Performance Aspects of Retrodirective RFID Tags ^†

Abstract

Although RFID(radio frequency identification) tags do not require a direct line of sight, their operational range is often characterized as being limited. Indeed, in the case of passive RFID tags, the interrogating signal from the transmitter needs to reach the tag’s radio transponder and trigger a nearly omnidirectional scattered signal to be harvested by the receiver. This two-way (from Tx to the tag and back to Rx) channel exhibits increased attenuation not only due to the doubled distance (in case Tx and Rx are collocated) but also to the uncontrolled (i.e., unfocused) backscattering. In the work at hand, we propose a way to control the backscattered radiation and focus the produced beam towards the direction of the reader (the Tx-Rx device). Indeed, one can utilize the concept of retrodirective arrays to immediately control the direction of departure of the backscatter link, maximizing the scattered power towards the reader and thus delivering an increase in the operational range of the tag. This of course means that in this case, the tag should be equipped with a minimum of two element radiators. Thus, retrodirective RFID array tags are introduced in the current work to increase the operating range with minimal costs and levels of complexity since 90° hybrids are used to achieve proper backscattering. To evaluate the proposed passive tag array, performance aspects are addressed. Specifically, we examine the Bit Error Rate with respect to the Signal to Noise Ratio for the retrodirective tag, the one antenna, the broadside, and the spatial diversity array. The results prove that the proposed tag allows for a significant increase in the operational range.

1. Introduction

The concept behind the use of simple electromagnetic systems to assist in radio frequency identification is to utilize numerous tags (with at least one placed at each desired identification point, product, asset, device, etc.), ideally at little to no cost (and thus extremely easy to build, transfer, place, handle, and configure) and accessible effortlessly (this means mainly wirelessly) from acceptable distances. In the author’s opinion, RFID’s greatest constraints are not the lack of mass production or its level of complexity; they are its operational coverage and the amount of space around the tag in which it can communicate. Of course, the channel is wireless, and (assuming that far-field testing is conducted) the limit is set by the Friis formula. But usually, the performance of passive tags is far worse than this. And it is not just the possible obstacles between the tag and the reader that can be blamed. The main reason is that the wave that reaches the tag is scattered in all directions in an uncontrolled manner, which, after a critical distance, makes the tag invisible to the reader. Here, we focus on this very mechanism of scattering and in a way modulate the tag’s radar cross-section to present a main beam scattered towards the incoming wave’s direction. Although, at first, such an endeavor would seem to require signal processing to estimate the direction of its arrival and subsequent active signal response, this is not necessary, in addition to being complicated and expensive. The stated claim is presented in detail and validated in the following text.

It can be easily deduced from the preceding paragraph that there is an urgent need to increase the reliable communication distance from the tag while maintaining minimal levels of complexity and minimal costs [1]. In order to improve its performance and achieve this goal, the employment of a small array antenna, not only on the reader but also on the tag, was proposed by Ingram et al [2]. In this case, while the reader can be designed effectively [3,4,5,6] without very strict constraints on its complexity, this is not the case for the RFID tag array. Tag arrays should be extremely inexpensive but at the same time extremely effective. Furthermore, their analysis and design, when they are embedded in complex environments and must conform to the host surface, are challenging [7,8,9], as can be seen from Figure 1.

Here, we propose the design of retrodirective tag arrays, i.e., those that passively scatter the incident power back in the direction of the incoming wave. This retrodirective response can be achieved by the utilization of a lossless passive feeding network [10,11] attached to the tag array antenna.

To assess the merits of such a proposal, we need to study the respective channel. In [2], the resulting channel was investigated, employing spatial multiplexing and transmit diversity for active tags. Thus, it was based only on the temporal characteristics and the stochastic properties of the exchanged information.

Here, a backscatter channel model incorporating the spatial signature of the incident and backscattered signals is contributed to RF tag application, (see Equation (3)). Up to now, related works on pinhole channels on RF tags with multiple antennas have neglected the spatial aspects of incident and backscattered signals. Taking into account the directions of arrivals (DoAs) and the directions of departures (DoDs) of the propagating signals, beamforming gains can be attained. This can be achieved with minimal extra costs, since we propose the exploitation of the spatial signature of the channel to be performed in the RF domain (not in the digital domain). This is accomplished by employing 90° hybrids to achieve proper retrodirective backscattering. Various cases are examined, and the relative results are given to present the performance aspects of the retrodirective tags.

