11.IJAEST-Vol-No-5-Issue-No-1-A-NEW-APPROACH-TO-COPE-WITH-THE-CAPTURE-EFFECT-IN-RFID-TAG-IDENTIFICAT by ISERP ISERP

SATEESH.K et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 5, Issue No. 1, 078 - 086

A NEW APPROACH TO COPE WITH THE CAPTURE EFFECT IN RFID TAG IDENTIFICATION BY USING GENERAL BINARY TREE PROTOCOL Student (M.Tech)

Meetme.ksk@gmail.com

FAYAZ AHAMAD.SK

Dr. SRI RAMA KRISHNA.K

Lecturer Professor & Head Department of Electronics & Communication Engineering TIFAC CORE in Telematics V R Siddhartha Engineering College Vijayawada, A.P-520007 skfayaz_01@gmail.com srk_kalva@yahoo.com

KANTIKIRAN .M Lecturer

kantikiran@gmail.com

SATEESH.K

Abstract—Tag anti-collision is an important issue in RFID systems because the reader must recognize all tags efficiently. In RFID wireless communication systems, tag identification will encounter the capture effect, where a reader decodes a tag ID even when multiple tags simultaneously transmit their signals. This letter proposes a tag anti-collision algorithm−the generalized binary tree protocol (GBT). GBT separates the identification process into several binary tree (BT) cycles to solve the problem caused by the capture effect and reduce the waste of idle slots. Unrecognized tags, hidden by the capture effect in a BT cycle, will be identified in subsequent cycles. The formal analysis of identification delay for GBT is derived and simulation and analytical results show that GBT significantly outperforms other existing algorithms. Keywords- RFID, tag identification, anti-collision, capture effect.

I. INTRODUCTION Radio frequency identification (RFID) passive tag singulation is the process where a single reader collects the identifiers (IDs) of all the passive tags in its broadcast range. Since the tags share the same wireless medium for backscattering, singulation algorithms are collision resolution protocols. There are two main classes of such protocols. In probabilistic approaches, a mechanism similar to Aloha is used, where the reader broadcasts a query, telling each tag to randomly choose time slot in which to reply [2]. A collision occurs when two or more tags choose the same time slot. In contrast, the Query Tree Protocol (QT) in [1] is a deterministic approach. In this case, the reader successively sends longer query prefixes. If a tag’s ID matches the prefix, the tag responds with its entire ID. A collision occurs when two or more tags’ IDs match the same prefix. Since the query prefixes become longer, eventually only one tag will respond. [3], [4], and [5] provide improvements to QT, but they are all based on the same underlying principle. In [1], after the reader broadcasts a bit string query prefix, it is assumed that it can distinguish one of three responses, namely {no response, one response, collision}. In other words, the capture effect, which is a receiver decoding a signal even in

ISSN: 2230-7818

the presence of other interfering signals, is ignored. If the capture effect is modelled, QT would no longer be guaranteed to singulate all the tags in the reader’s range, since ― capturing‖ a tag ID in the midst of a collision would leave all the other tags in that collision unsingulated. In this paper, here introduce two modifications to QT that always singulate all the tags even when the capture effect is considered. We call these the Generalized Query Tree Protocols (GQT1, GQT2). An important performance metric for these protocols is the time required to singulate all the tags. We provide analytical bounds and simulation results on the singulation times of GQT1 and GQT2. TAG anticollision is important in RFID systems and there are currently two main types of anti-collision methods: alohabased protocols [6] and tree-based protocols [7][8]. Alohabased protocols estimate the number of tags and assign the proper number of slots to reduce the probability of tag collisions. Tree-based protocols continuously split a set of tags into two subsets−an immediate node expands two child nodes in a binary tree, until all tags are identified. Tree-based protocols can be classified into query tree (QT) and binary tree (BT) protocols. QT uses tag IDs to decide these splits, so its identification delay is significantly affected by the ID

