 Research
 Open Access
Tradeoff between maximum cardinality of collision sets and accuracy of RFID readertoreader collision detection
 Linchao Zhang†^{1}Email author,
 Filippo Gandino†^{1},
 Renato Ferrero†^{1},
 Bartolomeo Montrucchio†^{1} and
 Maurizio Rebaudengo†^{1}
https://doi.org/10.1186/16873963201310
© Zhang et al.; licensee Springer. 2013
 Received: 30 November 2012
 Accepted: 26 April 2013
 Published: 17 May 2013
Abstract
As the adoption of the radiofrequency identification (RFID) technology is increasing, many applications require a dense reader deployment. In such environments, readertoreader interference becomes a critical problem, so the proposal of effective anticollision algorithms and their analysis are particularly important. Existing readertoreader anticollision algorithms are typically analyzed using single interference models that consider only direct collisions. The additive interference models, which consider the sum of interferences, are more accurate but require more computational effort. The goal of this paper is to find the difference in accuracy between single and additive interference models and how many interference components should be considered in additive models. An indepth analysis evaluates to which extent the number of the additive components in a possible collision affects the accuracy of collision detection. The results of the investigation shows that an analysis limited to direct collisions cannot reach a satisfactory accuracy, but the collisions generated by the addition of the interferences from a large number of readers do not affect significantly the detection of RFID readertoreader collisions.
Keywords
 Collision Detection
 Time Division Multiple Access
 Antenna Gain
 Interference Model
 Interference Range
Introduction
Radiofrequency identification (RFID) is increasingly being used in industries and infrastructures for the purpose of automatic identification and tracking[1]. An RFID system includes some RFID readers and many tags. A reader can query tags by means of a wireless communication. The majority of the RFID systems operate at ultrahigh frequency (UHF). RFID is used for many applications, such as traceability[2], item removal detection[3], anticounterfeit[4] and positioning[5], and for the establishment of smart environments, such as smart retailers[6], smart hospitals[7], and smart universities[8]. Although the need of covering large areas has been partially satisfied by using MIMO RFID readers[9], the majority of the RFID applications, especially the largest, require a dense reader deployment, where RFID readers operate in close proximity. Consequently, UHF RFID systems are easy to suffer from the interference generated during simultaneous interrogation activities[10]. In this case, a reader can suffer a readertoreader collision due to the interference generated by the simultaneous operations of other RFID readers[11]. When the reader queries a tag, the readertoreader interference is too strong with respect to the weak signals received from the tag, thus compromising the interrogation.
In recent years, many RFID readertoreader anticollision protocols have been proposed. The European standard for UHF RFID communication^{a} proposes listen before talk, an anticollision protocol based on carrier sense multiple access (CSMA). PULSE is a subsequent CSMA approach that attempts at increasing the throughput by using an additional control channel[12]. The first approach based on time division multiple access (TDMA) is Colorwave[13], which provides a simple and distributed mechanism for scheduling the query sections and is suitable for lowcost readers. More recent techniques have been proposed in order to improve the performance of Colorwave: in[14], a probabilistic parameter improves the collision resolution, and in[15], an adaptable and selfish algorithm strongly increases throughput. In the Neighbor Friendly Reader Anticollision (NFRA) protocol[16], a central server manages a contention among readers to schedule the query sections. NFRA provides high throughput, but it is not suitable to lowcost devices. The same technique has been enhanced in[17], where fairness among readers is improved by giving more opportunities of querying tags to the readers in the densest areas, and in[18], where the readers are scheduled in the contention phase according to the geometric distribution in order to reduce the quantity of empty time slots. Besides, the researches in[19, 20] provide a novel and prospective approach to limit the readertoreader interference by separating the transmission phase and listening phase of the RFID readers.