It is noted that in cases in which the identification distance is much more than 10 m and the objects are large enough (e.g., containers or large boxes), the most reasonable choice is to use active tags with antenna beamforming. Instead, we propose the beamforming to be performed automatically and without processing via the retrodirective response. In Figure 1 and Figure 2, we can see the tags are positioned on the planar surfaces of such objects. The retrodirective tag beamforming system does not contribute to the cost, as is demonstrated in Figure 2.

2. Materials and Methods

In the current section, the spatial signature equipped, pinhole channel model for RF tags is studied. Backscatter radio systems operate in a channel that is a cascade connection of two conventional ones: the reader’s transmitter tag and the tag reader’s receiver channels. This is the so-called pin- (key-)hole two-way channel. Compared to the usual wireless channel, it exhibits deeper fades, thus requiring extra measures to be classified as reliable. Previous works have shown that these extra measures can be based on the diversity of the rich scattering environment. This, of course, holds when the tag antennas are uncorrelated, which is not the case when the tag is equipped with an array (phased) antenna. Now, the antenna elements are in close proximity to one another, and the pinhole diversity fails. In the current work, we show that even in this case, when the tag is armed with a (say, two-element) array antenna, a performance increase can still be achieved by properly designing the array’s passive feeding network.

Let us present the channel model. The forward part of the keyhole channel ${\mathit{H}}_f$ models the N_TX Tx antenna-initiated propagation to the N_TAG antennas of the tag. The backscatter part of the keyhole channel ${\mathit{H}}_b$ models tag-initiated propagation to the N_RX Rx antennas of the reader’s receiver. The received signal is given as follows [12]:

$$\mathit{z}={\displaystyle \frac{1}{2}}{\mathit{H}}_b\cdot \mathit{S}\cdot {\mathit{H}}_f\cdot \mathit{x}+\mathit{n}.$$

(1)

Here, we use time-invariant channel. In (1), the elements of the channel matrices are assumed to be complex Gaussian variables. Their real and imaginary parts are $~N(0,{\displaystyle \frac{{\sigma }_{f,b}^2}{2}})$. $\mathit{z}$ is N_RXx1 column vector of the received baseband signal. ${\mathit{H}}_f$is the N_TAGxN_TX matrix of the forward channel, ${\mathit{H}}_b$ is the N_RXxN_TAG matrix of the backward channel, $\mathit{S}$ is the N_TAGxN_TAG tag’s signaling matrix, $\mathit{x}$ is the transmitted N_TXx1 column vector, and the noise vector $\mathit{n}$ is in the form of an N_RXx1 column.

$\mathit{S}$ is defined as the N_TAG port scattering matrix [13]. Here, this matrix is identified as the scattering matrix of the array antenna’s passive feeding network. In general, dependent both on the circuitry and the antennas, this matrix has various distinct forms. For example, when no active circuitry is present (meaning we focus on passive tags) and each antenna elementary radiator of the tag array is terminated with its own load termination (no signals are intercoupled between the antenna elements), then this matrix is proportional to the ${\mathit{I}}_{N_{TAG}}$ N_TAGxN_TAG identity matrix as follows:

$$\mathit{S}=\Gamma \cdot {\mathit{I}}_{N_{TAG}},$$

(2)

where $\Gamma$ is a diagonal matrix with each diagonal element being the respective array antenna’s reflection coefficient. Up to now, only this matrix has been used in applications.

Nevertheless, if the tag array antennas respond to the incoming wave in a way in which the signals are intercoupled between the antennas, then the use of off-diagonal elements in the representation of the S matrix is mandatory. This slight increase in analysis complexity compensate the designer with additional possible solutions. Indeed, an application in which all, not only the diagonal, elements of S are employed is identified in the current work. Here, the scattering matrix is the one that forms a retrodirective array [14].

Apart from the use of a ‘full’ S matrix to model the tag’s response in the case of the retrodirective characteristic, additional issues need to be considered. Usually, in the relative literature, in the channel shown in (1), the signals at the tag’s antenna(s) are assumed uncorrelated. Nonetheless, for a set of radiators to be collectively denoted as array antennas, they should be correlated. The solution of reducing the correlation by increasing the interelement distance is not available here due to widely accepted footprint constraints accompanying the RF tag design.

