**3. Wideband UHF RFID positioning system**

This section introduces a brief motivation for the realized RFID positioning system before describing the basic structure of the system.

As derived from Section 2, current passive RFID localization systems suffer either from a high effort in the calibration phase (fingerprinting) or from bandwidth limitations which hold down the system's overall accuracy. Higher accuracies may be achieved using phase-based ap‐ proaches at the expense of more complex hardware structures and necessary volume (see, for instance, phased array antennas [43]), only usable for fixed reader hardware. Therefore, an ideal passive mobile RFID positioning system should have:


*f* mod =300 kHz and is driven by a 2.45 GHz FMCW signal with a bandwidth of 75 MHz. The system is tested on a cable-based setup and delivers an RMSE of 1 cm with cable lengths

The system in [32] uses the phase difference observed at different frequencies to estimate the range between transponder and reader. The range estimation is performed according to Equation (16), whereas the maximum range *d*max due to phase ambiguities is given with

However, the choice of the bandwidth B strongly influences the system's capabilities. A high B generates a high accuracy but a low maximum range; a low B leads to a higher range but at the expenses of a lower accuracy. Simulations at an SNR of 10 dB results in errors of 2.5 m for a frequency separation of B=1 MHz, and errors of 0.1 m for a B of 26 MHz. One has to keep in mind that the separation of 26 MHz is only valid within the US frequency band for RFID that ranges from around 902 MHz to 928 MHz. The European band is smaller (865.6 MHz to 867.6

LANDMARC [33] is an extension and improvement of the SpotON system [25, 34]. The system consists of fixed RFID readers, active reference tags (landmarks) and tags to be localized. The system uses RSS values connected with the kNN (k-nearest neighbor) algorithm [35] to

[36] examines the localization error of the LANDMARC system using passive, instead of active RFID tags. As a result, the orientation of the tags has a major influence on the total performance of the system. Using the kNN algorithm, in 47.5 % of the cases, the error was less than 0.5 m and in 27.5 % of the cases, the error was less than 0.3 m. However, in comparison to the original LANDMARC system, the overall range is smaller due to the usage of passive RFID technology.

A system based on a particle filter is proposed in [37]. It uses two RFID readers mounted on a small mobile vehicle to localize itself using RSS values. The calibration phase is performed in a room of size 5 m × 10 m. Depending on the speed of the vehicle and the material on which the tags are located (plastics, concrete, metal) the average error is between 1.35 cm and 2.48 cm. This system is based on the mobile robot system in [38] that incorporates a SLAM algorithm

[41] describes a positioning system using fingerprints (RSS values and read rate) to localize tagged objects. First, a rough positioning is done using antenna cells, with each antenna illuminating a different room zone. This rough classification is realized using either Bayesian filter, kernel density estimation (KDE) based measurement models, support vector machines (SVM) or LogitBoost [42]. RSS-based values and read rate is used along with the algorithms to roughly estimate the position of the tagged object. One result was that the estimations based on RSS values perform better than the estimations based on the read rate. An even more

estimate the position. The average error of the system is given with 1 m [33].

2B . (19)

*<sup>d</sup>*max <sup>=</sup> *<sup>c</sup>*

between 1 m and 9.5 m.

94 Radio Frequency Identification from System to Applications

MHz) leading to a lower accuracy.

*2.2.5. Scene-based range estimation*

[39] based on Monte Carlo methods [40].

**•** direct position estimation.

The here proposed system offers high bandwidth, but with very low power, and is based on a ToA method performing direct position estimation. As a consequence, additional hardware effort is necessary to provide the generation and evaluation of the high bandwidth signals.

In the following, a brief overview of the system, particularly its principle working structure, is provided.

Assuming a scenario as given in Figure 5. The scenario consists of *n* tags, whereby the distance to the *i*th tag has to be evaluated. The RFID reader is indicated at the bottom (only the coupler with antenna in monostatic mode) with input signal *x*reader (into the antenna) and output signal *y*reader (from the antenna). s1 to sn describe the backscatter modulation factors of the trans‐ ponders, i.e., the factor with which the incoming signal from the reader is reflected with (principle of backscatter). If this factor is one, the complete signal is backscattered to the reader. Indeed, data from tag to reader is transmitted by varying this factor in time with the data to be sent [10, 44]. h1 to hn describe the bidirectional channel impulse responses between reader and tags. For reasons of simplification the following equations and terms are written without using the time *t*, although the expressions depend on it.

**Figure 5.** Scenario with passive RFID tags and reader in monostatic antenna setup

According to Figure 5 we can state (in time domain) by using the convolution ∗ :

$$\mathbf{y}\_{\text{reader}} = \mathbf{f}\left[\mathbf{h}\_1 \ast \mathbf{s}\_1\right] + \left(\mathbf{h}\_2 \ast \mathbf{s}\_2\right) + \dots \ + \left(\mathbf{h}\_i \ast \mathbf{s}\_i\right) + \dots \\ \ + \left(\mathbf{h}\_n \ast \mathbf{s}\_n\right) + \mathbf{h}\_{\text{Env}}\ \ \mathbf{J} \ast \mathbf{x}\_{\text{reader}}\tag{20}$$

For simplicity, let us assume that each backscatter modulation factor si has two modulation states according to

$$\mathbf{s}\_{i} = \begin{vmatrix} \mathbf{s}\_{i,1} & \text{for modulation state 1} \\ \mathbf{s}\_{i,2} & \text{for modulation state 2} \end{vmatrix} \tag{21}$$

thus, taking the difference results into observation of the *i*th tag with the *i*th channel. By assuming that the tag's data contain the position of the tag (i.e., a reference tag), the reader has to evaluate the *i*th channel, regarding the range, to estimate the distance between reader and *i*th tag. In a 2D scenario, three tags must be read to get the position data, and three channels to the tags must be evaluated in order to localize the reader itself. The principle is described