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II. QUERY TREE PROTOCOL In this section, we consider the Query Tree Protocol (QT), as explained in [1]. The algorithm works with the reader repeatedly sending a query, and then waiting for a response from the tags. In each query, the reader asks the tags if their IDs contain a certain prefix. All the tags that do, respond by sending their tag IDs. If more than one tag responds, the reader detects a collision. It then appends a 0 or 1 to the prefix, and makes another query with the new longer prefix. When only one tag responds, its ID can be decoded by the reader. Each query prefix is associated with a node in a full binary tree (the query tree). If a node has prefix xxx, then its two children have prefixes xxx0 and xxx1. Fig. 2, reproduced from [1], illustrates QT. Note that [1] does not take into account of the locations of the tags, as we model in Section II. That is, the backscattered signals of the responding tags for a particular query are assumed to be received simultaneously at the reader. The algorithm is shown below for completeness and comparison. At the end of the algorithm, the IDs of all the tags are stored in M. QT Protocol Reader 1) Q :=< 0, 1>, and M :=<>. 2) Suppose Q =<q1,,,,,,ql>, and M =<t1… tm>. 3) Broadcast query q1 to tags Q:=<q2,….,q1>, 4) Listen to responses from tags. .If no response, then do nothing. .Else, if the response is tag ID M :=< t1… tm, t>. . Else, a collision is detected, then unable to decode. Q :=< q2… ql, q10, q11>. 5) If Q is nonempty, go to 2).

distribution. BT uses the random numbers to operate these splits, so tags need memory to store their counters. In general, BT has better performance than QT, at the expense of more complex capability and higher cost of tags. Previous research all assumes that a successful slot, i.e., a slot where the reader can decode a tag ID, occurs only when one tag transmits its signal. Thus, they regard this successful slot as a leaf node and do not expand it. However, this assumption completely neglects the capture effect, where a reader decodes a tag ID even when multiple tags simultaneously transmit their signals, because the signal of one tag is significantly stronger than that of the others. Some realistic experiments demonstrated that the capture effect actually appears in RFID systems and the probability of occurrences depends on the relative attenuation between the tags [9][10]. Thus, previous anti-collision algorithms cannot recognize all tags, because they do not expand a successful node, causing that some tags hidden by the capture effect are not recognized. Two algorithms, general query tree 1 (GQT1) and general query tree 2 (GQT2), were proposed to solve the problem caused by the capture effect [11]. These algorithms continually expand a successful node to recognize possible tags hidden by the capture effect. Practically, when the reader sends query q and successfully decodes a tag ID, a reader using GQT1 enqueues two additional queries q+― 0‖ and q+― 1‖ for possible unidentified tags whose ID prefixis q. GQT2, an improvement on GQT1, lets the reader enqueue the same prefix q again after this successful slot. Additionally, the reader in GQT1 or GQT2 must send an acknowledgment indicating which tag was identified at this slot; thus, the recognized tag can keep silent and not respond to the newly queued queries. GQT1 and GQT2 actually solve the problem caused by the capture effect; however, they spend some idle slots for these extra queued queries when the frequency of the capture effect is low. Therefore, we propose the generalized binary tree protocol (GBT), which is modified from BT, to cope with the problem caused by the capture effect and reduce the waste of idle slots. GBT separates the overall identification process into several BT cycles. All unrecognized tags, caused from the capture effect in the current BT cycle, will be identified in the next BT cycle. The BT cycles are repeated until all tags are identified by the reader. The rest of this letter is organized as follows. Sections 2 we re-introduce QT as explained in [1], and explain its shortcomings in the context of the capture effect. In Section 3 we introduce, GQT1, and GQT2. Section 4 presents the concept, operation, and an example of GBT. Section 5 analyzes its performance and Section 6 shows analytical and simulation results comparing GBT with GQT1 and GQT2. Finally, Section V concludes this letter.

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Tag 1) Listen to query or ACK from reader. . If query prefix matches, then send tag ID. 2) If not silenced, then go to 1)

A. Singulation Time Upper Bound [1] Defines the identification time of QT as the number of queries required for the reader to singulate all n tags. For comparison purposes, we define the singulation time, T P  n  , as the total running time of singulating n tags, using protocol P, where PQT ,GQT 1,GQT 2 . We further assume that both a reader query and a tag response each take half a time unit. [1] Shows that the worst case time complexity (that is, an upper bound on T QT  n ) is given by

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

T QT  n   n k  2  log 2n

.