Due to the correlation of the received signal at each antenna, the system should be studied as a phased array one. In this case, it is necessary to incorporate the direction of arrivals (DOAs) and the directions of departures (DODs) into the model (finite scatterer model). Then it is, [15]:

$$\begin{gathered} {\mathit{H}}_f={\Psi }_r^{tag}\cdot h_f\cdot {\left({\Psi }_T\right)}^T; \\ {\mathit{H}}_b={\Psi }_R\cdot h_b\cdot {\left({\Psi }_t^{tag}\right)}^T, \end{gathered}$$

(3)

where ${\Psi }_T,{\Psi }_r^{tag},{\Psi }_R,{\Psi }_t^{tag}$ are the transmitter’s transmitting array, the tag’s receiving array, the receiver’s receiving array, and the tag’s transmitting array response column vectors. $h_f,h_b$ are the complex channel gain vectors for the forward and the backscattered links. Here, we focus on the narrowband case (we neglect delays), and we assume flat fading. Inserting (3) into (1)a, with spatial signature equipped, pinhole channel model for RF tags is provided.

3. Results

In this section, the performance of the retrodirective double-antenna tag is verified. Taking advantage of the presented channel model, we examine the case of a two-element tag equipped with a retrodirective signaling matrix. The reader uses one omni antenna, both for transmitting and for receiving. The tag uses two dipole antennas spaced at λ/2. We assume it is a flat-fading, time-invariant, and narrowband channel (neglecting delays). We refer to Figure 3 [12].

The performance of the retrodirective array is to be compared with a broadside array, thus we will use the retrodirective and the identity signaling matrix. For the system in Figure 3, the channel matrix for the forward link reads:

$${\mathit{H}}_f=\left[\begin{array}{c}1\\ e^{j\pi \mathit{sin}{\theta }_f}\end{array}\right]h_f{\left[1\right]}^T,$$

(4)

while the channel matrix for the backscattering link obeys:

$${\mathit{H}}_b=\left[1\right]h_b{\left[\begin{array}{c}1\\ e^{j\pi \mathit{sin}{\theta }_b}\end{array}\right]}^T.$$

(5)

The total channel matrix and receive signal follows:

$${\mathit{H}}_b\cdot \mathit{S}\cdot {\mathit{H}}_f\Rightarrow z={\displaystyle \frac{1}{2}}{\mathit{H}}_b\cdot \mathit{S}\cdot {\mathit{H}}_{f}x+\mathit{n}.$$

(6)

We can use as a scattering matrix the identity one, Equation (2), or the retrodirective one [15] that obeys:

$${\mathit{S}}_r=j\left[\begin{array}{cc}0& \Gamma \\ \Gamma & 0\end{array}\right].$$

(7)

For the two signaling matrices the total channel matrix reads:

$$\begin{array}{l}{H}_i=h_b{h}_f\Gamma \left(1+e^{jkd\left(\sin ({\theta }_f)+\sin ({\theta }_b)\right)}\right)\\ H_r=j{h}_b{h}_f\Gamma \left(e^{j\left(kd\sin ({\theta }_f)\right)}+e^{j\left(kd\sin ({\theta }_b)\right)}\right)\end{array}.$$

(8)

${\mathit{H}}_i$ is formed using the identity signaling matrix to model the broadside array while ${\mathit{H}}_r$ is formed using the retrodirective signaling matrix to model the retrodirective tag. Note that in the signaling matrix no coupling is taken into account for both cases. Since Tx antenna array works also as the Rx antenna array, then the ${\theta }_b={\theta }_f=\theta$ and the forward and backward channels are fully correlated, ($h_b=h_f=h$):

$$\begin{gathered} {\mathit{H}}_i=h^2\cdot \Gamma \cdot \left(1+e^{j2kd\mathit{sin}(\theta )}\right); \\ {\mathit{H}}_r=j2h^2\cdot \Gamma \cdot e^{jkd\mathit{sin}(\theta )}. \end{gathered}$$

(9)

Note that the respective case when the two tag antennas are uncorrelated reads:

$${\mathit{H}}_{diversity}=\Gamma \cdot \left(h_1^2+h_2^2\right).$$

(10)

