crosscorrelation peaks. The theoretical value of the LTL group velocity v g at sideband frequencies was then used to convert t into a physical tag position estimate P est = P m − t · v g , where P m = (1 + N )/2 is the midpoint sensor position, and N = 15 is the total number of elements in the LTL.
The reader transmitter comprised a pair of phase-locked function generators and an RF switch (Mini-Circuits ZASWA-2-50DRA+). One generator (TTi TG4042) was used for the HF carrier, and the other (TTi TG5012A) was used for modulation sequences. A 1 W amplifier (Mini-Circuits ZHL-2-8) amplified signals before injection into the LTL antenna. The tag responses were acquired with a digital oscilloscope (Keysight InfiniiVision DSOX3024T, sampling rate 1.25 GSa/s), while noise suppression, demodulation, and cross correlation were done in MATLAB using a PC. The matched filter couplers were custom-made using magnetoinductive waveguide sections and had a complementary bandpass-bandstop response at the carrier frequency [41]. Tags were placed above the midpoint of a spiral inductor, and tag-to-antenna separation was fixed by dielectric spacers. Fig. 10 shows an error in tag position estimation (e = P est − P) for each node index P over a range of sensor-tag separation distances using 1 W HF carrier power. Fig. 10(a)-(c) are for the antennas made with short, medium-long, and long cables, respectively. Each data point (circle) corresponds to a single TOA measurement using a Mifare 1 K Classic card-type tag with UID 0xF38AE495 and dimensions 85×55 mm. For all waveguides, the tag position was determined correctly (|e| < 0.5) over a sensor-tag separation from 1 to 10 cm, so that the correct position index could be obtained by rounding P est to the nearest integer. The variation in e is the smallest for the medium-long cables and largest for the long cables. The results conform to expectations based on the measured antenna dispersion characteristics and scattering parameters (Fig. 8) and based on the fact that the sensors were optimized for the medium-long cables.
The tag UID could be decoded correctly for separations below 11 cm. Each waveguide demonstrates a consistent error profile, which marginally deteriorates for larger separations. These results suggest that the error variability is inherent to the antennas and not caused by noise. Tags with different  UIDs showed comparable error variation. Smaller tags (such as 1-in diameter fobs) had expectedly shorter detection ranges, but produced the same error variability profiles. If multiple transponders were present along the antenna, ISO/IEC 14443 Type A anticollision protocols could be used to sequentially request transponder UIDs for positioning. Fig. 11(a) shows probability density functions (pdfs) fit using normal distributions to 100 samples of P est at each node with the tag placed directly on top of a sensor, using 1 W carrier power, and the antenna with the medium-long cables. The position estimates are both highly consistent and resistant to background noise, as is evident from the extremely narrow distributions. There was negligible change in mean values and a marginal increase in variances for larger tag separations. Fig. 11(b) and (c) show pdfs fit using 100 position estimates at the first node for the antennas with the short and long cables, respectively, over a range of sensor-tag separations. For both antennas, the uncertainty in P est increases with separation, owing to reduced signal-to-noise ratio (SNR). A slight upward shift in the pdf mean values can be seen, consistent with Fig. 10. The shift can be attributed to a slight variation in waveguide group delay caused by weaker antenna loading by a more distant tag. The effects of changing the tag-to-antenna range were more pronounced for suboptimal cable length. Nevertheless, the variance was still low at all nodes which guaranteed accurate positioning.

V. NEAR-FIELD LOCALIZATION WITH QUASI-2-D ANTENNAS
This section extends the discussion of tag localization to quasi-2-D antennas. These were formed by rearranging an LTL into a 2-D grid while maintaining sequential cable interconnects. Fig. 12(a) shows an LTL forming a planar 4 × 4 grid, in which each row was connected to the next, and the inductor centers are separated by distance h. Coupling coefficients κ = 2M/L and κ ′ = 2M ′ /L were defined, where M was the mutual inductance between a pair of nearest neighbors, and M ′ was the mutual inductance between a pair of diagonal neighbors. Fig. 12(b) shows how measured values of the coupling coefficients decay with increasing normalized distances h/W. For h/W > 1.456, |κ| < 0.03, and κ ′ was negligibly small, so that the quasi-2-D antenna can be expected to perform like a 1-D one. Fig. 13 shows scattering parameters, group delay, and per-element phase advance of the 2-D grid with d = 1.22 m. As the element separation h increased from 19 to 26 cm, the value of S 11 at the carrier frequency was reduced by 10 dB, while the value of S 21 increased by 0.8 dB. Similarly, the variation of the group delay between the sideband frequencies reduced as h increased. Further reductions in h resulted in significantly poorer matching and group velocity dispersion, while further increases saw scattering parameters converge to those of the 1-D antennas shown in Fig. 8. Presumably, the effects at small h are caused by non-nearest neighbor coupling [42]. Fig. 14 shows error variation in estimated tag positions for the 2-D grid over the same range of h. Fig. 14(a) shows e for a card-type tag with UID 0xF38AE495 at 1 cm range, while Fig. 14(b) is for a fob-type tag with UID 0x010D354A placed directly on top of the inductors. Both tags could be correctly located at all positions for h ≥ 19 cm. The fob tag  on average saw a slight reduction in location error compared to the card tag, caused by a weaker antenna loading by a smaller fob. Stronger loading may introduce local variations of group velocity in the antenna around the contact point owing to asymmetry, thus resulting in higher errors. The shape of the error variation profiles was again nearly identical for the two tags, suggesting the errors were determined by local group velocity variations within the antenna. Tags placed between inductors could not be accurately located but could still be read.