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97

**Figure 6.** Experimental hardware architecture of the realized RFID localization system based on passive UHF RFID tags

The frequency-coupled RF signal generators generate carrier signals at the center frequency of *f <sup>c</sup>* =900 MHz. The arbitrary waveform generator (AWG) creates the localization signal *x*reader (in baseband). After upconversion of the localization signal, it is filtered, amplified and emitted into the environment through the antenna. The backscattered signal from the tag, the envi‐ ronment, and all other tags which may be in read range is also amplified, filtered and down‐ converted into complex baseband. The baseband signals are low-pass filtered and sampled with an oscilloscope, as is the original transmitted localization signal. Further processing is

Based on the result of the last equation (24) in Section 3, it is necessary to evaluate the channel

3 the localization should be performed using direct distance estimation, thus, the signal's time of flight *t* has to be evaluated in order to determine the distance *d* with the help of the

with *c* usually being the propagation speed of electromagnetic waves complying to the speed of light. The factor one-half is introduced to compensate for the double distance the signal has

*<sup>d</sup>* <sup>=</sup> <sup>1</sup>

regarding the distance between tag and reader. As stated at the beginning of Section

<sup>2</sup> *c* ⋅ *t*, (25)

The experimental hardware architecture of the reader is shown in Figure 6.

realized in MATLAB. Exemplary signals are shown in Section 6.

**3.1. Derivation of the localization principle**

to travel, i.e., from the reader to the tag and back.

response hi

propagation speed *c*, i.e.,

in more detail in Section 4.

In a first attempt, all tags are set into modulation state 1. The resulting signal *y*reader,1 is

$$\mathbf{y}\_{\text{reader},1} = \left[ \mathbf{f} \mathbf{h}\_1 \ast \mathbf{s}\_{1,1} \right] + \left( \mathbf{h}\_2 \ast \mathbf{s}\_{2,1} \right) + \dots + \left( \mathbf{h}\_i \ast \mathbf{s}\_{i,1} \right) + \dots + \left( \mathbf{h}\_n \ast \mathbf{s}\_{n,1} \right) + \mathbf{h}\_{\text{Env}} \right] \ast \mathbf{x}\_{\text{reader}} \tag{22}$$

In a second attempt, only tag #*i* is set into modulation state 2, all other tags stay in modulation state 1. This can be described as one small sequence of data transmission from the *i*th tag to the reader (uplink). The resulting signal *y*reader,2 is

$$\mathbf{y}\_{\text{reader},2} = \left[ \mathbf{f} \mathbf{h}\_1 \ast \mathbf{s}\_{1,1} \right] + \left( \mathbf{h}\_2 \ast \mathbf{s}\_{2,1} \right) + \dots + \left( \mathbf{h}\_i \ast \mathbf{s}\_{i,2} \right) + \dots + \left( \mathbf{h}\_n \ast \mathbf{s}\_{n,1} \right) + \mathbf{h}\_{\text{Env}} \right] \ast \mathbf{x}\_{\text{reader}} \tag{23}$$

The difference Δ*y*reader between both resulting signals *y*reader,1 and *y*reader,2 is

$$
\Delta y\_{\text{reader}} = y\_{\text{reader},2} \cdot y\_{\text{reader},1} \\
= \left[ \left( \mathbf{h}\_{\text{i}} \ast \mathbf{s}\_{\text{i},2} \right) \cdot \left( \mathbf{h}\_{\text{i}} \ast \mathbf{s}\_{\text{i},1} \right) \right] \ast \mathbf{x}\_{\text{reader}} \\
= \left[ \mathbf{s}\_{\text{i},2} \cdot \mathbf{s}\_{\text{i},1} \right] \ast \mathbf{h}\_{\text{i}} \ast \mathbf{x}\_{\text{reader}} \\
\tag{24}
$$

thus, taking the difference results into observation of the *i*th tag with the *i*th channel. By assuming that the tag's data contain the position of the tag (i.e., a reference tag), the reader has to evaluate the *i*th channel, regarding the range, to estimate the distance between reader and *i*th tag. In a 2D scenario, three tags must be read to get the position data, and three channels to the tags must be evaluated in order to localize the reader itself. The principle is described in more detail in Section 4.

The experimental hardware architecture of the reader is shown in Figure 6.

**Figure 6.** Experimental hardware architecture of the realized RFID localization system based on passive UHF RFID tags

The frequency-coupled RF signal generators generate carrier signals at the center frequency of *f <sup>c</sup>* =900 MHz. The arbitrary waveform generator (AWG) creates the localization signal *x*reader (in baseband). After upconversion of the localization signal, it is filtered, amplified and emitted into the environment through the antenna. The backscattered signal from the tag, the envi‐ ronment, and all other tags which may be in read range is also amplified, filtered and down‐ converted into complex baseband. The baseband signals are low-pass filtered and sampled with an oscilloscope, as is the original transmitted localization signal. Further processing is realized in MATLAB. Exemplary signals are shown in Section 6.

#### **3.1. Derivation of the localization principle**

**Figure 5.** Scenario with passive RFID tags and reader in monostatic antenna setup

*y*reader= (h1∗s1) + (h2∗s2) + … + (hi∗si

96 Radio Frequency Identification from System to Applications

si={

the reader (uplink). The resulting signal *y*reader,2 is

states according to

According to Figure 5 we can state (in time domain) by using the convolution ∗ :

For simplicity, let us assume that each backscatter modulation factor si has two modulation

si,1 for modulation state 1

In a first attempt, all tags are set into modulation state 1. The resulting signal *y*reader,1 is

*y*reader,1 = (h1∗s1,1) + (h2∗s2,1) + … + (hi∗si,1) + … + (hn∗sn,1) + hEnv ∗ *x*reader (22)

*y*reader,2 = (h1∗s1,1) + (h2∗s2,1) + … + (hi∗si,2) + … + (hn∗sn,1) + hEnv ∗ *x*reader (23)