(1)

B. Capture Effect

(2)

∑

In [1], QT relies on the assumption that the tags’ response to a reader query falls into one of three choices. These are {no response, one response, collision}. More precisely, the reader receiver is assumed to be able to distinguish between the three cases, and decode a tag ID only for the case of a single tag backscattering. However, this assumption is rather strong, and ignores the capture effect. The capture effect describes a situation where a receiver May be able to decode a signal even in the presence of other interfering signals. In the context of QT, the reader receiver can only distinguish between two cases, namely {no response, response}.

distance between the reader and the backscattering tag. All tags are assumed to be physically identical, and have the same effective area for absorbing incoming radio energy from the reader. Suppose a reader query results in l tags responding, where l ∈ {... n}. Then, if the i th tag’s backscatter is considered the signal, its SIR is

Figure. 2(a). Capture effect in 2-state QT with tag IDs {000, 001, 101, and 110}.The capture effect enables the reader to decode 001 when the preﬁx 0 is queried. This causes the entire segment of the tree below the arc to be eliminated. As a result, the tag with ID 000 is not singulated.

Figure. 1. QT with tag IDs {000, 001, 101, 110}. The bit strings inside each node are query prefixes. In a query prefix that results in one tag responding, the associated node is a leaf, and the bit string below that leaf is the decoded tag ID. Note that the query prefix 01 is also associated with a leaf, but since it results in no response from the tags, there is no ID below it.

If there is no response, the reader can be certain that no tags have replied. If there is a response, the reader only knows that at least one tag has replied. It may or may not be able to decode a tag ID from the response, but this would still not allow it to know how many tags had replied. We call 3-state QT as the situation where no capture effect occurs. Note that TQT n applies to 3-state QT. 2-state QT is when there is capture effect. 2-state QT is faulty in the sense that the reader does not necessarily singulate all n tags in its range. That is, if the capture effect causes a reader to decode a tag ID from multiple signals due to multiple tags responding to a common preﬁx, then all but one of those tags would not be singulated, since that segment of the query tree with that common preﬁx would no longer grow. This is illustrated in Fig. 2. In this paper, model the capture effect using a parameterized signal-to-interference (SIR) threshold, γ, of the reader receiver. We assume a free space, path loss radio propagation model. Therefore, a backscattered signal arriving at the reader has power attenuated by a factor of d4, compared to the original reader transmission, where d is

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Where di is the distance between the reader and the ith tag, and i ∈{ 1,...,l}.If

l max SIRi   i 1

(3)

Then the capture effect occurs, and the reader decodes the ID of the kth tag, where

l k  argmax i 1SIRi Therefore, γ is a parameter that determines how effective the reader receiver is at extracting a tag ID in the midst of multiple signals. III. Generalized Query Tree Protocols We introduce two modifications to QT. Since these are natural generalizations of QT that can handle the capture effect, we call them the Generalized Query Tree Protocol (GQT1 and GQT2). We also provide bounds on the singulation time of these two protocols, in relation to TQT (n). In Section V, we provide simulations to verify these results.

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5 T GQT1 n   2  n 2

Combining the two bounds, we have,

5   5 T GQT1 n    2  n, T QT  n   n  2   2

Using the upper bound for TQT (n) in (1), we have

(4)

 5  9  T GQT1 n   2  n, n  k   log 2n    2  2

(5) GQT1 Protocol Reader 1) Q :=< 0, 1>, and M :=<>. 2) Suppose Q =<q1,,,,,,ql>, and M =<t1… tm>. 3) Broadcast query q1 to tags:=<q2,….,q1>, 4) Listen to responses from tags. .If no response, then do nothing. .Else, try to decode a tag ID. -If able to decode a tag ID t, then Q :=< q2… ql, q10, q11>, and M :=< t1… tm, t>.send ACK to tag with ID t. -Else unable to decode. Q :=< q2… ql, q10, q11>. 5) If Q is nonempty, go to 2).