When there is only one antenna in (10) only the $h_1$ coefficient exist. Since termination Γ is between two values ${\Gamma }^{\pm }$ then the received baseband complex envelope for four interesting cases reads:

$$2\cdot \left|V\right|=\left|H^{+}-H^{-}\right|=\left\{\begin{array}{cc}\left|\Delta \Gamma \right|h^2& \mathrm{One}\mathrm{Antenna}\\ \left|\Delta \Gamma \right|\left(h_1^2+h_2^2\right)& \mathrm{Spatial}\mathrm{diversity}\\ \left|\Delta \Gamma \right|2h^2& \mathrm{Retrodirective}\\ \left|\Delta \Gamma \right|h^2\left(1+e^{j2kd\mathit{sin}(\theta )}\right)& \mathrm{Broadside}\mathrm{Array}\end{array}\right..$$

(11)

In Equation (11), apart from the broadside and retrodirective array, the one antenna and the two antenna spatial diversity cases were included. In the previous the average DC component of the envelope is assumed zero since it can be easily eliminated, via a DC blocking capacitor, [16], from the total received signal. Equation (11) indicates that the results are scaled with the amplitude of ΔΓ and thus this cannot differentiate the Tag’s response between the available study cases. So, to assist the forthcoming outcomes, we assume $\left|\Delta \Gamma \right|=1$, meaning the reflection coefficient varies from perfect reflection to perfect absorption. Note that the h variables are random variables of Rayleigh, Rician or other channel coefficient. Also, the random variable θ is a uniform one over the full angular sector.

Since ASK is used, the error probability obeys:

$$P=Q\left({\displaystyle \frac{\left|V\right|}{\sqrt{2N_o}}}\right).$$

(12)

We aim to compute the average BER with respect to the SNR. This is computed as follows [17]:

$$\mathrm{average}\mathrm{BER}={\int }_0^{+\infty }P(\left|V\right|;N_o)f_{\left|V\right|}\left(\left|V\right|\right)d\left|V\right|.$$

(13)

Thus, we need to compute $f_{\left|V\right|}\left(\left|V\right|\right)$. For the cases listed in (11), the respective PDFs are calculated numerically through a Monte Carlo simulation, and using (13), we compute the results, which are shown in Figure 4. In the results, the average fading power of the Rayleigh channels is set to be equal to one.

Note that for BER = 10⁻², the retrodirective array provides a ~6 dB gain compared to the one-antenna case. The respective gain for the spatial diversity case is theoretically higher but cannot be attained since the incident signals to the different antenna elements are correlated. The broadside array performs badly. The stated results indicate that the retrodirective array has an increased operation range compared with that of the conventional tag. Indeed, to quantify and intuitively present the attained results, let us adopt the easily understood and widely accepted backscatter communication radio link budget formula from [18], which is as follows:

$$P=A-B\cdot {\mathit{log}}_{10}(R).$$

(14)

where A and B are constants relative to the channel and adopted system, and R is the tag–reader distance. Equation (14) indicates that there is a distance at which the signal power is such that the SNR is not adequate for the desired or needed BER. Now, as shown in (14), we can understand that B is mainly dependent on the propagation conditions (it can be easily identified as being the path loss exponent), which are the same for the one-antenna tag and for the retrodirective two-element array tag. This is not the case for A. A is dependent on the specific system used. As Figure 4 shows, the A parameter for the retrodirective two-element array tag should be 6 dBs greater than that of a one-antenna conventional tag. Thus, in the retrodirective case, the critical distance is clearly greater, with the ultimate limit determined by the chip sensitivity [19].

By examining (11) and the 6dB gain that exhibit the used Tag compared to the one antenna case, useful conclusions can be drawn. The use of the retrodirective mechanism allows for linear, (with the number of the antenna elements used), scaling of the attained gain with respect to the single element, conventional, Tag. Furthermore, this gain seams not to depend on the BER target used. Those characteristics are extremely important indicating that retrodirective RFID Tags are extremely robust and potent. Another point that should be addressed is that to the counterpoint that multielement Tags are not low profile radiators anymore, the author refers the reader to [20] where a four element array fits into the area that hosts one element.

4. Conclusions

The operation range of RFID tags in a lot of applications has been deemed inadequate. In addition to the doubled distance between the reader and tag, the uncontrolled backscattering of the latter adds significantly to this problem. To control the backscattering and alleviate the operational range problem, in the current work, the use of the retrodirective concept is proposed. Using a retrodirective array, we can immediately control the direction of departure of the backscatter link. This maximizes the scattered power towards the reader and thus allows (as the presented results prove) for a significant increase in the operational range of the tag.