Δ*y*reader= *y*reader,2 - *y*reader,1 = (hi∗si,2) - (hi∗si,1) ∗ *x*reader= si,2 - si,1 ∗hi∗ *x*reader, (24)

The difference Δ*y*reader between both resulting signals *y*reader,1 and *y*reader,2 is

In a second attempt, only tag #*i* is set into modulation state 2, all other tags stay in modulation state 1. This can be described as one small sequence of data transmission from the *i*th tag to

) + … + (hn∗sn) + hEnv ∗ *x*reader (20)

si,2 for modulation state <sup>2</sup> (21)

Based on the result of the last equation (24) in Section 3, it is necessary to evaluate the channel response hi regarding the distance between tag and reader. As stated at the beginning of Section 3 the localization should be performed using direct distance estimation, thus, the signal's time of flight *t* has to be evaluated in order to determine the distance *d* with the help of the propagation speed *c*, i.e.,

$$d = \frac{1}{2} \ c \cdot t,\tag{25}$$

with *c* usually being the propagation speed of electromagnetic waves complying to the speed of light. The factor one-half is introduced to compensate for the double distance the signal has to travel, i.e., from the reader to the tag and back.

In order to have a high positioning accuracy the signal must be broad regarding bandwidth, but the free spectrum for RFID, especially in Europe, is too small for that application. Therefore, higher out-of-band frequencies must be used. However, due to legal regulations, high bandwidth signals must be very low power, if applied. Ultra-wideband (UWB) signals [45] are such kind of signals and regulated by the Federal Communications Commission (FCC) and its counterparts in other regions, in order not to disturb any other in-band applications. UWB signals are defined as signals with bandwidths greater than 500 MHz or 20 % of the arithmetic mean of lower and upper cutoff frequency. The bandwidth used for the proposed system is 100 MHz due to the capability of UHF RFID tags working worldwide from around 840 MHz up to 960 MHz. Based on these conditions, although the proposed system only occupies 11 % of the arithmetic mean of the cutoff frequencies, the idea is to use low-power spreading signals for the ranging process. These signals are used to calculate the channel to a specific tag and back, thus extracting the time of flight information. As the low-power signals are hard to evaluate directly, the SNR is increased by performing coherent integration [46].

**3.3. Example**

shifted signal:

Let us derive the principle at a simplified example. Assuming the channel of the *i*th trans‐

with *a* representing the reciprocal of the attenuation, *δ t* - *T*delay the time delay *T*delay of the channel with the Dirac delta function *δ t* , and an initial phase shift of *φ*0. Furthermore, the transponder modulation states si,1 and si,2 are given with 0 (full tag absorption) and 1 (full tag

, (27)

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99

Localizing with Passive UHF RFID Tags Using Wideband Signals

*<sup>φ</sup>*0<sup>∗</sup> *<sup>x</sup>*reader <sup>t</sup> <sup>=</sup>

. (28)

*hi <sup>t</sup>* <sup>=</sup>*<sup>a</sup>* <sup>⋅</sup>*<sup>δ</sup> <sup>t</sup>* - *<sup>T</sup>*delay <sup>⋅</sup> *<sup>e</sup> <sup>j</sup>φ*<sup>0</sup>

<sup>=</sup>*<sup>a</sup>* <sup>⋅</sup>*<sup>δ</sup> <sup>t</sup>* - *<sup>T</sup>*delay <sup>⋅</sup> *<sup>e</sup> <sup>j</sup>φ*0<sup>∗</sup> *<sup>x</sup>*reader *<sup>t</sup>*

*<sup>x</sup>*reader *<sup>t</sup>* ⋅Δ*y*reader *<sup>t</sup>* <sup>=</sup> *<sup>x</sup>*reader <sup>t</sup> <sup>⋅</sup> (*<sup>a</sup>* <sup>⋅</sup>*<sup>δ</sup> <sup>t</sup>* - *<sup>T</sup>*delay <sup>⋅</sup> *<sup>e</sup> <sup>j</sup>φ*0<sup>∗</sup> *<sup>x</sup>*reader <sup>t</sup> ) (29)

*x*reader t - *T*delay =*δ t* - *T*delay ∗ *x*reader t (30)

*<sup>x</sup>*reader *<sup>t</sup>* ⋅Δ*y*reader *<sup>t</sup>* <sup>=</sup>*<sup>a</sup>* <sup>⋅</sup> *<sup>e</sup> <sup>j</sup>φ*<sup>0</sup> <sup>⋅</sup>*Rx*reader *<sup>τ</sup>* - *<sup>T</sup>*delay (31)

<sup>⋅</sup>|*Rx*reader *<sup>τ</sup>* - *<sup>T</sup>*delay <sup>|</sup><sup>2</sup> =|*a*|<sup>2</sup> <sup>⋅</sup>|*Rx*reader *<sup>τ</sup>* - *<sup>T</sup>*delay <sup>|</sup><sup>2</sup> (32)

{|*a*|<sup>2</sup> <sup>⋅</sup>|*Rx*reader *<sup>t</sup>* - *<sup>T</sup>*delay <sup>|</sup>2} (33)

The convolution of *x*reader t with the time-shifted Dirac impulse *δ t* - *T*delay delivers a time-

The correlation of *x*reader t - *T*delay with the original reader signal *x*reader t results in a time-

The wanted time delay *T*delay is evaluated by searching for the the maximum within the term

Performing the square of the absolute value to Equation (31), finally, leads to

Δ*y*reader *t* = si,2 - si,1 ∗hi *t* ∗ *x*reader t = 1 - 0 ∗*a* ⋅*δ t* - *T*delay ⋅ *e*

ponder is noise-free and multipath-free given with just

reflection). Equation (24) may now be written as

Performing the correlation to Equation (28) leads to

shifted cross-correlation signal *Rx*reader *τ* - *T*delay :

