DETECTION ERROR IN RFID SYSTEMS
4.3. Proposed Missing-Tag Event Detection Protocols
In this section, we propose two modified versions of RUN protocols, namely mRUN1 and mRUN2, for missing-tag event detection considering not only unexpected tags but also the detection error. Both the ALOHA frames and assumed tracking counters supposedly available at the reader are utilized to mitigate the effects of the phenomena.
4.3.1. Protocol Description
The proposed protocols plan to use n detection rounds, which might be initially set as +∞, for a detection of the missing-tag event. In the i-th (i ≤ 1 ≤ n) round, the reader broadcasts a message consisting of a frame size fi and a random seed Ri. Tags upon receiving the message randomly respond to the reader in one of the fi timeslots where the random slot selection is based on the hash function described in Section 4.2.
Here, owing to the hash function, the reader knows exactly which slots are non-empty if no tags in E are missing.
The reader is assumed to have tracking counters that are initially set to zero. The purpose of the counters is to mitigate the effects of the detection error on the protocols’
performance. In particular, if a slot, which is expected to be non-empty, is observed as empty, the proposed protocols increase counters involved in the slot by one. If any counter reaches a predefined threshold denoted by Cth, mRUN1 and mRUN2 stop executing and declare that the missing-tag event happens. Otherwise, the reader es- timates the number of un-expected tags |U| by which the optimal frame size used for the next round and the remaining number of detection rounds denoted by fi+1 and ni+1, respectively, can be re-estimated. These assumptions are valid in RFID domains thanks to the power of the reader, and were used in several works [67, 64]. If the reader does not detect the missing-tag event after the total number of detection rounds, it declares that the number of missing tags m is less than T .
More specifically, mRUN1 requires |E| counters denoted by C1, ã ã ã , C1 to monitor
1 |E|
the existence of the corresponding |E| expected tags. During the i-th frame, if the missing-tag event is detected in several slots, the counters of all expected tags involved in the slots are increased by one. The reader then keeps transmitting the same frame size and the random seed in next reading rounds. In the other cases where no missing event is detected, the counters are kept unchanged and the detection process continues with different frame size and random seed. The transmission is repeated until a counter reaches Cth. Thanks to this mechanism, the missing event caused by real missing tags happens again at the same slots. Moreover, the probability that the existing tags
67
Figure 4.3: Flowchart of mRUN1 protocol.
are notified as the missing tags due to the detection error is significantly reduced.
Nevertheless, mRUN1 although can find exactly which tag is missing, it costs more hardware implementation at the reader (for |E| counters) and the time (number of timeslots) to monitor each tag.
On the other hand, the reader uses only one counter denoted by C2for mRUN2 to monitor the missing-tag event. If the event is found in a detection round, the reader increases C2 by one and stops executing the remaining slots of the current frame (This mechanism is different from that of mRUN1 where all the slots of each frame are utilized). Then, the reader retransmits the same frame size and the random seed. In this case, if the event is still detected at the same slot, C2 is increased by one again, and this retransmission process is repeated until C2 reaches Cth. During the process, if the
Start
Detect a missing-tag
event
Yes
No
Yes i ≤ 𝑛i
No
Cj 1 = C th No Yes
End
The missing-tag event happens The missing-tag event
does not happen or happens due to D.E.
j
Cj 1 = C1 + 1 i = i + 1
Estimate |¢i|
Calculate 𝑛i , fi
Check all slots involved in the event and observe
missing tag j
Broadcast the same fi, 𝑅i and observe empty, non-empty slots Broadcast fi, 𝑅i and
observe empty, non-empty slots Cj 1 = 0, j = [1, |➪|]
Initialize:
|¢|, |➪|, 𝑚, 𝑇, 𝛼, 𝑃de , 𝑡, Cth i
= 1, fi = 2|➪|, 𝑛i = +∞
Detect Yes missing-tag
event at the k-th slot again
Detect
missing-tag event Yes at the earliest
(k-th) slot No
Yes C2 = C No
th
i ni
No Yes
End
The missing-tag event happens The missing-tag event
does not happen or happens due to D.E.
C2 0 i i 1 Estimate Ui
Calculate ni , fi
C2= C2 + 1 Stop executing, do not check the remaining slots
Broadcast the same fi , Ri and recheck
the status of the k-th slot Broadcast fi , Ri and
observe empty, non-empty slots
No
Figure 4.4: Flowchart of mRUN2 protocol.
event is not detected, C2 is set to zero and a new message with different frame size and random seed is created and broadcasted to the tags. mRUN2, different from mRUN1, only deals with the missing-tag event without showing the specific missing tags. Also, since only one counter is employed, mRUN2 reduces the hardware complexity and, the total protocol execution time in comparison with mRUN1. The proposed protocols are summarized in Figs. 4.3 and 4.4. Furthermore, we also explicitly contrast our study to RUN protocol in Table. 4.1.
Table 4.1: A comparison of related works on missing-tag event detection.
Work Detect missing -tag event
Determine exactly missing-tag
Consider
unexpected tag Consider DE.