VI. SYSTEM SCALABILITY
The lengths of our waveguide antennas were limited by the constraints of a laboratory experiment. This section discusses achievable antenna sizes. A limit will be imposed by waveguide attenuation and dispersion, which corrupt signals generated by tags. The effects were simulated in MAT-LAB 1 using a model adopted from [34]. A tag injected an amplitude-modulated signal s(t) = sin(2π f c t)[1 + m(t)] into the nth element of the antenna, where m(t) is the 1 Registered trademark. subcarrier-modulated tag UID encoded in Manchester code according to the ISO/IEC14443 Type A protocol. The message signal was generated as m(t) = a m u(t) sin(2π f c t/16), where u(t) was the binary UID signal, and a m the amplitude. The tag signal s(t) was then propagated to both ends of the antenna, taking antenna loss and dispersion into account, and uncorrelated white noise n(t) was added to the signals prior to filter-couplers (see Fig. 9). A sampling rate of 8 f c was used, and the tag UID was 0x010D354A. The SNR was defined as where f (t) is the impulse response of the filter-couplers, J is the number of samples, and the asterisk represents linear convolution. The SNR, so defined, describes the ratio of the power of the tag signal at the entry to the waveguide to the noise power within the passbands of the filters. The signal power at each end is generally different, and such a definition avoids the need for two SNR values. For antennas with large N , high SNR may be needed to offset propagation losses. The maximum antenna length was determined by requiring that the tag localization error does not exceed half an element. Fig. 15 shows localization error against tag position for d = 1.22 m. Fig. 15(a) assumes no noise, and the error profile is anti-symmetric around the midpoint sensor, where the error is zero. The exact shape arises owing to the combined effect of dispersion and smoothing during tag response downconversion. The error was maximum for tags at antenna extremes because only one of the outputs was affected by dispersion. Fig. 15(b) and (c) shows localization error in the presence of receiver noise, with SNR of 30 and 25 dB, respectively. The maximum achievable line length became shorter as SNR was reduced, with the error once again being highest at antenna ends. The effect became more pronounced for antennas with higher loss. The maximum number of sensors for each configuration was 265, 171, and 135, respectively. Correlated noise, such as radio frequency interference picked up by sensors, is not included in the simulation, but its effects have been discussed previously [34].  Table III gives an overview of the other cable lengths used and different values of SNR. As can be expected, the optimized geometry with 1.22-m cables performs the best, and antennas exceeding 100 elements are feasible for the values of SNR above 20 dB. At low SNRs, tags could still be located but their UIDs could no longer be read correctly. This is explained by higher processing gain in UID cross correlation, as opposed to the bit-wise correlation required for UID decoding. Achieving high values of SNR as well as being able to power tags via long lossy antennas would require increased carrier powers.

VII. CONCLUSION
Our experiments and theoretical analysis suggest that the waveguide topologies considered in this article can be employed for practical NFC systems that require communication with and localization of distributed transponders, using a single set of electronics. The maximum antenna length realized experimentally was 48 m, and theoretical estimates show that antennas of several 100 s of meters are feasible with favorable SNR. The maximum read node separation demonstrated here was 3 m. This separation can be increased to system dimensions by interspersing functional and nonfunctional nodes, in the process allowing the functional nodes to be irregularly spaced. A simple learning algorithm may then be used to identify the functional nodes. In contrast to multiplexed antenna systems, increasing the number of read nodes carries no hardware overhead. The antennas are flexible and can be arranged in different shapes, as demonstrated by a quasi-2-D grid arrangement. Furthermore, localization to the nearest node was found to be accurate irrespective of the range or tag type used, provided the field was strong enough to power the tag.
The localization method used is based on comparing the TOA of tag signals reaching both ends of an antenna. The antennas were consequently optimized for low group velocity, with the associated drawback of increased propagation loss. Scenarios that do not require tags to be localized impose less stringent requirements on waveguiding properties of antennas, which could as a result be made longer and rely on simpler topologies. On the other hand, the need to extract signals from both antenna ends limits deployment options by requiring lengthy return cables and two receivers. Single-ended localization systems may offer additional flexibility with sensor layout, reduce system complexity, and remove the need for a return cable. The feasibility of such systems should be assessed in future work.