85:8·C.Wang et al. Reflection Object(Heart) Sr =hT-AhT (SA+B→T+SAT+Sc→T) dA-B △dBT≈△h cos pr Ah PT D'D C SA-C-T Fig.5.Reflection model of heart displacement. To extract the reflection signal S.1 from the superposed signal S,we could subtract the complex signal S.o[41]. which can be measured simply by removing the reflection object. Figure 6 shows the RSSI and phase variation of the reflection signals from periodic signal of the water bag according to the subtraction Sr.1=S,-Sr.0.We note that,for each reflection signal,the RSSI variation is irregular and its value is usually less than -60dBm,as the power of the reflection signal is rather weak and easy to be affected.In fact,since the reflection object,ie.,the water bag,only moves a small distance,theoretically the RSSI variation should be very small according to Friis Equation [16].Meanwhile,the phases of the reflection signal from different tags all have obvious periodical patterns in the waveforms.Moreover,they not only have some similarities in the waveform contours,but also have differences in the waveform details among each other. Therefore,this implies that all the tags are subjected to similar reflection influence,but the performance in sensitivity are different among different tags. 3.3.2 Estimating Heart Displacement via a Single Tag.After extracting the reflection signal,it is essential to further figure out the relationship between the heart displacement and the reflection RF-signal.Since the phase of reflection signal is more sensitive to the heart displacement than RSSI,we use the phase as a metric for RF-signal to depict the corresponding relationship.According to Eq.(3),let A be the wave length of RF-signal,the phase of reflection signal S,.can be calculated from the reflection path length as: 8g=2x(女月+d-8+d87+0eon)mod2元， (4) 入 where the superscript'indicates the reflection signal and Ocons is the constant phase deviation due to reflection. Since d is fixed during the whole propagation and econs is constant,when the reflection object moves from BtoB',the phase change△9only depends on the change of path length△da-→sand△dg-T,as: △85=2mAdA-8+Adg-7 mod 2. (5) 入 Without loss of generality,we first consider the path length change Adg.Assume that the points D and D'are respectively the projection of the points B and B'on the horizontal line of T in Figure 5,then the edge length dsp =dg'p.When the reflection object moves from B to B',the reflection path changes from ds to dgT,which are,respectively,the hypotenuses of two right triangles ABDT and AB'D'T.Let or and to denote the angle /BTD and /B'T D',respectively.Then,the path length change Ads-can be calculated as follows: △dg→T=dgT-dsT= dsp dsD (6) sin sinor Proc.ACM Interact.Mob.Wearable Ubiquitous Technol.,Vol.2,No.2,Article 85.Publication date:June 2018.85:8 • C. Wang et al. B A T B‘ !" #$ #$ % !&'() * !" +,- #) ./ 0 ")(1") 2.1('() 3 .1() 3 .4()5 D’ D Reflection Object (Heart) #1 C Fig. 5. Reflection model of heart displacement. To extract the reflection signal Sr,1 from the superposed signal Sr , we could subtract the complex signal Sr,0 [41], which can be measured simply by removing the reflection object. Figure 6 shows the RSSI and phase variation of the reflection signals from periodic signal of the water bag according to the subtraction Sr,1 = Sr −Sr,0. We note that, for each reflection signal, the RSSI variation is irregular and its value is usually less than −60dBm, as the power of the reflection signal is rather weak and easy to be affected. In fact, since the reflection object, i.e., the water bag, only moves a small distance, theoretically the RSSI variation should be very small according to Friis Equation [16]. Meanwhile, the phases of the reflection signal from different tags all have obvious periodical patterns in the waveforms. Moreover, they not only have some similarities in the waveform contours, but also have differences in the waveform details among each other. Therefore, this implies that all the tags are subjected to similar reflection influence, but the performance in sensitivity are different among different tags. 3.3.2 Estimating Heart Displacement via a Single Tag. After extracting the reflection signal, it is essential to further figure out the relationship between the heart displacement and the reflection RF-signal. Since the phase of reflection signal is more sensitive to the heart displacement than RSSI, we use the phase as a metric for RF-signal to depict the corresponding relationship. According to Eq.(3), let λ be the wave length of RF-signal, the phase of reflection signal Sr,1 can be calculated from the reflection path length as: θ r T = 2π( dT→A + dA→B + dB→T λ + θcons) mod 2π, (4) where the superscript r indicates the reflection signal and θcons is the constant phase deviation due to reflection. Since dT→A is fixed during the whole propagation and θcons is constant, when the reflection object moves from B to B ′ , the phase change ∆θ r T only depends on the change of path length ∆dA→B and ∆dB→T, as: ∆θ r T = 2π ∆dA→B + ∆dB→T λ mod 2π. (5) Without loss of generality, we first consider the path length change ∆dB→T. Assume that the points D and D′ are respectively the projection of the points B and B ′ on the horizontal line of T in Figure 5, then the edge length dBD = dB′D′. When the reflection object moves from B to B ′ , the reflection path changes from dB→T to dB′→T, which are, respectively, the hypotenuses of two right triangles △BDT and △B′D′T. Let ϕT and ϕ ′ T to denote the angle ∠BT D and ∠B ′T D′ , respectively. Then, the path length change ∆dB→T can be calculated as follows: ∆dB→T = dB′T − dBT = dBD sinϕ ′ T − dBD sinϕT . (6) Proc. ACM Interact. Mob. Wearable Ubiquitous Technol., Vol. 2, No. 2, Article 85. Publication date: June 2018