DETECTION ERROR IN RFID SYSTEMS
4.4. Numerical Results and Discussions
In this section, we evaluate the performance of the proposed protocols mRUN1 and mRUN2 with different system parameters via computer simulations. Similarly to [95], the value of the key parameters used in the simulation results are given in Table. 4.2, unless and otherwise specified. The detection error is assumed to be happen at any slots with responses. The simulation results are obtained by Matlab software and Monte Carlo method with 1000 iteration runs. The obtained results are compared with those of the conventional RUN, and also the recently published two-phase Bloom filter-based missing tag detection protocol (BMTD) [91] to show the merit of the proposed ones.
It is noted in BMTD that a Bloom filter is exploited at the reader to first deactivate the unexpected tags, and then test the membership of the other expected ones.
Before showing the performance of the proposed protocols, we investigate physical- layer perspectives of the detection error to validate our assumption in Section 4.2. In particular, we consider the transmission within a timeslot assuming the Rayleigh fading channel model with AWGN. The Signal-to-Noise Ratio (SNR) is set to be 10dB, while the threshold γth is supposed to be 3dB higher than the noise power. We then plot in Fig. 4.5 the detection error probability Pde with respect to the number of transmitting tags. It is interesting to observe that the probability is quite significant in our model
th
j=1 j=1
Table 4.2: Simulation parameters for missing-tag event detection protocols.
Symbol Description Values
|E| Number of expected tags 100
|U| Number of unexpected tags 1000
m Number of missing-tag 1
T Threshold to detect missing tags m
α Required reliability 0.9
Pde Probability of detection error 0.01
Cth Counter threshold -
f Frame size Equation. 4.10 , ,
n Number of frames required to ensure detection Tln(1/2) ln(1−α) C1 i The i-th tag counter, i ∈ [1, |E|] -
C2 Reader counter -
0.3 0.25 0.2 0.15 0.1 0.05
0
1 2 3 4 5
Number of tags per slot
Figure 4.5: Detection error probability Pde versus the number of tags in a slot.
especially when the number of tags in the slot is small. It implies that this phenomenon should be taken into account when designing missing-tag event detection protocols. In this chapter, to highlight the importance of the protocol design, we adopt a simple detection error model where the average detection error probability is the same at each non-empty slot. The more practical model will be investigated in future works.
We now plot in Fig. 4.6 theoretical and simulation results of the number of slots used in our proposed protocols for a given number of missing tags. The detection error probability Pde and the threshold Cth are supposedly 0.01 and 2, respectively. Note that they can be also set to other possible values. We can see that the theoretical resul t matches with the simulation one, which confirms the correctness of our analysis. It is also validated that the proposed protocols execute fewer timeslots when the number
Detection error probability
Detection error probability
73
mRUN1 Theoretical mRUN1 Simulation mRUN2 Theoretical mRUN2 Simulation
mRUN1 Theoretical mRUN1 Simulation mRUN2 Theoretical mRUN2 Simulation
|U| = 1000, |E| = 100, m = T, α = 0.9, P
3500 de
= 10-2, C = 2
th
3000 2500 2000 1500 1000 500
0
1 5 9 13 17 21 25 29 33 37 41 45 49 No. of missing-tags
Figure 4.6: Theoretical and simulation results of the number of slots with respect to the number of missing tags.
|U| = 1000, |E| = 100, α = 0.9, m = 1, T = 1, C = 2
3000 th
2500
2000
1500
1000
500
0
10-3 10-2
Detection error probability, P
de
10-1
Figure 4.7: Theoretical and simulation results of the number of slots with respect to the detection error probability.
of missing tags increases. Moreover, mRUN1 uses more timeslots for a missing-tag event detection than mRUN2. This is because while mRUN2 only deals with the event, mRUN1 needs to identify the involved missing tags. Besides, the validity of our analysis can be confirmed again in Fig. 4.7 where the number of slots is re-plotted with respect to the detection error probability, and the same behaviour of the performance of the proposed protocols is observed as that in Fig. 4.6.
No. of slotsNo. of slots
m m
m
N
|U| = 1000; |E| = 100; m = 1; T = 1; α = 0.9 1
0.8
0.6
0.4
0.2
0
10-3 10-2
Detection error probability, P
de
10-1
Figure 4.8: True-alarm and false-alarm probabilities with respect to the detection error probability of mRUN1.
