Missed 0.7 0.75 0 05 0.25 0.25 SNR-20dB C=3 SNR=17dB -X C=4 SNR=14dB-- 0 5 11 14 17 20 23 26 29 33 5 10 15 20 25 30 10 15 20 30 35 4 SNR(dB) Number of missing tags Number of missing tags F5g.10. Missing tag identification accuracy Fig.11.Missing tag identification accuracy with Fig.12.Identified and missed tags with dif- across different channel conditions. different number of missing tags. ferent number of missing tags,SNR=17dB,and KMax=20. accuracy on the Moo RFID tag [29]which is developed based B.P-MTI investigation on the WISP project. C.Identifying missing WISP tag Wireless communication is error-prone in practice,and thus whether P-MTI can accurately identify missing tags in the We prototype a missing tag identification system where a presence of channel noise is worth investigating.We simulate software defined RFID reader monitors 5 WISP tags.Figure 1000 tags uniformly distributed in the coverage of each RFID 9(a)depicts the received signals at the reader when all the 5 reader,among which 20 tags are missing.We specify the WISP tags are present in the first measurement instance.We number of measurements M =CKMax log(N),where N intentionally take away one tag to emulate a missing tag event. 1000 and KMax =20 with different C.We randomly select Figure 9(b)plots the received signals from the 4 remaining the missing tags for simulation.Figure 10 plots the average tags.Figure 9(c)plots the differential of the two measure- accuracy of identifying the missing tags across different signal ments,and the signals when only the missing tag responds. to noise ratio(SNR).As expected,when SNR is very low,P- We note that the magnitude of received signal strength is MTI cannot always identify the missing tags.At moderate and influenced by the wireless channel as well as the automatic high SNRs (e.g.,17-32dB),P-MTI achieves high accuracy.In again control of RFID reader.Although the magnitude of particular,with the SNR>17dB,the identification accuracies received signal differs due to channel attenuation and gain are consistently higher than 98%when C 3.P-MTI control,we see that the differential exhibits similar patterns can further improve the accuracy with extra measurements with the signals when only the missing tag responds.With (i.e.,with larger C)according to the application requirement. the knowledge of the differential signals,we can accurately Generally,with more measurements P-MTI can achieve higher identify the missing tag by solving the convex optimization accuracy at the cost of extra communication and computation problem (7).For clarity,here we only present the instance overhead in the presence of noise.According to Figure 10, when only one tag is missing.In the experiments when more we find that the marginal accuracy improvement diminishes than one tag are missing,we find that P-MTI can accurately with the increased number of measurements.For instance,the identify them as well accuracy with C=4 is only slightly higher than that with V.EVALUATION C =3.We thus set C=3 to balance the accuracy and overhead in practice In the following,we turn to large-scale simulations to eval- uate our missing tag identification scheme.We first analyze Another parameter that P-MTI needs to specify is the the proposed P-MTI.We then compare P-MTI with state-of- estimated maximum number of missing tags.The number of the-art protocols IIP [16]and Protocol-3 [28]. missing tags can sometimes exceed the estimated maximum number.We investigate identification accuracy of P-MTI with A.Simulation setup and performance metrics different number of missing tags which may exceed the We build a custom simulator based on CVX solver [2]and estimated maximum number of KMax=20,under noisy channel run the simulations on MATLAB.For P-MTI,we study the conditions (i.e.,SNR=14,17,and 20dB).Figure 11 plots the various scenarios with different number of tags and readers and average accuracy of identifying the missing tags when the wireless channel conditions.For fair comparison,we adopt the number of missing tags varies from 5 to 40.According to the same system parameters used in benchmark protocols [16,28]. results,we see that when the number of missing tags is smaller In particular,the transmission time of a short response is than KMax (i.e.,<20),P-MTI can accurately identify the specified as ts =0.8ms and the transmission time of a 96- missing tags.When the number of missing tags exceeds KMax, bit tag ID is specified as ttag =2.4ms,which gives an ap- the accuracy decreases.Therefore,the RFID reader needs to proximate bitrate of 40kbps.We focus on the communication adjust KMax to ensure that no more than KMax tags would be time between RFID readers and tags,and ignore the negligible missing.Figure 12 plots in detail the missing tag identification processing time on backend server.All results are obtained by results with different number of missing tags,SNR=17dB,and averaging over 100 runs if not specified otherwise. KMax=20.Although P-MTI may fail to identify some tags0 0.25 0.5 0.75 1 5 8 11 14 17 20 23 26 29 32 Accuracy SNR(dB) C=1 C=2 C=3 C=4 Fig. 10. Missing tag identification accuracy across different channel conditions. 