There are two major changes that GQT1 makes to QT. In 3state QT, when a query prefixes results in no response or a single response, we can be sure that there are no more IDs with that prefix. In other words, this is the stopping condition of lengthening a prefix (by appending a 0 or 1). However, if the capture effect is taken into consideration, a stopping condition that guarantees singulation of all tags is that there is no response. Therefore, the first change to QT is that in GQT1, the prefix is always lengthened if there is a response. (The one exception is if the prefix length is already k bits.) The second change is that after an ID has been decoded by the reader, it sends an ACK signal to that specific tag, to tell it to silence itself. That is, the reader lets the tag know it has already singulated it, and the tag need not send any more backscatter responses for the rest of the singulation process. This is important, since when the prefix is lengthened and queried again, it may still match the ID of the previously singulated tag. For example, suppose there are three tags with respective IDs {10000, 10111, 10110}, and the reader broadcasts a query with prefix 10. All three tags will respond. Suppose the capture effect allows the reader to decode 10000 from the three responses. If the reader does not send an ACK signal to the first tag, and it broadcasts the next query with prefix 100, the first tag will respond again, which is unnecessary. This second change is also a result of the the differing stopping conditions of 3-state QT and GQT1. GQT1 is shown below. GQT1 leverages the capture effect to prevent query prefixes from becoming very long, and thus, reduces the size of the query tree. As the SIR threshold, γ, of the reader receiver increases, less ― captures‖ occur, and the singulation time increases. An upper bound of TGQT1 (n) is thus when γ is sufficiently large, and therefore, the capture effect will never take place. In this case, the algorithm runs exactly the same as QT, with the exception that there are two extra queries for each ID, since the stopping condition for GQT1 is that there is no response. This results in an additional time of 2n. Recall that both a reader query and a tag response each take half a Time unit. Suppose that ACKing a tag also takes half a time unit. Therefore, the total ACKing time is n/2. We thus have the following upper bound for n ≥ 2. TGQT1 ( ) ≤ TQT ( ) +

A. GQT1

A lower bound of TGQT1 (n) is when γ is sufficiently small, and the capture effect always occurs if more than one tag responds. In this case, the query tree will consist of a root node (which is just a place holder), n other internal nodes representing the n queries that each result in a decoded tag ID, and the leaves of the tree. This is illustrated in Fig. 4. Since the tree is a full binary tree, we have n+1 = r−1, where r is the number of leaves. Therefore, the number of nodes in the tree, excluding the root, is n+r = 2n+2. Including the total ACKing time, we have the following lower bound for n ≥ 2.

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Tag 1) Listen to query or ACK from reader. . If query prefix matches, then send tag ID. .Else if ACK is intended for myself, silence myself. 2) If not silenced, then go to 1)

B.GQT2

There is only one slight change that GQT2 makes to GQT1. To further take advantage of the capture effect, GQT2 does not a append a 0 or 1 to the prefix when the reader decodes a tag ID. Rather, the reader re-broadcasts the same prefix. Since the ACK silences the tag that was just singulated in the previous query, another tag can be ― captured‖ using the same prefix. Only when no ID can be decoded from a response does the reader append 0 or 1 to the prefix. GQT2 is shown below. An upper bound of TGQT2 (n) follows the same reasoning of the upper bound of TGQT1 (n). The only difference is that there is only one extra query for each ID, since after decoding a tag ID from a prefix, it only has to re-broadcast the same prefix to detect that there is no response, which is the stopping condition. The upper bound for n ≥ 2 is thus,

3 T GQT 2  n   T QT  n   n 2

A lower bound of TGQT1 (n) is when γ is sufficiently small, and the capture effect always occurs if more than one tag

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responds. In this case, the initial prefixes {0, 1} are sufficient to decode all the IDs, one-by-one with the capture effect. This contributes a time of n. There are also two extra queries, one for each prefix that results in the stopping condition. Including the total ACKing time, the lower bound for n ≥ 2 is thus

to terminate the identification process. The reader must experience RC +1 slots before the end, that is, the reader finishes the identification process when RC = −1.

