IEEE TRANSACTIONS ON MOBILE COMPUTING,VOL.XX,NO.XX,2020 11 imaginary Moreover,in COTS RFID systems,the unit of the RSSI by ImpinJ R420 is dBm,while the unit of the received power is Watt,they can be transformed as: 10RSS1/10 (19) Rrad Rload real Pioad= 1000 Fig.16.Equivalent circuit of tag Hence,the power ratio in Eq.(18)can be represented by the RSSI deviation,as: between the antenna and the tag as Opol,so the received power can be represented as: PR-PrGTGRcos(0pa)(r RSSI(t)-RSSI(to)0gFid(o Pload(t) R(t) =201g R(to) (20) 2 (14) According to Eq.(20),when the tag is fixed during the where A is the wavelength,r is the distance between the swipe,the RSSI difference is only related to the impedance receiver and the transmitter.However,when the reader's change due to the touch position at time t relative to time to. antenna transmits signals to the tag,the received power of As the swipe is a continuous process,the user touches the the tag is probable not be power delivered to the tag IC to tag first,and then moves the finger to different positions on activate itself,there is a chance of power lost in the transfer.the tag,so we consider the untouched state before touching Fig.16 shows the equivalent circuit of a tag.The total the tag as the reference time to,which is easy to derive impedance includes two parts,one is from the tag antenna during the interaction.That is: (Zant =Rrad jXant),and the other is from the tag IC (Zioad Rioad +jXIc).So the dissipated power by the The RSSI deviation due to touch on the tag is in- tag's load is: dependent of the position or orientation of the tag, which supports our findings in Observation 3. Plod Rond Voe RLoad Based on the RSSI deviation,we are able to derive 2 2Zant Zoad2' (15) the absolute candidate touch positions regardless of here Voc is the open-circuit voltage,I is the current,Z the position or polarization angle of the tag. R+jX,R refers to the resistance,a real part caused by The above key insight also works with different tag types the circuit resistivity,X refers to the reactance,a complex more than E51,experiment results are shown in Fig.28. part caused by inductance or capacitance or both.Based on Eq.(15),when the impedance of the tag antenna and that of the tag IC are conjugate matching,as Rant RLoad,Xant 7 DESIGN OF TOUCH GESTURE DETECTION Xioad =0,the power transfer reaches the maximum: We use a single linear dipole tag E51 as the touch interface. Voe As the RSSI deviation pattern is symmetrical for the swipe Ptoud 8Rrad (16) on the two antennas of a linear dipole tag in Observation 2, Normally,it is assumed that received power calculated by we leverage the monotonic trend of the half tag to use one half as the slider and the other half as buttons. the Friis equation in Eq.(14)is totally delivered the tag IC when conjugate matching exists,as PR=Po.If the Generally,the touch tag plays a role of "touch bar" supporting three touch gestures as the click,the press and perfect matching does not exist,the actual power received by the tag IC is less than that predicted by the Friis equation: hold,and the swipe.Before identifying which gesture is performed,it is necessary to generate the RSSI deviation 4Rload Rrad Pioad=PRTZant +Zloadl (17) template for estimating the touch position in advance,as illustrated in Fig.2.Based on the RSSI deviation template, Correspondingly,the reported RSSI will change due to the touch gesture estimation can be performed as follows. different mismatching conditions.When a user swipes on 1)Data Preprocessing:First,determine the reference value a tag,the position and polarization angle of the tag is for computing the RSSI deviation by recalling the RSSI value fixed,i.e.,Pr remains unchanged in Eq.(17),the main just before touch.Then,smooth the received signals to filter outliers caused by the ambient noise or the multi-path effect, changing parameter is about the impedance of the tag due to the capacitive coupling,denoted as R= and calculate the real-time RSSI deviation When touching the center of the tag.boh the 2)Gesture Detection:Based on the RSSI variation in con- secutive time intervals,we can determine which touch ges- the two tag antennas are touched at the same time,it is probable that the new conjugate matching is built,so the ture is actually performed,including the click,the press and power transferred to the tag IC is similar to that when hold,and the swipe.Click means touching one position of the tag is untouched.As the tag impedance accounts for the tag with short time;Press and hold means touching one the power transfer,pick up a power reference at time to, position of the tag with long time;Swipe means touching then the received power ratio of a tag only depends on different positions of the tag continuously and smoothly. the impedance change due to the touch position at time t 3)Touch Estimation:With the extracted RSSI deviation and the estimated touch gesture,we can derive the absolute relative to time to,as: touch position on the tag referring to the template.For the Pioad(t) R(t) (18) swipe,we can further estimate the distance,direction and PLoad(to) R(to) speed with consecutive touch positions.IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. XX, NO. XX, 2020 11 �"# �%&' �&)* �+, �-"&' Antenna IC imaginary real �%&' + �-"&' �&)* � +�+, &)* + �-"&' Fig. 