RUN Yes No Yes No
mRUN1 Yes Yes Yes Yes
mRUN2 Yes No Yes Yes
Start
Initialize:
U , E , m, T , , Pde , t, Cth i 1, fi 2 E , ni
C2 0
69 01
01
!
01 01
!
01
Σ1
, ,
Xln 1
− ,
1
#)
f
4.3.2. Parameter Optimization under Impacts of Unexpected Tags and De- tection Error
The proposed protocols try to quickly detect a missing-tag event with at least to a required probability α, (0 ≤ α < 1) whenever the number of missing tags m exceeds the threshold T . Therefore, protocols’ parameters such as fi and ni before the i-th round should be optimally selected to not only satisfy those pre-defined requirements but also improve the performance efficiency of the protocols. To do this, our protocols first estimate the number of unexpected tags |U| that may result in incorrect observations in each frame. In particular, if we denote by pi the probability that an expectedly empty slot is observed as non-empty in the i-th frame, it can be calculated as
pi = (1 − Pde) 1 |U|
1 − 1 −
f , (4.5)
where Pde is defined as the detection error probability, while [1 − Pde] is the probability that the detection error does not happen in that slot. This equality is held thanks to the random responses from tags over the frame. The expected number of those slots in the i-th frame denoted by E[Xi ] can also be computed as
E[Xi ] = (fi − ki) (1 − Pde) 1 |U|
1 − 1 −
f , (4.6)
where ki is the number of slots out of the fi ones that is expectedly non-empty. Based on (4.6), the estimate of |U| before the i-th round can be found using the observed values of Xi over the previous frames as follows
i−1
U (1−Pde)(f01 l l−kl) (4.7)
| i| = − i − 1
l=1 ln
, .
1 − fl
When this estimate does not change by more than a predefined threshold t% in c consecutive frames, the estimate is understood as the real value of |U|.
Given the estimate of |U|, we now find the optimal values of fi and ni. In particular, we first denote by Pfp a probability that slots, which expectedly include a particular missing tag, are observed as non-empty after n executed frames. The probability can be written as
Pfp = (
[1 − Pde]
"
1 − 1 |U|+|E|−m n
1 − f . (4.8)
+ m Here, 1 −
1 − 1
|U| |E|−
is the probability that at least one tag in our system responds during the slot that expectedly includes the missing tag’s response. Since
i
i
fp
| | | |−
(1−α)
1 − 1 −
f 1 −
f 1 −
f
the proposed protocols are required to detect the missing-tag event with a probability greater or equal to α when m ≥ T , the following condition should be satisfied
or equivalently,
1 − PT ≥ α, (4.9)
f ≥ 1
1 − 1 − (1−α) nT 1
1
|U|+|E|−m
. (4.10)
1−Pde
In this case, f can be numerically selected as the minimum value satisfying (4.10) to improve the performance efficiency of the proposed protocols in terms of timeslots con- sumption, given the estimate of Pde. In this chapter, we assume that the detection error probability Pde is known a priori thanks to a certain method using measured trans- mission data. The method could be based on, for example, expectation-maximization (EM) approach [99]. Studies that try to improve the estimation accuracy of Pde will be investigated in future works. Consequently, given the frame size f , the total number of slots used to detect a missing-tag event denoted by S is written as
n S =
1 − 1 −
1 . (4.11)
1 U + E m
nT
1−Pde
To find the optimal value of n that minimizes the executed time for a detection of the event, we can set the differentiation of S with respect to n to be 0, and use Newton- Raphson searching method.
4.3.3. Expected Detection timeslots
Here, the expected detection timeslots of two protocols mRUN1 and mRUN2 respec- tively denoted by D1and D2 are analyzed. Let g be the probability that a missing-tag event is detected at a given timeslot among f slots. Then, g can be computed as
"
1 |E|# 1 m
1 |E|+|U|−m
In (4.12) that the first term represents for the case where at least one tag in E re- sponds at the considered slot, while the detection error happens here. The second term describes another situation where at lease one missing tag maps to the slot in the pre-computed frame, and the others do not select this slot in the executed frame.
Therefore, if we denote by D the number of timeslots used for the first detection of a
g = Pde + 1 − . (4.12)
71
f
1 f
missing-tag event, the average value of D denoted by E[D] can be calculated for given values of f and n as follows
fn fn
E[D] = Σ
jP {D = j} = Σ
jg(1 − g)j−1, (4.13)
where P {D = j} is defined as the probability that the first missing-tag event is detected at slot j.
Since mRUN1 executes all slots of each frame, the expected number of slots in mRUN1 (D1) can be calculated as follows
D =
,E[D], + 1
f + (C — 1) f, (4.14)
where ⌊ a⌋ represents the largest integer smaller than or equal to a.
On the other hand, mRUN2 stops executing the remaining slots in each frame when a missing-tag event is detected. Therefore, D2 is written as
D2 = E[D] + (Cth — 1)
E[D] −
,E[D], f
. (4.15)