<sup>|</sup>*x*reader *<sup>t</sup>* ⋅Δ*y*reader *<sup>t</sup>* <sup>|</sup><sup>2</sup> =|*a*|<sup>2</sup> <sup>⋅</sup>|*<sup>e</sup> <sup>j</sup>φ*0|<sup>2</sup>

*<sup>T</sup>*delay =argmax *<sup>τ</sup>*


#### **3.2. Mathematical model**

Drawing up on Section 3, Equation (24), one can see that it is possible to derive the channel's impulse response upon evaluating the difference between both modulation states of the RFID transponder. Necessary for calculating the distance between tag and reader is the signal propagation time *t* of the up- and downlink channel. Multiplying half of *t* with the propagation speed results into the distance *d* between tag and reader (Equation (25)). As the bandwidth is limited to 100 MHz (Subsection 4.1), the pulse width is 10 ns minimum. Accordingly, a pulse width of 10 ns corresponds to a distance of around 3 m, supposing the speed of light in air is approximately 30 cm per nanosecond. Furthermore, the distance to be covered by this passive localization system is limited to the distance passive RFID tags are able to handle, which is, currently, limited to around 8 m [47]. In addition, the transmitted signal consists of more than one single pulse. These conditions lead to the fact, that the transmit signal and the receiving signal cannot be separated in time, as in ordinary RADAR applications. Another alternative is the principle of correlation, that can be used to determine the time shifted replica of the transmit pulse signal within the receiving signal [48]. The discrete correlation *Rxy τ* between two signals *x t* and *y t* is given with

$$\mathbf{R}\_{xy}\mathbf{I}\boldsymbol{\tau}\mathbf{J} = \sum\_{k=\omega}^{+\omega} x\mathbf{I}\boldsymbol{k}\mathbf{J} \cdot y\mathbf{I}\boldsymbol{\tau} + k\mathbf{J} = x\mathbf{I}\boldsymbol{t}\mathbf{J} \cdot y\mathbf{I}\boldsymbol{t}\mathbf{J}.\tag{26}$$

The correlation term shows the time-shifted replicas of the signal *x t* within the signal *y t* . A local maximum within the correlation term means a high correlation between *x t* and *t* , i.e., a high linear match. The point in time of the maximum shows the time shift between *x t* and *y t* , that is used to calculate the time between transmitted signal *x t* and received signal *y t* .

#### **3.3. Example**

In order to have a high positioning accuracy the signal must be broad regarding bandwidth, but the free spectrum for RFID, especially in Europe, is too small for that application. Therefore, higher out-of-band frequencies must be used. However, due to legal regulations, high bandwidth signals must be very low power, if applied. Ultra-wideband (UWB) signals [45] are such kind of signals and regulated by the Federal Communications Commission (FCC) and its counterparts in other regions, in order not to disturb any other in-band applications. UWB signals are defined as signals with bandwidths greater than 500 MHz or 20 % of the arithmetic mean of lower and upper cutoff frequency. The bandwidth used for the proposed system is 100 MHz due to the capability of UHF RFID tags working worldwide from around 840 MHz up to 960 MHz. Based on these conditions, although the proposed system only occupies 11 % of the arithmetic mean of the cutoff frequencies, the idea is to use low-power spreading signals for the ranging process. These signals are used to calculate the channel to a specific tag and back, thus extracting the time of flight information. As the low-power signals are hard to

evaluate directly, the SNR is increased by performing coherent integration [46].

Drawing up on Section 3, Equation (24), one can see that it is possible to derive the channel's impulse response upon evaluating the difference between both modulation states of the RFID transponder. Necessary for calculating the distance between tag and reader is the signal propagation time *t* of the up- and downlink channel. Multiplying half of *t* with the propagation speed results into the distance *d* between tag and reader (Equation (25)). As the bandwidth is limited to 100 MHz (Subsection 4.1), the pulse width is 10 ns minimum. Accordingly, a pulse width of 10 ns corresponds to a distance of around 3 m, supposing the speed of light in air is approximately 30 cm per nanosecond. Furthermore, the distance to be covered by this passive localization system is limited to the distance passive RFID tags are able to handle, which is, currently, limited to around 8 m [47]. In addition, the transmitted signal consists of more than one single pulse. These conditions lead to the fact, that the transmit signal and the receiving signal cannot be separated in time, as in ordinary RADAR applications. Another alternative is the principle of correlation, that can be used to determine the time shifted replica of the transmit pulse signal within the receiving signal [48]. The discrete correlation *Rxy τ* between

The correlation term shows the time-shifted replicas of the signal *x t* within the signal *y t* . A local maximum within the correlation term means a high correlation between *x t* and *t* , i.e., a high linear match. The point in time of the maximum shows the time shift between *x t* and *y t* , that is used to calculate the time between transmitted signal *x t* and received

*x k* ⋅ *y τ* + *k* = *x t* ⋅ *y t* . (26)

**3.2. Mathematical model**

98 Radio Frequency Identification from System to Applications

two signals *x t* and *y t* is given with

signal *y t* .

*Rxy τ* = ∑ *k*=-∞ +∞

Let us derive the principle at a simplified example. Assuming the channel of the *i*th trans‐ ponder is noise-free and multipath-free given with just

$$\{h\_i \mathbf{\tilde{f}} \mathbf{\tilde{f}}\} = a \cdot \delta \mathbf{\tilde{f}} \, t \, \mathbf{\tilde{t}} \, \mathbf{\tilde{t}} \, e^{\mathbf{\tilde{f}} \cdot \mathbf{\tilde{t}}} \, e^{j \psi\_0} \,\tag{27}$$

with *a* representing the reciprocal of the attenuation, *δ t* - *T*delay the time delay *T*delay of the channel with the Dirac delta function *δ t* , and an initial phase shift of *φ*0. Furthermore, the transponder modulation states si,1 and si,2 are given with 0 (full tag absorption) and 1 (full tag reflection). Equation (24) may now be written as