16. Equivalent circuit of tag between the antenna and the tag as θpol, so the received power can be represented as: PR = PT GT GR cos2 (θpol)( λ 4πr ) 2 , (14) where λ is the wavelength, r is the distance between the receiver and the transmitter. However, when the reader’s antenna transmits signals to the tag, the received power of the tag is probable not be power delivered to the tag IC to activate itself, there is a chance of power lost in the transfer. Fig. 16 shows the equivalent circuit of a tag. The total impedance includes two parts, one is from the tag antenna (Zant = Rrad + jXant), and the other is from the tag IC (Zload = Rload + jXIC ). So the dissipated power by the tag’s load is: Pload = |I| 2Rload 2 = V 2 ocRload 2|Zant + Zload| 2 , (15) here Voc is the open-circuit voltage, I is the current, Z = R + jX, R refers to the resistance, a real part caused by the circuit resistivity, X refers to the reactance, a complex part caused by inductance or capacitance or both. Based on Eq. (15), when the impedance of the tag antenna and that of the tag IC are conjugate matching, as Rant = Rload, Xant + Xload = 0, the power transfer reaches the maximum: P max load = V 2 oc 8Rrad . (16) Normally, it is assumed that received power calculated by the Friis equation in Eq. (14) is totally delivered the tag IC when conjugate matching exists, as PR = P max load . If the perfect matching does not exist, the actual power received by the tag IC is less than that predicted by the Friis equation: Pload = PR 4RloadRrad |Zant + Zload| 2 . (17) Correspondingly, the reported RSSI will change due to different mismatching conditions. When a user swipes on a tag, the position and polarization angle of the tag is fixed, i.e., PR remains unchanged in Eq. (17), the main changing parameter is about the impedance of the tag due to the capacitive coupling, denoted as R = 4RloadRrad |Zant+Zload| 2 . When touching the center of the tag, both the IC loop and the two tag antennas are touched at the same time, it is probable that the new conjugate matching is built, so the power transferred to the tag IC is similar to that when the tag is untouched. As the tag impedance accounts for the power transfer, pick up a power reference at time t0, then the received power ratio of a tag only depends on the impedance change due to the touch position at time t relative to time t0, as: Pload(t) Pload(t0) = R(t) R(t0) . (18) Moreover, in COTS RFID systems, the unit of the RSSI by ImpinJ R420 is dBm, while the unit of the received power is Watt, they can be transformed as: Pload = r 10RSSI/10 1000 . (19) Hence, the power ratio in Eq. (18) can be represented by the RSSI deviation, as: RSSI(t)−RSSI(t0) = 20 lg Pload(t) Pload(t0) = 20 lg R(t) R(t0) . (20) According to Eq. (20), when the tag is fixed during the swipe, the RSSI difference is only related to the impedance change due to the touch position at time t relative to time t0. As the swipe is a continuous process, the user touches the tag first, and then moves the finger to different positions on the tag, so we consider the untouched state before touching the tag as the reference time t0, which is easy to derive during the interaction. That is: • The RSSI deviation due to touch on the tag is in￾dependent of the position or orientation of the tag, which supports our findings in Observation 3. • Based on the RSSI deviation, we are able to derive the absolute candidate touch positions regardless of the position or polarization angle of the tag. The above key insight also works with different tag types more than E51, experiment results are shown in Fig. 28. 7 DESIGN OF TOUCH GESTURE DETECTION We use a single linear dipole tag E51 as the touch interface. As the RSSI deviation pattern is symmetrical for the swipe on the two antennas of a linear dipole tag in Observation 2, we leverage the monotonic trend of the half tag to use one half as the slider and the other half as buttons. Generally, the touch tag plays a role of “touch bar”, supporting three touch gestures as the click, the press and hold, and the swipe. Before identifying which gesture is performed, it is necessary to generate the RSSI deviation template for estimating the touch position in advance, as illustrated in Fig. 2. Based on the RSSI deviation template, the touch gesture estimation can be performed as follows. 1) Data Preprocessing: First, determine the reference value for computing the RSSI deviation by recalling the RSSI value just before touch. Then, smooth the received signals to filter outliers caused by the ambient noise or the multi-path effect, and calculate the real-time RSSI deviation. 2) Gesture Detection: Based on the RSSI variation in con￾secutive time intervals, we can determine which touch ges￾ture is actually performed, including the click, the press and hold, and the swipe. Click means touching one position of the tag with short time; Press and hold means touching one position of the tag with long time; Swipe means touching different positions of the tag continuously and smoothly. 3) Touch Estimation: With the extracted RSSI deviation and the estimated touch gesture, we can derive the absolute touch position on the tag referring to the template. For the swipe, we can further estimate the distance, direction and speed with consecutive touch positions