3 T GQT 2  n   2  n 2

Combining the two bounds, we have,

3   3 T GQT 2  n    2  n, T QT  n   n  2   2

(6) . . Using the upper bound for TQT (n) in (1), we have

1) Listen to query or ACK from reader. . If query prefix matches, then send tag ID. .Else if ACK is intended for myself, silence myself. 2) If not silenced, then go to 1)

Tag

Figure.2. (b) the ﬂow chart of binary tree algorithm

(7) GQT2 Protocol Reader 1) Q :=< 0, 1>, and M :=<>. 2) Suppose Q =<q1,,,,,,ql>, and M =<t1… tm>. 3) Broadcast query q1 to tags:=<q2,….,q1>, 4) Listen to responses from tags. .If no response, then do nothing. .Else, try to decode a tag ID. -If able to decode a tag ID t, then Q :=< q2… ql, q1>, and M :=< t1… tm, t>.send ACK to tag with ID t. -Else unable to decode. Q :=< q2… ql, q10, q11>. 5) If Q is nonempty, go to 2).

 3  7  T GQT 2  n    2  n, n  k   log 2n    2   2

IV GENERALIZED BINARY TREE PROTOCOL

GBT separates the identiﬁcation process into several BT cycles. GBT regards each successful slot, unlike GQT1 and GQT2, as a leaf node and does not expand it. Unidentiﬁed tags, hidden by the capture effect in the current cycle, will be recognized in the next BT cycle. Like BT, GBT stores the Tag Counter (TC) and Reader Counter (RC) in the tags and the reader, respectively. The tag uses TC to determine how many more slots to wait before transmitting its ID. Thus, every tag transmits its ID when TC =0. The reader uses RC

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Above table show the pseudo-code of the GBT reader and tag, respectively. In the beginning, RC and all TCs are initialized to zero and the reader sends a start command to all tags. After receiving the start command, all tags transmit their IDs because their TCs equal 0. The reader then detects the state in each slot and informs all tags of that state. The reader and tags also adjust their counters according to the current state. If the reader does not detect a signal, i.e., it is an empty slot, the reader decreases RC by one and all tags decrease their TCs by one. However, when a collision slot occurs, the reader increases RC by one. The tags involved in this collision, i.e., tags with TC =0, add a random binary number (0 or 1) to TC, and tags with TC≠0 increase their TCs by one. GBT requires special handling for successful slots because of the capture effect. The reader additionally maintains a Boolean parameter: Extension Flag (EF), indicating whether the reader has already reserved the first slot of the next BT cycle for unidentified tags hidden by the capture effect. EF is set to False when RC=0, which represents a new BT cycle. When a successful slot occurs, the reader uses EF to determine whether the first slot of the next BT cycle has been reserved. If EF is False, the reader changes EF to True and reserves a slot for initializing the next BT cycle. GBT achieves this reservation by keeping RC unchanged because RC is decreased by one due to the successful slot, and it is increased by one due to the reservation. On the other hand, when EF is True, the reserved

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slot is already settled, so the reader only decreases RC by one. At this point, the reader responds a successful feedback, which also conveys the ID of the identiﬁed tag, IID, and RC, to all tags. After receiving this successful feedback, each tag involved in this slot, i.e., tags with TC =0, checks whether its ID matches IID. If they are the same, the tag has been identiﬁed in this slot and it decreases TC by one to keep it silent afterwards.

that it will wait until the next BT cycle. Similarly, at the fifth slot, tag C is identified and tag D resets TC as the received RC The first BT Cycle lasts from the first to the fifth slot. In the beginning of the second cycle, two unidentified tags (B and D) have RC =0 at the sixth slot and will collide. They are identified at the seventh and eighth slots because they choose 0 and 1, respectively. Finally, the third cycle only occupies one empty slot, so RC becomes −1 and the identification process is terminated. Pseudo code of GBT: Reader 01. RC=0 02. Send start command 03. While (0≤RC)

The tree presentation of GBT

05. EF=False 06. Listen to signals 07. If no signal 08. RC=RC-1 09. Respond empty 10. Else 11. Try to decode ID from signals 12. If an ID is decoded 13. If EF=False 14. EF=True 15. Else 16. RC=RC-1 17. Respond successful (IID, RC) 18. Else 19. RC=RC+1 20. Respond collision

04. IF (RC=0)

*denotes the tags hidden by capture effect b) The procedure of GBT Figure.3 An example of GBT.

