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Fig. 6. Effects of number of categories on the actual reliability of the proposed four schemes and ES with different required reliability.

Figure 6 Effects of number of categories on the actual reliability of the proposed four schemes and ES with different required reliability.

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Fig. 2. The missing tag iceberg query procedure of the MAC-HZE scheme. B. MAC-HZE Scheme The MAC-HZE scheme is similar to the MAC-SZE scheme, the main difference between them is that a homogeneous-zero estimator is adopted in the MAC-HZE scheme. We define a homogeneous slot as the one selected by the tags from only one category and a heterogeneous slot as the one selected by the tags from at least two categories. Both the heterogeneous slots and empty slots are also called non-homogeneous slots. The MAC-HZE scheme also comprises w rounds. In round k, the reader first broadcasts (f;, R,). Here f, is also set as n to maximize the efficiency. After round k, the reader can calculate the number of slots from expected homogeneous to actual empty for each category as shown in Fig. 2, based on which missing tag cardinality of each category can be estimated. The above procedure is conducted for w rounds, after which the set of categories J satisfying the constraints Eqs. (1) and (2) can be obtained. _ Here we set X“ = 1 if in the k” round the slot [ is
Fig. 2. The missing tag iceberg query procedure of the MAC-HZE scheme. B. MAC-HZE Scheme The MAC-HZE scheme is similar to the MAC-SZE scheme, the main difference between them is that a homogeneous-zero estimator is adopted in the MAC-HZE scheme. We define a homogeneous slot as the one selected by the tags from only one category and a heterogeneous slot as the one selected by the tags from at least two categories. Both the heterogeneous slots and empty slots are also called non-homogeneous slots. The MAC-HZE scheme also comprises w rounds. In round k, the reader first broadcasts (f;, R,). Here f, is also set as n to maximize the efficiency. After round k, the reader can calculate the number of slots from expected homogeneous to actual empty for each category as shown in Fig. 2, based on which missing tag cardinality of each category can be estimated. The above procedure is conducted for w rounds, after which the set of categories J satisfying the constraints Eqs. (1) and (2) can be obtained. _ Here we set X“ = 1 if in the k” round the slot [ is
Then, the estimated number of unidentified missing tags in category C; in the k’" round, denoted as m,,, can be obtained as follows: Since in the k’" round, there are m,, Missing tags in category C; to be identified and the number of unidentified tags is Ne we have:
Then, the estimated number of unidentified missing tags in category C; in the k’" round, denoted as m,,, can be obtained as follows: Since in the k’" round, there are m,, Missing tags in category C; to be identified and the number of unidentified tags is Ne we have:
Fig. 3. The missing tag iceberg query procedure of the MAC-SSZE scheme article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2018.2863726, IEE Transactions on Vehicular Technology We can obtain Theorem 5 for the estimated missing tag cardinality of category C; in the k’" round as follows.
Fig. 3. The missing tag iceberg query procedure of the MAC-SSZE scheme article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2018.2863726, IEE Transactions on Vehicular Technology We can obtain Theorem 5 for the estimated missing tag cardinality of category C; in the k’" round as follows.
Fig. 4. The missing tag iceberg query procedure of the MAC-SHZE scheme. category, and ‘0’ otherwise. As shown in Fig. 4, in the k” round, there are 7 homogeneous slots, which will be included in the sub-frames. Tags t4, fo, tia, tis and fj6 are identified as missing since their replying slots are detected as empty. Therefore, they will be excluded in next round. The reader can estimate the missing tag cardinality of each category based on the number of slots from expected homogeneous to actual empty.
Fig. 4. The missing tag iceberg query procedure of the MAC-SHZE scheme. category, and ‘0’ otherwise. As shown in Fig. 4, in the k” round, there are 7 homogeneous slots, which will be included in the sub-frames. Tags t4, fo, tia, tis and fj6 are identified as missing since their replying slots are detected as empty. Therefore, they will be excluded in next round. The reader can estimate the missing tag cardinality of each category based on the number of slots from expected homogeneous to actual empty.
Fig. 5. Effects of number of categories on the execution time of the proposed four schemes and ES with different required reliability
Fig. 5. Effects of number of categories on the execution time of the proposed four schemes and ES with different required reliability
Fig. 7. Effects of standard deviation of the missing tag cardinality of each category on the execution time of the proposed four schemes and ES with differer required reliability.
Fig. 7. Effects of standard deviation of the missing tag cardinality of each category on the execution time of the proposed four schemes and ES with differer required reliability.
Fig. 8. Effects of standard deviation of the missing tag cardinality of each category on the actual reliability of the proposed four schemes and ES with different required reliability.
Fig. 8. Effects of standard deviation of the missing tag cardinality of each category on the actual reliability of the proposed four schemes and ES with different required reliability.
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