0 0.25 0.5 0.75 1 5 10 15 20 25 30 35 40 Accuracy Number of missing tags SNR=20dB SNR=17dB SNR=14dB Fig. 11. Missing tag identification accuracy with different number of missing tags. 0 20 40 5 10 15 20 25 30 35 40 Number of tags Number of missing tags Identified Missed Fig. 12. Identified and missed tags with dif￾ferent number of missing tags, SNR=17dB, and KMax=20. accuracy on the Moo RFID tag [29] which is developed based on the WISP project. C. Identifying missing WISP tag We prototype a missing tag identification system where a software defined RFID reader monitors 5 WISP tags. Figure 9(a) depicts the received signals at the reader when all the 5 WISP tags are present in the first measurement instance. We intentionally take away one tag to emulate a missing tag event. Figure 9(b) plots the received signals from the 4 remaining tags. Figure 9(c) plots the differential of the two measure￾ments, and the signals when only the missing tag responds. We note that the magnitude of received signal strength is influenced by the wireless channel as well as the automatic again control of RFID reader. Although the magnitude of received signal differs due to channel attenuation and gain control, we see that the differential exhibits similar patterns with the signals when only the missing tag responds. With the knowledge of the differential signals, we can accurately identify the missing tag by solving the convex optimization problem (7). For clarity, here we only present the instance when only one tag is missing. In the experiments when more than one tag are missing, we find that P-MTI can accurately identify them as well. V. EVALUATION In the following, we turn to large-scale simulations to eval￾uate our missing tag identification scheme. We first analyze the proposed P-MTI. We then compare P-MTI with state-of￾the-art protocols IIP [16] and Protocol-3 [28]. A. Simulation setup and performance metrics We build a custom simulator based on CVX solver [2] and run the simulations on MATLAB. For P-MTI, we study the various scenarios with different number of tags and readers and wireless channel conditions. For fair comparison, we adopt the same system parameters used in benchmark protocols [16, 28]. In particular, the transmission time of a short response is specified as ts = 0.8ms and the transmission time of a 96- bit tag ID is specified as ttag = 2.4ms, which gives an ap￾proximate bitrate of 40kbps. We focus on the communication time between RFID readers and tags, and ignore the negligible processing time on backend server. All results are obtained by averaging over 100 runs if not specified otherwise. B. P-MTI investigation Wireless communication is error-prone in practice, and thus whether P-MTI can accurately identify missing tags in the presence of channel noise is worth investigating. We simulate 1000 tags uniformly distributed in the coverage of each RFID reader, among which 20 tags are missing. We specify the number of measurements M = CKMax log(N), where N = 1000 and KMax = 20 with different C. We randomly select the missing tags for simulation. Figure 10 plots the average accuracy of identifying the missing tags across different signal to noise ratio (SNR). As expected, when SNR is very low, P￾MTI cannot always identify the missing tags. At moderate and high SNRs (e.g., 17-32dB), P-MTI achieves high accuracy. In particular, with the SNR≥17dB, the identification accuracies are consistently higher than 98% when C ≥ 3. P-MTI can further improve the accuracy with extra measurements (i.e., with larger C) according to the application requirement. Generally, with more measurements P-MTI can achieve higher accuracy at the cost of extra communication and computation overhead in the presence of noise. According to Figure 10, we find that the marginal accuracy improvement diminishes with the increased number of measurements. For instance, the accuracy with C = 4 is only slightly higher than that with C = 3. We thus set C = 3 to balance the accuracy and overhead in practice. Another parameter that P-MTI needs to specify is the estimated maximum number of missing tags. The number of missing tags can sometimes exceed the estimated maximum number. We investigate identification accuracy of P-MTI with different number of missing tags which may exceed the estimated maximum number of KMax=20, under noisy channel conditions (i.e., SNR=14, 17, and 20dB). Figure 11 plots the average accuracy of identifying the missing tags when the number of missing tags varies from 5 to 40. According to the results, we see that when the number of missing tags is smaller than KMax (i.e., <20), P-MTI can accurately identify the missing tags. When the number of missing tags exceeds KMax, the accuracy decreases. Therefore, the RFID reader needs to adjust KMax to ensure that no more than KMax tags would be missing. Figure 12 plots in detail the missing tag identification results with different number of missing tags, SNR=17dB, and KMax=20. Although P-MTI may fail to identify some tags