IEEE INFOCOM 2018-IEEE Conference on Computer Communications (a)Signal on the first tag (b)Signal on the second tag (c)Relative spinning signal Fig.8:Spinning signals.It is difficult to see the periodicity on the received phase sequence at the two tags.Performing the subtraction between two phase values on two tags,reveals the periodic and well aligned spinning signal. 3D scenarios.To get a visual impression,we show the spinning signals induced by dual tags respectively,as well as their 100000 /sin(2×0.1)N relative spinning signal,in Fig.8,under a quite noisy setting. 0:0 sin(2×0.4) It is clear that the relative spinning signal becomes far more 0:001:00 sin(2×0.6) regular and well reveals the intrinsic spinning frequency as 000001 sin(2×0.8) expected,compared with the spinning signal purely collected from each tag.Hence,it is reasonable and feasible that we Fig.9:Illustration of compressive reading.As the tag is read at the first,third,fourth and sixth millisecond,the utilize RSS to reflect and inspect the frequency of spinning. measurement matrix and result are constructed as above. V.SYSTEM IMPLEMENTATION This section begins with the practical challenges we face where is the measurement matrix.is the Fourier basis. when applying relative spinning signal in spinning sensing, S is the sparse coefficient vector in Fourier domain,and n and then presents the solution to address these challenges. denotes the measurement noise.The time-domain signal s is A.Challenges not compact but its frequency representation S is sparse. Making sensing of spinning or vibration using RFID tags is Suppose the tag is read M times during N millisec- to inspect the motion through the random and low-frequency onds.The input is a sequence of two-tuple samples,denoted readings of tags,where each reading is viewed as one sampling as {(t1,[t]),(t2,0[t2l),...,(tM,[tm])},where its phase of motion status.A COTS tag can be read for about 40 times value at time tm is equal to [tm].Note that all time variables per second on average (i.e.,sampling frequency equals 40Hz). are integers and expressed with unit of millisecond.Our goal As stated by the Nyquist-Shannon sampling theorem,for a is to know the phase value at any given time,i.e.recovering given analog signal of bandlimit,the sampling rate should be the signal.Then,the M x N measurement matrix and M x 1 at least twice the highest frequency contained in the signal in result vector are respectively constructed as follows: order to guarantee perfect reconstruction of the original signal. Thus,Tagtwins is able to recover spinning signal with up to Φ[m,n= (1,if tm exists and tm =n (15) 20Hz frequency according to the sampling theorem,which 0.otherwise obviously can not meet practical needs in most applications. where m 1,...,M and n 1,...,N.The existence of tm Therefore,the central task of applying RSS is to recover the means the tag is read at time tm,i.e.,the sequence contains a spinning signal,even high-frequency signal(>20Hz),through tuple of (tm,[tm]).Each row only has one non-zero element. the random and discrete readings. Correspondingly, B.Classic Compressive Reading y(m]=sin(20[tm]) (16) The work [2]utilizes compressive sensing to recover the spinning signal which is derived from a single tag (see Eqn.6). Note that the spinning signal derived by a single tag is defined Such approach is called as Compressive Reading(CR).The in Egn.6 instead of the original phase value.[2]further signal is periodic and thereby has a very sparse representation aggregates the reading into many frames.However,according in the frequency domain,where it can be represented into to our empirical study,we find that the recovery results are a linear combination of phasors via the exponential Fourier almost identical whether one uses frame or not.To visually series.CR firstly converts the spinning signal into the fre- understand the measurement matrix and result,we illustrate an quency domain,and then utilizes the inherent randomness of example in Fig.9.Finally,the signal could be reconstructed tag's readings to construct the measurement matrix and the reliably through solving an l or 2 optimization problem. corresponding result.Specifically,the spinning signal s can One of the great advantages of CR is that it constructs the be represented as follows: measurement matrix based on the collected readings,rather than builds it in advance and then guides the reader's reading. y=Φs+7=Φ亚-1S+7 (14) This allows us to employ COTS readers for sensing without0 1 2 3 4 5 6 x 104 −1.5 −1 −0.5 0 0.5 1 1.5 Time (ms) s(t) 1st period 2nd period 3rd period (a) Signal on the first tag 0 1 2 3 4 5 6 x 104 −1.5 −1 −0.5 0 0.5 1 1.5 Time (ms) s(t) 1st period 2nd period 3rd period (b) Signal on the second tag 0 1 2 3 4 5 6 x 104 −1.5 −1 −0.5 0 0.5 1 1.5 Time (ms) s(t) 1st period 2nd period 3rd period (c) Relative spinning signal Fig. 8: Spinning signals. It is difficult to see the periodicity on the received phase sequence at the two tags. Performing the subtraction between two phase values on two tags, reveals the periodic and well aligned spinning signal. 