$$\begin{aligned} \left[ \Delta y\_{\text{reader}} \begin{bmatrix} t \\ t \end{bmatrix} \right] &= \left[ \mathbf{s}\_{i,2} \cdot \mathbf{s}\_{i,1} \right] \ast \mathbf{h}\_{\text{i}} \mathbf{f} \mathbf{t} \right] \ast \mathbf{x}\_{\text{reader}} \begin{bmatrix} t \\ t \end{bmatrix} = \left[ \mathbf{1} \cdot \mathbf{0} \right] \ast a \cdot \delta \left[ t \cdot T\_{\text{delay}} \right] \cdot e^{\langle \mathbf{t} \rangle} \ast \mathbf{x}\_{\text{reader}} \begin{bmatrix} t \\ t \end{bmatrix} = \\ &= a \cdot \delta \left[ \mathbf{t} \cdot T\_{\text{delay}} \right] \cdot e^{\langle \mathbf{t} \rangle\_0} \ast \mathbf{x}\_{\text{reader}} \mathbf{f} \mathbf{t} \end{aligned} \tag{28}$$

Performing the correlation to Equation (28) leads to

$$\times\_{\text{reader}}[\mathbf{t}\mathbf{t}] \cdot \Delta y\_{\text{reader}}[\mathbf{t}\mathbf{t}] = \times\_{\text{reader}}[\mathbf{t}\mathbf{t}] \cdot \left(a \cdot \delta \mathbf{f} \mathbf{t} \cdot T\_{\text{delay}} \mathbf{J} \cdot e^{j\varphi\_0} \ast \ge\_{\text{reader}} \mathbf{f} \mathbf{t}\right) \tag{29}$$

The convolution of *x*reader t with the time-shifted Dirac impulse *δ t* - *T*delay delivers a timeshifted signal:

$$\propto\_{\text{reader}} \sf{\sf t - T}\_{\text{delay}} \sf{\sf t - T}\_{\text{delay}} \sf{\sf t - T}\_{\text{delay}} \sf{\sf t \times}\_{\text{reader}} \sf{\sf t - T}\_{\text{reader}} \sf{\sf t - T}\_{\text{in}} \tag{30}$$

The correlation of *x*reader t - *T*delay with the original reader signal *x*reader t results in a timeshifted cross-correlation signal *Rx*reader *τ* - *T*delay :

$$\left\{ \mathbf{x}\_{\text{reader}} \mathbf{f} \right\} \cdot \Delta \mathbf{y}\_{\text{reader}} \mathbf{f} \mathbf{f} = \mathbf{a} \cdot \mathbf{e}^{j\varphi\_0} \cdot \mathbf{R}\_{\mathbf{x}\_{\text{raular}}} \mathbf{f} \mathbf{\tau} \cdot \mathbf{T}\_{\text{delay}} \mathbf{f} \tag{31}$$

Performing the square of the absolute value to Equation (31), finally, leads to

$$\|\cdot\|\_{\text{reader}}\|\mathbf{f}\cdot\mathbf{J}\mathbf{y}\_{\text{reader}}\mathbf{f}\mathbf{f}\|^{2} = \|a\|^{2} \cdot \|e^{j\phi\_{0}}\|^{2} \cdot \|\mathcal{R}\_{\mathbf{x}\_{\text{mode}}}\|\mathbf{\underline{\mathfrak{r}}} \cdot \mathbf{T}\_{\text{dekey}}\mathbf{J}\|^{2} = \|a\|^{2} \cdot \|\mathcal{R}\_{\mathbf{x}\_{\text{mode}}}\|\mathbf{\underline{\mathfrak{r}}} \cdot \mathbf{T}\_{\text{dekey}}\mathbf{J}\|^{2} \tag{32}$$

The wanted time delay *T*delay is evaluated by searching for the the maximum within the term |*x*reader *t* ⋅Δ*y*reader *t* |2:

$$T\_{\text{delay}} = \underset{\tau}{\text{argmax}} \left\{ \|\!|a|^2 \cdot \|\!|R\_{\text{x}\_{\text{naive}}}\mathbf{f}t - T\_{\text{delay}}\mathbf{J}\|^2 \right\} \tag{33}$$

By receiving *T*delay the distance *d* between reader and tag can be calculated by evaluating Equation (25) with

$$d = \frac{1}{2} \cdot c \cdot T\_{\text{delay}}.\tag{34}$$

As the CRLB states in Equation (36), possible increases in precision are possible by either increasing the effective bandwidth of the signals or increasing the signal-to-noise ratio. If the given bandwidth is fixed, only an increase in SNR results in a higher measurement precision. As stated earlier, the SNR is increased by performing coherent integration. For instance, integration over *n* =10,000 signals, results in an SNR increase of factor 10,000, but only in a precision increase of 10,000=100. Theoretically, it is possible to increase the SNR as high as wanted, but receiver restrictions and timeouts limit the SNR to a certain level. These restric‐ tions, mainly due to phase and quantization noise, define the limitations or the lower bounds

The applied hardware setup delivers the following SNR values for the quantization and phase

, (38)

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101

SNRsignal . (40)

SNRphase≈34 dB=2,512. (39)

SNRquantization <sup>≈</sup><sup>50</sup> dB=10<sup>5</sup>

+

1 SNRphase

SNRsignal is the power of the signal to the Gaussian noise power at the receiver. Figure 7 shows the maximum precision *σx* over certain SNRsignal values and coherent integrations with a factor of *n*. The effective bandwidth of the signal is given with *BRMS* =36.66 MHz. The SNR values and the effective bandwidth are derived from the receiver properties and the shape of the transmit pulse. Also, the factor one-half is considered due to half of the distance from tag to

As from Figure 7, it is shown that the lower bound for the standard deviation is around 1 cm. By increasing the number of coherent integrations *n*, the bound can be shifted to the left, which means, that the lower limit of the precision is reached for a lower SNRsignal value. For the proposed system, one measurement takes 1 µs, which increases to 1 s, if the coherent integra‐

+

1

noise. Thus, the receiver has an quantization error leading to an SNR of

SNRquantization

reader that reduces the precision *σx* in Equation (36) by a factor of 0.5.