4.4.1. False-Alarm and True-Alarm Probabilities
In order to show the efficiency and reliability of missing-tag event detection pro- tocols, the performance of the proposed protocols is now evaluated via the so-called false-alarm and true-alarm probabilities denoted by Pfa and Pta, respectively. In par- ticular, we suppose that among Nm times of detection of the missing-tag event, N ta times are caused by the real missing tags, while N fa times are due to the detection error where Nm = N ta + N fa. Then, Pfa and Pta can be, respectively, calculated as
m m
Pfa = mfa , (4.16)
Nm
N ta Pta = .
Nm
We then plot in Figs. 4.8 and 4.9 the probabilities Pfa and Pta of mRUN1 and mRUN2, respectively, versus the detection error probability Pde in 1000 times of a successful detection of missing-tag event, given different values of Cth. We can see that when Pde is small (Pde < 0.01), the proposed protocols easily achieve a perfect performance with almost 100% true-alarm detection even with small values of Cth (Cth ≤ 2). Nevertheless, as Pde increases, the probability that the status of a slot is wrongly observed increases. Therefore, the number of times of false-alarm detection also increases. In this case, we can evidently see the usefulness of larger values of Cth
in improving the reliability of the proposed protocols. It is believed that for a given value of the detection error probability, we always select a suitable value of Cth that
mRUN1 TA, C th = 3
th
mRUN1 FA, C = 3 mRUN1 TA, C th = 2
th
mRUN1 FA, C = 2 mRUN1 TA, C th = 1 mRUN1 FA, C th = 1
Probabilities
75
|U| = 1000; |E| = 100; m = 1; T = 1; α = 0.9 1
0.8
0.6
0.4
0.2
0
10-3 10-2
Detection error probability, P
de
10-1
Figure 4.9: True-alarm and false-alarm probabilities with respect to the detection error probability of mRUN2.
Table 4.3: Optimal selection of Cth in mRUN1 and mRUN2, given Pta = 0.95 and m = T = 5.
Pde Cth (mRUN1) Cth (mRUN2)
1.2 × 10−4 1 1
7 × 10−3 2 2
2 × 10−2 3 3
4 × 10−2 4 3
6 × 10−2 5 3
8 × 10−2 6 4
helps the protocols to meet a predefined requirement of the true-alarm probability.
Table. 4.3 describes an example of selecting optimal values of Cth corresponding to the detection error probability for given Pta = 0.95.
4.4.2. Performance Comparison with Conventional Protocols
In order to show the merit of the proposed protocols, we now compare the per- formance of mRUN1 and mRUN2 with that of the conventional RUN and BMTD protocols. In particular, we present in Figs. 4.10 and 4.11 the numbers of slots used in all the protocols with respect to the number of missing tags (Pde is set to 2) and the detection error probability (both m and T are set to 5), respectively, given Cth = 2. It is seen that although more slots are executed in mRUN1 and mRUN2 to handle the detection error, they are significantly reduced when the number of missing tags or the probability increases. In Fig. 4.11, the performance of the four protocols is observed
mRUN2 TA, C th = 3 mRUN2 FA, C th = 3 mRUN2 TA, C th = 2 mRUN2 FA, C th = 2 mRUN2 TA, C th = 1 mRUN2 FA, C th = 1
Probabilities
to be almost the same when Pde reaches 0.1.
|U| = 1000, |E| = 100, α = 0.9, P = 10-2, C = 2
3000 de th
2500
2000
1500
1000
500
0
1 5 9 13 17 21 25 29 33 37 41 45 49 No. of missing-tags
Figure 4.10: The numbers of slots with respect to the number of missing tags of conventional RUN, BMTD, proposed mRUN1 and mRUN2.
On the other hand, we plot in Fig.4.12 the true-alarm and false-alarm probabilities of the four protocols with respect to the probability Pde, given m = T = 1 and Cth = 2.
We can see that even when Pde is small (10−3), the conventional RUN is obviously unreliable (Pta ≈ 70%) while our protocols achieve almost 100%. This is because the detection error has been taken into account in our proposed protocols while it is completely ignored in RUN and BMTD. Although Pta decreases when Pde increases, mRUN1 and mRUN2 always outperform RUN and BMTD in terms of achieving a required reliability with an optimal selection of Cth.