3D scenarios. To get a visual impression, we show the spinning signals induced by dual tags respectively, as well as their relative spinning signal, in Fig. 8, under a quite noisy setting. It is clear that the relative spinning signal becomes far more regular and well reveals the intrinsic spinning frequency as expected, compared with the spinning signal purely collected from each tag. Hence, it is reasonable and feasible that we utilize RSS to reflect and inspect the frequency of spinning. V. SYSTEM IMPLEMENTATION This section begins with the practical challenges we face when applying relative spinning signal in spinning sensing, and then presents the solution to address these challenges. A. Challenges Making sensing of spinning or vibration using RFID tags is to inspect the motion through the random and low-frequency readings of tags, where each reading is viewed as one sampling of motion status. A COTS tag can be read for about 40 times per second on average (i.e., sampling frequency equals 40Hz). As stated by the Nyquist-Shannon sampling theorem, for a given analog signal of bandlimit, the sampling rate should be at least twice the highest frequency contained in the signal in order to guarantee perfect reconstruction of the original signal. Thus, Tagtwins is able to recover spinning signal with up to 20Hz frequency according to the sampling theorem, which obviously can not meet practical needs in most applications. Therefore, the central task of applying RSS is to recover the spinning signal, even high-frequency signal (> 20Hz), through the random and discrete readings. B. Classic Compressive Reading The work [2] utilizes compressive sensing to recover the spinning signal which is derived from a single tag (see Eqn. 6). Such approach is called as Compressive Reading (CR). The signal is periodic and thereby has a very sparse representation in the frequency domain, where it can be represented into a linear combination of phasors via the exponential Fourier series. CR firstly converts the spinning signal into the fre￾quency domain, and then utilizes the inherent randomness of tag’s readings to construct the measurement matrix and the corresponding result. Specifically, the spinning signal s can be represented as follows: y = Φs + ⌘ = Φ −1S + ⌘ (14) Φ =   100000 001000 000100 000001   Timeline (1,0.1) X (3,0.4) (4,0.6) X (6,0.8) y =   sin(2 ⇥ 0.1) sin(2 ⇥ 0.4) sin(2 ⇥ 0.6) sin(2 ⇥ 0.8)   Fig. 9: Illustration of compressive reading. As the tag is read at the first, third, fourth and sixth millisecond, the measurement matrix and result are constructed as above. where Φ is the measurement matrix, is the Fourier basis, S is the sparse coefficient vector in Fourier domain, and ⌘ denotes the measurement noise. The time-domain signal s is not compact but its frequency representation S is sparse. Suppose the tag is read M times during N millisec￾onds. The input is a sequence of two-tuple samples, denoted as {(t1, ✓[t1]),(t2, ✓[t2]),...,(tM, ✓[tM])}, where its phase value at time tm is equal to ✓[tm]. Note that all time variables are integers and expressed with unit of millisecond. Our goal is to know the phase value at any given time, i.e. recovering the signal. Then, the M ⇥ N measurement matrix and M ⇥ 1 result vector are respectively constructed as follows: Φ[m, n] = ( 1, if tm exists and tm = n 0, otherwise (15) where m = 1,...,M and n = 1,...,N. The existence of tm means the tag is read at time tm, i.e., the sequence contains a tuple of (tm, ✓[tm]). Each row only has one non-zero element. Correspondingly, y[m] = sin(2✓[tm]) (16) Note that the spinning signal derived by a single tag is defined in Eqn. 6 instead of the original phase value. [2] further aggregates the reading into many frames. However, according to our empirical study, we find that the recovery results are almost identical whether one uses frame or not. To visually understand the measurement matrix and result, we illustrate an example in Fig. 9. Finally, the signal could be reconstructed reliably through solving an l1 or l2 optimization problem. One of the great advantages of CR is that it constructs the measurement matrix based on the collected readings, rather than builds it in advance and then guides the reader’s reading. This allows us to employ COTS readers for sensing without IEEE INFOCOM 2018 - IEEE Conference on Computer Communications