If they are different, the tag is a unidentified tag due to the capture effect, so it sets its TC as the received RC value. This setting lets the tag transmit its ID at the reserved slot in the next BT cycle. Also, tags with TC≠0 just decrease their TCs by one. Figure 3 shows the operation of GBT where there are four tags: A, B, C, and D First the reader sends a start command to begin the identification process. At the second slot, the reader identifies tag A because of the capture effect, even though tag B also transmits its ID. Thus the reader changes EF to True and sends a successful feedback with IDA and RC. After receiving this feedback, tag A perceives that it has been recognized and keeps silent while tag B knows that a capture effect occurred and it sets its TC to the RC, meaning

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Tag 01. TC=0 02. Receive start command 03. While (0≤TC) 04. If (TC=0) 05. Sends its ID 06. Receive feedback f (IID, RC) 07. If f=successful 08. If ID=IID 09. TC=TC-1 10. Else 11. TC=RC 12. Else If f=collision 13. TC=TC + Rand (0, 1) 14. Else 15. Received feedback f (IID, RC) 16. If f=collision 17. TC=TC+1 18. Else

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19. TC=TC-1 V.

MATHEMATICAL ANALYSIS

The GBT identiﬁcation delay is analyzed in terms of slots under the assumption that the probability of the capture effect is α. Since GBT consists of several

(b) Average singulation time of GQT2. Figure. 4. GQT1, GQT2 simulation results.

D BT  n     1    2 1

n

n

i 0

 

  i   D BT i   D BT  n  i  1

  D 1 BT  0   0    1 1  1  D BT     

,

(a) Average singulation time of GQT1.

BT cycles, we ﬁrst let denote the number of consumed slots of a BT cycle under the capture effect when the number of unrecognized tags is n. When a capture effect happens at a slot, the number of consumed slots is one, since BT will not further expand the corresponding node. On the other hand, when the capture effect does not occur, n unidentiﬁed tags will collide, so they are randomly separated into two subsets. Thus, D BT  n  can be written by Eq. (8).

D BT  n     1    2

n

n

i 0

 

To calculate the GBT identiﬁcation delay, the number of identiﬁed tags in each cycle must be known. Let r j denote e number of tags recognized during the j-th BT cycle, and

denote the number of unrecognized tags in the beginning the j-th BT cycle. Thus u j and r j can be obtained as j 1

u j  n  r j i 1

(9)

  i  1  D BT i   D BT  n  i 

n 1 n   1        D BT  i  i 0  i  , 1 n 1  2 1   

IJ 1 2

1 n



(8)

 D BT  0   1    D BT 1  1 

Similarly, the number of successful slots, obtained with the recursive equation:

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  , can be

D1 BT n

Figure. 5. Identiﬁcation delay of GBT versus α.

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ď&#x20AC;˝ D 1 BT

results

ď&#x20AC;¨u ď&#x20AC;Š j

for

GBT,

GQT1,

and

(10)

Using Eqs. (9) and (10) alternatively, we obtain u1 , r1 , u 2 , r 2 , u 3 , r 3 ... u m , r m , where u1 = n and r m = u m . Finally,

the GBT identiďŹ cation delay, D BT ď&#x20AC;¨ n ď&#x20AC;Š , is the sum of the delay of all BT cycles plus one, and can be easily obtained as m

D BT ď&#x20AC;¨ n ď&#x20AC;Š ď&#x20AC;˝ ď&#x192;Ľ D BT j ď&#x20AC;˝1

ď&#x20AC;¨u ď&#x20AC;Š ď&#x20AC;Ť 1 j

(11)