**•** Non-constant tag reflection factors which vary by frequency and power

of the localization system to a certain precision.

1 SNR <sup>=</sup> <sup>1</sup>

Challenges this localization system is facing are mainly:

and phase noise leads to an SNR of

The total SNR is defined as

tion factor is *n* =1,000,000.

**4.2. Challenges**

**•** Multipath fading

Multipath fading and receiver noise corrupt and distort the distance estimation. Gaussian noise on the low-power signals can be suppressed through coherent integration at the receiver. However, the increase in SNR due to integration is at the cost of receiving time [46]. The effect of multipath fading is more severe as it distorts the measurements in a way that is nonpredictable without any a priori knowledge of the channel, which is given for a localization system working without channel prediction. The deployment of high-gain (low beam width) antennas with an electronic beam former can reduce the amount of multipath fading to an acceptable level.

#### **4. Challenges and limitations**

This section reveals the limitations and challenges of the proposed UHF RFID positioning system. Theoretical calculations show an accuracy limit at around 1 cm with the given hardware and signal limitations.

#### **4.1. Limitations**

The limitation of the system regarding the accuracy can be estimated using the Cramér-Rao Lower Bound (CRLB) [49], which defines a lower bound for an unbiased estimator *θ* ^. This means that the unbiased estimator of *θ* is always worse or equal to the CRLB. For an unbiased estimator *θ* ^ the standard deviation *σθ* ^(*θ*) is defined as [50]:

$$
\sigma\_{\hat{\theta}}^{\circ}(\theta) \gtrsim\_{\bullet} \overline{\text{CRLB}\_{\hat{\theta}}(\theta)} \tag{35}
$$

Estimating the time-of-flight corresponds to the following CRBL definition of the standard deviation *σx* of the localization, i.e., the precision [50, 51]:

$$\sigma\_x \ge \frac{c}{2\pi \cdot \mathcal{B}\_{\text{RMS}} \cdot \sqrt{2 \cdot \text{SNR}}} \tag{36}$$

*c*describes the propagation speed, SNR is the signal-to-noise ratio and *BRMS* is the effective bandwidth of the signal used and is defined as

$$B\_{RMS} = \left\| f^{\,^2 \| \mathcal{S}(f) \| ^2 \mathbf{d}f} \right\| \left\| f \right\| \mathcal{S}(f) \left\| ^2 \mathbf{d}f \right\|\tag{37}$$

with the Fourier transform of the signal *S*( *f* ) over the signal bandwidth *B*.

As the CRLB states in Equation (36), possible increases in precision are possible by either increasing the effective bandwidth of the signals or increasing the signal-to-noise ratio. If the given bandwidth is fixed, only an increase in SNR results in a higher measurement precision. As stated earlier, the SNR is increased by performing coherent integration. For instance, integration over *n* =10,000 signals, results in an SNR increase of factor 10,000, but only in a precision increase of 10,000=100. Theoretically, it is possible to increase the SNR as high as wanted, but receiver restrictions and timeouts limit the SNR to a certain level. These restric‐ tions, mainly due to phase and quantization noise, define the limitations or the lower bounds of the localization system to a certain precision.

The applied hardware setup delivers the following SNR values for the quantization and phase noise. Thus, the receiver has an quantization error leading to an SNR of

$$\text{SNR}\_{\text{quantization}} \approx 50 \text{ dB} = 10^5,\tag{38}$$

and phase noise leads to an SNR of

$$\text{SNR}\_{\text{phase}} \approx 34 \text{ dB} = 2,512. \tag{39}$$

The total SNR is defined as

By receiving *T*delay the distance *d* between reader and tag can be calculated by evaluating

Multipath fading and receiver noise corrupt and distort the distance estimation. Gaussian noise on the low-power signals can be suppressed through coherent integration at the receiver. However, the increase in SNR due to integration is at the cost of receiving time [46]. The effect of multipath fading is more severe as it distorts the measurements in a way that is nonpredictable without any a priori knowledge of the channel, which is given for a localization system working without channel prediction. The deployment of high-gain (low beam width) antennas with an electronic beam former can reduce the amount of multipath fading to an

This section reveals the limitations and challenges of the proposed UHF RFID positioning system. Theoretical calculations show an accuracy limit at around 1 cm with the given

The limitation of the system regarding the accuracy can be estimated using the Cramér-Rao Lower Bound (CRLB) [49], which defines a lower bound for an unbiased estimator *θ*

means that the unbiased estimator of *θ* is always worse or equal to the CRLB. For an unbiased

Estimating the time-of-flight corresponds to the following CRBL definition of the standard

*c*describes the propagation speed, SNR is the signal-to-noise ratio and *BRMS* is the effective

d *f* / *∫ B*


^(*θ*)≥ CRLB<sup>θ</sup>

*<sup>σ</sup><sup>x</sup>* <sup>≥</sup> *<sup>c</sup>*

*f* 2|*S*( *f* )|<sup>2</sup>

with the Fourier transform of the signal *S*( *f* ) over the signal bandwidth *B*.

^(*θ*) is defined as [50]:

<sup>2</sup> ⋅ *c* ⋅*T*delay. (34)

^(θ) (35)

d *f* (37)

<sup>2</sup>*<sup>π</sup>* <sup>⋅</sup> *<sup>B</sup> RMS* <sup>⋅</sup> <sup>2</sup> <sup>⋅</sup> SNR (36)

^. This

*<sup>d</sup>* <sup>=</sup> <sup>1</sup>

Equation (25) with

acceptable level.

**4.1. Limitations**

estimator *θ*

**4. Challenges and limitations**

100 Radio Frequency Identification from System to Applications

hardware and signal limitations.