Although RFID readertoreader collisions are a relevant problem, an established method for the analysis and evaluation of readertoreader anticollision protocols does not exist (e.g.,[21, 22]). The characteristics of the employed interference model are particularly relevant. Even considering the same deployment and the same attempts to query tags, two different models may detect different collisions. Single interference models only consider direct collisions, where the highpower transmission of a reader interferes with the lowpower answers of tags to another reader. These models are easy to implement and provide rapid simulations. Additive models do not limit the analysis to direct collisions but consider the sum of the interferences from a group of readers. They are more similar to the real behavior of RFID networks but require more computational effort.
This paper investigates the characteristics of the additive interference models for detecting RFID readertoreader collisions. In particular, the effects of the quantity of readers involved in the collisions (i.e., the cardinality of the collision set) are analyzed. The goal of the paper is to identify to which extent the collisions detected with a specific cardinality affect the accuracy of the results, in order to establish whether all the additive components must be considered for an accurate result, or instead if it is possible to limit the analysis without considering a part of the collision sets. A preliminary analysis about the interference generated by the collision sets with different cardinality has been presented in[23]. The investigation presented in the current work is based both on an analytical analysis and on simulations. The results show that an analysis of anticollision protocols limited to direct interferences provides a low level of accuracy since many collisions are not detected. However, few collisions are due to collision sets with high cardinality, so the models used for the evaluation of RFID readertoreader anticollision protocols can be limited to small collision sets.
The next section describes the state of the art of the RFID interference models. The ‘Experimental setup Experimental setup’ section illustrates the proposed evaluation algorithm and describes the considered scenario. Data obtained from the evaluation are presented in the ‘Experimental results’ section. Final comments are made in the ‘Conclusion’ section.
Related works
An established dichotomy among the readertoreader interference models regards the cardinality of the set of colliding readers[24]. The single interference models assume that all the collisions involve pairs of readers that query tags at the same time. Given a pair of readers, it is always possible to determine if they collide or not independently of the activity of the other readers in the network. Considering the set A of readers in the network, the list of pairs of readers that collide when transmitting simultaneously is a binary relation R on the set A. Since the relation R is a subset of the Cartesian product A × A, it corresponds to a graph, called collision graph. The nodes of this graph are the elements of A, and an edge exists between two nodes x and y if (x,y) ∈ R. On the contrary, the additive interference models evaluate the sum of the power of all the signals received by a reader in order to determinate if a collision occurs. Considering, for example, three readers x, y, and z, according to the single interference models, if x is placed far enough, it is disturbed neither by y nor by z. However, in the additive interference models, if all the three readers query tags at the same time, the combination of the signals emitted by y and z can be powerful enough to interfere with the transmission of x. Therefore, it is not possible to build a single collision graph, i.e., to identify a priori the readers that interfere among them. Instead, for a reader x, a plurality of collision sets exists: each collision set groups the readers that interfere with x only if all of them transmit at the same time.
In the following, the main interference models are reviewed. In the adopted notation, reader x is the one that queries tags and that can be subject to readertoreader interference from other readers in the network. The power of the signal emitted by reader i is denoted as P_{ i }. This signal propagates in the space, and it decays with distance: the signal that arrives at reader j has power P_{i,j}, with P_{i,j} < P_{ i }.
Single interference models
Single interference models consider only the interference between pairs of readers. The main examples of this family of models are described in the following.
Disk graph model
Although outside the circle of radius d the signal of the reader is too weak for querying tags, it is strong enough to disturb the simultaneous transmission of other readers. As the distance grows, the attenuation of the signal prevents the reader from disturbing the activity of the other readers: the maximum distance D beyond which no interference is generated is called interference range or collision range.
while in the disk graph model, the threshold D is replaced by the maximum between the interference ranges D_{ x } and D_{ y } of the two readers.
In a unit disk graph, the degree of a node, i.e., the number of incident edges, corresponds to the number of readers that collide with that node in the case of a simultaneous transmission. Therefore, the degree distribution of the unit disk graph describes the discrete probability distribution of the number of distinct collisions that occur in the RFID network. This probability distribution can be calculated taking into account also the border effects of the area where readers are deployed[27].
Protocol model
since condition 1 applies also to the protocol model, as well as in the unit disk graph model, a reader can only identify tags located within its interrogation range d.