Adding one in Eq. (11) is because GBT needs a last cycle, which has only one empty slot, to ascertain that there are no unidentiďŹ ed tags and it can terminate the identiďŹ cation. There are two extreme cases: where the capture effect always occurs (Îą =1); and, where it never occurs (Îą =0). When Îą =1,

ď&#x20AC;¨ ď&#x20AC;Š (is equal to n+1 because each BT cycle recognizes a

D BT n

Figure.6.Simulation GQT2

and GQT2. 3-state gives the best performance (since the capture effect is ignored in this case). GQT2 performs better than GQT1 at the same Îł. At Îł dB and n , GQT2 requires approximately additional seconds compared to 3-state QT. In the performance evaluation, we compare the performance of GBT, GQT1, and GQT2 for different values of Îą. Each tag has a 96-bit ID, which is unique and chosen from a uniform distribution. Above Figure 3 shows the results from GBT simulation and mathematical analysis. Since the number of identified tags in the j-th BT cycle, must be an integer in Eq. (10), the ceiling đ?&#x2018;&#x;đ?&#x2018;&#x2014; and floor functions â&#x152;&#x160;đ?&#x2018;&#x;đ?&#x2018;&#x2014;â&#x152;&#x2039; are used to obtain the analytical results. From Fig. 3, the simulation result lies between the mathematical results with the ceiling and floor functions. The use of ceiling function causes in overestimation of the number of recognized tags in each BT cycle, resulting in a lower bound of identification delay. On the other hand, the use of floor function causes in underestimation and produces an upper bound. Also as đ?&#x203A;ź increases, although the number of BT cycles increases, the duration of each cycle becomes smaller, generating a lower overall GBT identification delay. An unusual phenomenon occurs when Îą= 0.7. The reason is that the values of đ?&#x2018;&#x;đ?&#x2018;&#x2014; â&#x2C6;&#x2019; â&#x152;&#x160;đ?&#x2018;&#x;đ?&#x2018;&#x2014;â&#x152;&#x2039; when Îą = 0.7 are much closer to 1 than those when đ?&#x203A;ź = 0.6 and đ?&#x203A;ź = 0.8. A larger truncation for đ?&#x2018;&#x;đ?&#x2018;&#x2014; produces larger underestimation of the number of recognized tags, resulting in a higher bound of identification delay. VII.CONCLUSION This letter proposes the GBT algorithm to cope with the problem caused by the capture effect. GBT reserves the ďŹ rst slot in the next cycle to handle unidentiďŹ ed tags hidden by the capture effect. Analytical and simulation results show that GBT signiďŹ cantly outperforms the existing algorithms, GQT1 and GQT2.

tag. When Îą =0, GBT uses only one BT cycle to recognize all tags; therefore, it is reduced to the original BT and has the same performance, except that it has one additional slot. VI.ANALYTICAL AND SIMULATION RESULTS

Figure. 4(a) and Figure.4 (b) show the average singulation times of GQT1 and GQT2, i.e. TGQT1 n and TGQT2 n, respectively. The upper and lower bounds in (4) and (6) are also shown respectively, in the two plots. As expected, as Îł increases, there are less â&#x20AC;&#x2022; capturesâ&#x20AC;&#x2013;, and the average singulation time increases. In both protocols, Îł dB is sufďŹ cient for the average singulation time to approximate the upper bound, and Îł â&#x2C6;&#x2019; dB for the lower bound. Fig. 7 compares the average singulation times of 3-state QT, GQT1

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REFERENCES

[1] C. Law, K. Lee, and K.-Y. Siu, â&#x20AC;&#x2022; Efficient memory less protocol for tag identiďŹ cation,â&#x20AC;&#x2013; in Proceedings of the 4th International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, Boston, MA, Aug. 2000, pp. 75â&#x20AC;&#x201C;84. Multiple object identiďŹ cation with passive [2] H. Vogt, â&#x20AC;&#x2022; RFID tags,â&#x20AC;&#x2013; in IEEE International Conference on Systems, Man and Cybernetics, Hammamet, Tunisia, Oct. 2002.

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