^ the standard deviation *σθ*

bandwidth of the signal used and is defined as

deviation *σx* of the localization, i.e., the precision [50, 51]:

*BRMS* = *∫ B* *σθ*

$$\frac{1}{\text{SNR}} = \frac{1}{\text{SNR}\_{\text{quantization}}} + \frac{1}{\text{SNR}\_{\text{phase}}} + \frac{1}{\text{SNR}\_{\text{signal}}}.\tag{40}$$

SNRsignal is the power of the signal to the Gaussian noise power at the receiver. Figure 7 shows the maximum precision *σx* over certain SNRsignal values and coherent integrations with a factor of *n*. The effective bandwidth of the signal is given with *BRMS* =36.66 MHz. The SNR values and the effective bandwidth are derived from the receiver properties and the shape of the transmit pulse. Also, the factor one-half is considered due to half of the distance from tag to reader that reduces the precision *σx* in Equation (36) by a factor of 0.5.

As from Figure 7, it is shown that the lower bound for the standard deviation is around 1 cm. By increasing the number of coherent integrations *n*, the bound can be shifted to the left, which means, that the lower limit of the precision is reached for a lower SNRsignal value. For the proposed system, one measurement takes 1 µs, which increases to 1 s, if the coherent integra‐ tion factor is *n* =1,000,000.

#### **4.2. Challenges**

Challenges this localization system is facing are mainly:


**Figure 7.** Cramér-Rao Lower Bound of the localization system

The measurement procedure is as follows. The HF switch toggles to impedance Z1. Subse‐ quently, the reader transmits and receives its signals as shown in Figure 9. Then, the switch toggles to Z2 and, again, the reader transmits and receives its signals. Dependent on the number of coherent integrations, this procedure is repeated up to *n*. Finally, the sampled signals are evaluated in MATLAB. Figure 9 displays the transmit and receive signals for a given setup (anechoic chamber at a distance of 100 cm). The upper half of the figure shows the transmit signal – based on the Barker code [+1,-1] – used for both modulation states, Z1 and Z2. The lower half of the figure indicates the received signals for Z1 and Z2, respectively. As the received signals are complex-valued, real and imaginary parts are depicted for each RX signal. As seen in Figure 9, the received signals match each other for a certain period of time, until the difference in reflection (of Z1 and Z2) emerges (beginning at around 500 ns). These signals are used to determine the time shift between TX and RX signal and thus the distance between

**Figure 9.** Exemplary transmit (TX) and receive (RX) pulses of the reader for Z1 and Z2, divided in real (R) and imaginary

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103

The following two subsections show the measurement results, i.e., the result of the correlation difference, for two environments. First, a measurement in an anechoic chamber (Figure 10,

reader and tag. Evaluations of the correlations can be found in [48, 55].

(I) signal components for an antenna to antenna distance of *d* =100 cm

left), second, a measurement in an office environment (Figure 10, right).

**Figure 10.** Measurement environments; left: anechoic chamber, right: office

**Figure 8.** Measurement setup of RFID localization system

Multipath fading due to reflections, scattering and diffraction can be suppressed by using highgain antennas with a high-focussed beam. Hence, electronic beam steering is necessary to cover the area to detect RFID tags. Using an omni-directional antenna avoids electronic beam steering at the cost of more multipath fading. Another alternative, to minimize multipath fading is the use of a much higher bandwidth. In future, UWB technology combined with RFID could have a major effect on improvements in positioning accuracy [52, 53].

The non-constant tag reflection factors that vary over frequency and power are able to strongly deteriorate the position estimation [16], if disregarded. One solution for this problem is revealed in [54].

#### **5. Measurement results**

This section shows the obtained measurement results. The first measurements are taken in an anechoic chamber, the second measurements are taken in an office environment. Both measurements are one-dimensional measurements.

#### **5.1. Measurement setup**

The measurement setup is given as in Figure 8. It consists of the reader unit as described in Section 3, an reader antenna (Antenna #1) and an RFID tag with tag antenna (Antenna #2) followed by a HF switch for emulating the tag modulation states with impedances Z1 and Z2. For the sake of simplicity Z1 and Z2 are chosen as *Short* and *Open*, i.e., Z1 =0 Ω and Z2 =*∞* Ω.

**Figure 9.** Exemplary transmit (TX) and receive (RX) pulses of the reader for Z1 and Z2, divided in real (R) and imaginary (I) signal components for an antenna to antenna distance of *d* =100 cm

The measurement procedure is as follows. The HF switch toggles to impedance Z1. Subse‐ quently, the reader transmits and receives its signals as shown in Figure 9. Then, the switch toggles to Z2 and, again, the reader transmits and receives its signals. Dependent on the number of coherent integrations, this procedure is repeated up to *n*. Finally, the sampled signals are evaluated in MATLAB. Figure 9 displays the transmit and receive signals for a given setup (anechoic chamber at a distance of 100 cm). The upper half of the figure shows the transmit signal – based on the Barker code [+1,-1] – used for both modulation states, Z1 and Z2. The lower half of the figure indicates the received signals for Z1 and Z2, respectively. As the received signals are complex-valued, real and imaginary parts are depicted for each RX signal. As seen in Figure 9, the received signals match each other for a certain period of time, until the difference in reflection (of Z1 and Z2) emerges (beginning at around 500 ns). These signals are used to determine the time shift between TX and RX signal and thus the distance between reader and tag. Evaluations of the correlations can be found in [48, 55].

The following two subsections show the measurement results, i.e., the result of the correlation difference, for two environments. First, a measurement in an anechoic chamber (Figure 10, left), second, a measurement in an office environment (Figure 10, right).