Capture threshold model
where G_{t,x} is the propagation gain (including the antenna gains) from tag t to reader x and G_{y,x} is the propagation gain from reader y to reader x. The capture threshold model is implemented by the NS2 simulator[29] that uses a value of 10 dB for β_{ c t }.
The capture threshold model is a generalization of the protocol model. The two models are equivalent if the following conditions hold:

Isotropic path loss is considered; thus, the propagation gain between points a and b is${G}_{a,b}={\left(\frac{ab}{{d}_{0}}\right)}^{\eta}$, where d_{0} is a constant and η is the path loss exponent.

The readers are homogeneous: they transmit with the same power P_{ x } and the ratio$\frac{{P}_{y,x}}{{P}_{t,x}}$ can be considered constant.

The value of Δ is set to$\sqrt[\eta ]{{\beta}_{\mathit{\text{ct}}}\frac{{P}_{y,x}}{{P}_{t,x}}}1$.
and the equivalence with Equation 3 is proved.
In contrast to Equation 1, condition (7) states that in the capture threshold model the interference range cannot be assumed as directly proportional to the interrogation range.
Additive interference models
where I_{ x } is the interference sensed by reader x and$\mathcal{N}$ is the background noise power.
The main models that were proposed to evaluate Equation 8 are reviewed in the following.
Singlechannel model
where G_{ x } and G_{ t } represent the antenna gains of the reader and the tag, respectively, and α is the path loss exponent, whose value generally ranges from 2 to 4. A value of α = 2 results in free space propagation, which corresponds to a lineofsight communication between readers without interposing obstacles. P_{0} is the path loss at the reference distance d_{0} = 1 m. P_{0} depends on the considered propagation model: in free space propagation,${P}_{0}={\left(\frac{\lambda}{4\pi}\right)}^{2}$, where λ is the signal wavelength (in meters).
where x_{ i }−x is the distance between the simultaneously interfering reader x_{ i } and the target reader x.
Physical model
where N is the number of readers in the network (in addition to reader x).
The physical model is a simplification of the singlechannel model. The two models are equivalent if all the interfering readers are homogeneous with antenna gain${G}_{y}=\frac{{G}_{x}}{{P}_{0}}$ and if the gain of the tag’s antenna is${G}_{t}=\frac{{G}_{x}}{{P}_{0}\phantom{\rule{2.77695pt}{0ex}}{E}_{\text{tag}}}$.
IRRR model
where α_{BW} denotes the ratio of the spectrum power in the used channel to the available bandwidth. PL is the path loss between x and t: since it depends on their distance, the path loss P_{0} at the reference distance d_{0} = 1 m is adopted in the second formulation of Equation 18. The total path loss between x and t is obtained by summing two contributions: the first one for the forwarding readertotag query communication and the second one for the returning tagtoreader response. Fading effects are ignored because a lineofsight propagation is assumed for the reader’s query and the tag’s response.
where h_{ y } is a fading coefficient in the channel between x and y, and β_{mask_y} is the limit level of the spectrum mask.
where${\kappa}_{1}=\frac{{\alpha}_{\text{BW}}\phantom{\rule{2.77695pt}{0ex}}{E}_{\text{tag}}\phantom{\rule{2.77695pt}{0ex}}{G}_{x}\phantom{\rule{2.77695pt}{0ex}}{G}_{t}{\lambda}_{x}^{4}}{{\left(4\pi \right)}^{4}}$ and${\kappa}_{2}=\frac{{h}_{i}\phantom{\rule{2.77695pt}{0ex}}{G}_{x}\phantom{\rule{2.77695pt}{0ex}}{G}_{i}{\lambda}_{i}^{2}}{{\left(4\pi \right)}^{2}}$.
An alternative way to calculate I_{ x } is provided in[31] by assuming a uniform random distribution of the readers. Firstly, the average interference generated by a single reader y is calculated by integrating Equation 19 in the annulus where the reader y can be located. I_{ x } is then estimated by multiplying the average interference for the average number of simultaneously active readers (given by the number of the readers in the network and their probability of querying tags).
The IRRR model extends the singlechannel model by considering the availability of more than one channel for the communication among readers and tags. Furthermore, it considers fading effects in the interference among readers. The main difference between the two models lies in the estimation of P_{t,x}: in the singlechannel model, the contribution of the antenna gains of the reader and the tag is counted twice, while in the IRRR model, it is considered only once.
Rayleigh and shadow fading model
where K_{1} is a constant that includes the antenna gains of the reader and the tag, the wavelength, and the modulation indexing, and q models the path loss and its value depends on the environment where the signal propagates.
where 10^{0.1ζ} takes into account the effect of shadowing and X_{ xy } is a random variable with Rayleigh distribution that describes the deviation in the attenuation of the signal from reader y to reader x. K_{2} is a constant that, similarly to K_{1}, considers the antenna gains of the two readers, the wavelength, and the modulation indexing.
Experimental setup
The difference between single interference and additive interference models is the cardinality n of the considered collision set. Obviously, additive interference models recognize a higher number of collisions with respect to single interference models. The goal of this section is to numerically evaluate to which extent the accuracy in detecting reader interference improves as n increases.
In order to avoid considering redundant collision sets, only minimal collision sets are considered in this paper. Considering a target reader x, the set of readers C = {x_{0},x_{1},x_{2},...,x_{ n }} is a collision set for x if the simultaneous transmissions of all the members of C generate a reader interference with x; set C is a minimal collision set for x if the interference is avoided when at least one member of C does not transmit at the same time as the others. Any subset of the minimal collision set cannot generate a collision; in other words, a minimal collision set does not include any other collision set. The general idea is to collect all the minimal collision sets in order to observe how many collisions can be detected by considering a collision set of cardinality at most n. In the rest of the paper, we refer to a minimal collision set of cardinality n as collisionsetn.
Evaluation parameters
Parameters  Values 

Path loss exponent (α)  2 
SIR threshold (Γ)  10 
Reader antenna gain (G_{ r })  6 dBi 
Tag antenna gain (G_{ t })  1 dBi 
Tag’s power reflection coefficient (E_{tag})  $\frac{3}{4}$ 
Reader’s transmit power (P_{ x })  30 dBm 
Path loss at the reference distance d_{0} (P_{0})  $\frac{1}{{G}_{x}^{2}}$ 
Readertotag distance (x−t)  5 m 
Noise power (𝒩)  0 
It can be observed that the transmitting power P_{ x } has no effect in the evaluation of Equation 25 for determining the occurrence of a collision, but it only affects the interrogation range. With the considered values of antenna gains and interrogation range in Table1, we set the transmitting power to 30 dBm in order to make sure that the conventional RFID tags can be energized at 5 m.
The RFID readers are randomly deployed in a 1,000×1,000 m field. The position of each reader is specified in the Cartesian coordinate system, where the coordinate of each reader is randomly generated. The coordinates of all the readers are uniformly distributed and they are independent, i.e., the deployment follows a spatial Poisson point process. Besides, the number of readers varies from 20 to 50 in order to investigate the effect of reader densities. In order to reduce the effect of randomness, each simulation is repeated 1,000 times.
Algorithm 1 Calculate the collision sets in the RFID reader set R with cardinality lower than Card_{max}
Evaluation algorithm
A branch and bound algorithm is adopted to collect all the minimal collision sets for each reader i ∈ R. The branch consists of the recursive exploration of the tree that lists all the collision sets for reader i. The bound is given by the identification of a minimal collision set: when this happens, all the sets that contain that collision set are discarded.
As shown in Algorithm 1, all the elements j ∈ R∖{i} are first sorted by the descending order of the interference P_{ j i } received by i. Then a recursive procedure is called to check which are the minimal collision sets among all the subsets of R∖{i}. In this procedure, a stack is used to store the current subset of R∖{i} in order to evaluate whether the sum of the interference of the readers in this subset can generate a collision to the target reader. When the set in the stack turns out to be a minimal collision set, all the supersets that contain the set present in the stack are ignored. Besides, a control parameter Card_{max} is introduced to indicate that only the subsets with cardinality lower than Card_{max} are considered.