**Figure 10.** Measurement environments; left: anechoic chamber, right: office

Multipath fading due to reflections, scattering and diffraction can be suppressed by using highgain antennas with a high-focussed beam. Hence, electronic beam steering is necessary to cover the area to detect RFID tags. Using an omni-directional antenna avoids electronic beam steering at the cost of more multipath fading. Another alternative, to minimize multipath fading is the use of a much higher bandwidth. In future, UWB technology combined with RFID

The non-constant tag reflection factors that vary over frequency and power are able to strongly deteriorate the position estimation [16], if disregarded. One solution for this problem is

This section shows the obtained measurement results. The first measurements are taken in an anechoic chamber, the second measurements are taken in an office environment. Both

The measurement setup is given as in Figure 8. It consists of the reader unit as described in Section 3, an reader antenna (Antenna #1) and an RFID tag with tag antenna (Antenna #2) followed by a HF switch for emulating the tag modulation states with impedances Z1 and Z2. For the sake of simplicity Z1 and Z2 are chosen as *Short* and *Open*, i.e., Z1 =0 Ω and Z2 =*∞* Ω.

could have a major effect on improvements in positioning accuracy [52, 53].

revealed in [54].

**5. Measurement results**

**5.1. Measurement setup**

measurements are one-dimensional measurements.

**Figure 7.** Cramér-Rao Lower Bound of the localization system

102 Radio Frequency Identification from System to Applications

**Figure 8.** Measurement setup of RFID localization system

#### **5.2. Anechoic chamber measurements**

The results of the measurement carried out in an anechoic chamber are depicted in Figure 11. The x-axis describes the real distances between the antennas, the y-axis describes the estimated distances. For normalization (cables, amplifiers, etc.) issues, the system is range-normalized to a distance of *d* =90 cm (measurement with lowest variance). The coherent integration factor was chosen to be *n* =100, i.e., each location was measured once with 100 transmit signals coherently integrated. The total RMSE error is 1.74 cm, which is the accuracy for a measurement distance from 80 cm to 280 cm. The fitting line in Figure 11 describes the regression line of the estimated distances. Hence, we can state that the system performs in the expected error ranges under very low multipath conditions.

**5.3. Office measurements**

track regarding the ideal line.

**6. Result and discussion**

**7. Summary and conclusion**

5.2).

The results of the measurement carried out in the office environment are shown in Figure 12. Again, the x-axis describes the real distances between the antennas, the y-axis describes the estimated distances. The system is normalized to the distance of *d* =90 cm, performed in the anechoic chamber. The coherent integration factor was chosen to be *n* =100. The total RMSE error is 6.82 cm, which is the accuracy for a measurement distance from 70 cm to 260 cm. The fitting line describes the regression line of the estimated distances. The estimated values describe a nearly linear relation from 70 cm to 190 cm. The following estimated values are around 10 cm below the ideal line, the estimated value at the distance of 260 cm is back on

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105

The above measurements show that it is basically possible to gain range information down to accuracies of a few centimeters from the different modulation states of UHF RFID tags using wideband signals. However, there exist some simplifications, including the high-gain antennas and the tag modulation impedances given with open and short circuit (see also Subsection

The idea behind the introduced localization system is based on the fact that current RFID-based localization systems either need a high effort in pre-calibration phases, suffer from bandwidth limitations, particularly in small frequency bands, e.g., as in Europe or need more complex hardware structures (phased array antennas) that only may be used in stationary, immobile applications. Therefore, a passive RFID-based positioning system should have ideally (Section 3) no change in hardware, high bandwidth, no pre-calibration phases and should be used in mobile applications. The suggested system includes these issues in the following way. There is no pre-calibration phase necessary as the system uses direct range estimation. This, however, is only possible due to the high bandwidth used along with low-power signals to stay within the required power spectrum densities. Changes in hardware would incorporate high bandwidth filter structures, a fast signal generator for the transmit pulses and a high accurate A/D converter for the incoming signals. Finally, it can be stated that such a localization system for mobile indoor positioning is possible, if the required hardware prerequisites are created.

This chapter dealt with the concepts of localization comprising primarily UHF and microwave RFID systems. After describing the fundamental principles behind localization, a survey was given for state-of-the-art RFID localization systems. Subsequently, a novel RFID localization system using wideband signals was introduced. A theoretical derivation of the range deter‐ mination was given in Section 4, whereas Section 5 revealed the limits and challenges of the proposed localization system, e.g., through evaluation of the Cramér-Rao lower bound.

**Figure 11.** Results of the measurement carried out in anechoic chamber

**Figure 12.** Results of the measurement carried out in an office environment

#### **5.3. Office measurements**

**5.2. Anechoic chamber measurements**

104 Radio Frequency Identification from System to Applications

under very low multipath conditions.

**Figure 11.** Results of the measurement carried out in anechoic chamber

**Figure 12.** Results of the measurement carried out in an office environment

The results of the measurement carried out in an anechoic chamber are depicted in Figure 11. The x-axis describes the real distances between the antennas, the y-axis describes the estimated distances. For normalization (cables, amplifiers, etc.) issues, the system is range-normalized to a distance of *d* =90 cm (measurement with lowest variance). The coherent integration factor was chosen to be *n* =100, i.e., each location was measured once with 100 transmit signals coherently integrated. The total RMSE error is 1.74 cm, which is the accuracy for a measurement distance from 80 cm to 280 cm. The fitting line in Figure 11 describes the regression line of the estimated distances. Hence, we can state that the system performs in the expected error ranges The results of the measurement carried out in the office environment are shown in Figure 12. Again, the x-axis describes the real distances between the antennas, the y-axis describes the estimated distances. The system is normalized to the distance of *d* =90 cm, performed in the anechoic chamber. The coherent integration factor was chosen to be *n* =100. The total RMSE error is 6.82 cm, which is the accuracy for a measurement distance from 70 cm to 260 cm. The fitting line describes the regression line of the estimated distances. The estimated values describe a nearly linear relation from 70 cm to 190 cm. The following estimated values are around 10 cm below the ideal line, the estimated value at the distance of 260 cm is back on track regarding the ideal line.