Experimental results
This section evaluates through simulation data the relationship between the cardinality of the collision set and the number of detected collisions. Different scenarios are considered by keeping a fixed field and increasing the number of readers deployed from 20 to 50. In particular, the analysis is focused on the last scenario (i.e., 50 readers), which is used as a case study.
Number of readers affected by collisionsetn
Considering the scenario with 50 readers, it can be observed that almost all the readers have collision sets with cardinality from 1 to 5. The number of readers affected by collisionset2 until collisionset5 are almost the same as the number of readers affected by direct collisions (i.e., collisionset1), which reflects that single interference models are not enough to cover all the collisions in a dense RFID deployment. From collisionset6, the number of affected readers starts to reduce in a great scale. The RFID reader can be affected until the sum of 14 readers’ interference are considered. The simulations demonstrate that all the possible collision sets with more than 14 readers cannot generate a total interference that can hamper the target reader, which means that it is not necessary to consider additional interferences generated by more than 14 readers.
Average number of collisionsetn
Under the scenario with 50 readers as shown in Figure3d, the average number of collisionsetn first climbs up when n grows from 1 to 9. After reaching the peak with n = 9, it starts to fall down until n = 14. The average number of collisionset15 stays at 0, which is in accordance with Figure2. That is because all the reader sets with cardinality higher than 14 have a subset (i.e., a minimal collision set) that already generates an interference perceived by the target reader.
When n < 9, the average number of collisionsetn climbs up because of two reasons: firstly, the probability of generating collisions increases as the number of interfering readers grows, and secondly, the number of potential subsets that may generate collisions grows with the cardinality n. For example, the total number of subsets with cardinality 1 is${(}_{1}^{50})=50$, while the number of subsets with cardinality 4 grows to${(}_{4}^{50})=230,300$. Although the maximal number of subsets continues to grow when 9 < n < 20, the subsets that can generate collisions fall down since many collision sets include minimal collision sets with cardinality lower than 9.
Throughput analysis
where s_{ n } represents the average number of sets with n additive components. In the case study of 50 readers deployed on a 1,000×1,000 m square, the evaluation of (27) according to p and n is shown in Figure5. It can be observed that:

If p is high, also the average number of possible collisions is high, so the probability of successfully querying tags is very low.

If p is high, the distribution curve of the quantity of collisions according to the cardinality of the collision set initially increases up to an absolute maximum and then it decreases.

If p is low, the distribution curve constantly decreases and the most common collisions have only one component.
which considers the distribution of the collision sets.
Accuracy analysis
It can be observed that although the distribution of the collision sets is similar to a Gaussian distribution, the actual collision probability with cardinality n decreases as the value of n increases. Figure8 also shows that the majority of the collisions are due to sets composed by few readers, while the majority of the existing sets include many readers. Therefore, a large part of the collision sets cannot be considered in the analysis of the performance of a protocol, without affecting significantly the accuracy of the results.
Conclusion
This paper has studied the characteristics of the additive interference models for detecting RFID readertoreader collisions. The impacts of the cardinality of the collision sets on the accuracy of collision detection has been analyzed. An evaluation based both on simulations and on an analytical analysis has shown that a model limited to direct interferences provides a low level of accuracy since many collisions could be not detected (e.g., 29% in the analyzed case study). However, a few collisions are due to collision sets with high cardinality, so the models used for the evaluation of RFID readertoreader anticollision protocols can be limited to small collision sets. These results open an important issue on the simulation strategies used for evaluating RFID readertoreader anticollision protocols and on the reliability of the simulation results.
Endnote
^{a}ETSI EN 300 328 V1.8.1.
Notes
Declarations
Acknowledgements
This work was supported in part by Grant ‘Nanomaterials and technologies for intelligent monitoring of safety, quality and traceability in confectionery products (NAMATECH)’ from Regione Piemonte, Italy.
Authors’ Affiliations
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