Proceedings. The First International Conference on Sensor Device Technologies and Applications SENSORDEVICES July 2010 Venice, Italy

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1 roceedings The First International Conference on Sensor Device Technologies and Applications SENSORDEVICES July 2010 Venice, Italy Los Alamitos, California Washington Tokyo

2 2010 First International Conference on Sensor Device Technologies and Applications Thresholds for the Identification of Commercial Wireless SAW ID-Tags Gustavo Cerda-Villafana, Yuriy S. Shmaliy Electronics Department Guanajuato University, Salamanca, Mexico Abstract assive Surface Acoustic Wave (SAW) sensors intended to measure different physical quantities are often manufactured to have Radio Frequency Identification (RFID) tags with time position encoding. The optimum threshold is proposed for the identification of commercial SAW ID-tags. We first find the generic identification error probability for such tags employing the Marcum function of first order and then minimize it in order to find the optimal threshold. The results are obtained for the ideal conditions of equal 30 db SNR. As examples of applications, we give the estimate number of reflectors for an ID error probability lesser than 1 and 0.1% (1 slip per 100 and 1000 readings). Keywords-SAW sensor; Marcum function; identification tags. I. INTRODUCTION In wireless sensor networks and smart measurement systems, the identification (ID) of individual sensors has become an integral part of the design. The currency has also gained a wireless radio frequency (RF) ID tag (RFID-tag) in which the inherent sensor function is removed. In a family of such devices a special place occupy passive surface acoustic wave (SAW) coded sensors and delay-line identifiers, called RFID-tags, operating in the gigahertz frequency range. Their basic component is a piezoelectric plate (quartz, lithiumniobate, etc.) with the interdigital transducer (IDT) and a series of code reflectors. The latter are combined with one or several strips and placed at the precisely determined positions. rinciples of encoding implemented in modern SAW RFID-tags as outlined in [1]. The time position encoding is most widely used in commercial SAW tags [1]. Here, the total time delay is divided into slots of certain duration. The slots are united into groups of several slots with one slot empty between the groups. In early designs [2], a single group of up to 32 slots was used to organize binary coding. In [3], [4], four slots per group were exploited and investigated with the same aim. In [5, 6], decimal groups have been used. In each of these designs, every reflected pulse can have an individual amplitude, frequency, and phase. Therefore, different methods of encoding and decoding [1, 7-9] have been developed. In a family of such devices, a special place occupy passive Surface Acoustic Wave (SAW) coded sensors and ID-tags operating in the gigahertz frequency range. Their basic component is a piezoelectric plate (quartz, lithiumniobate, etc.) having identification marks deposited properly to organize a label with typically either amplitude shiftkeying (ASK) [7], [10] or phase shift-keying (SK) [8], [10]. The attempts have also been made to use frequency coding [9]. It has to be remarked now that a rigorous statistical analysis of errors in passive SAW sensing has been provided only for phase measurements [11-14]. Regarding the SAW tags, a few solutions are dealing mostly with the noise description problems [6, 15]. The identification error probability is only discussed in [16]. It is therefore still unclear, from an analytical point of view, the error level of time position encoding. Hence, studying this error level and its minimization would shed light if other methods of encoding could be implemented. In this paper, we consider the ID error probability of the SAW RFID-tags with time position encoding as used in commercial products. We find optimum thresholds in the sense of the minimum error probability. The paper is organized as follows. In Section II, we discuss the measurement signal model and formulate the problem. The identification errors and error probability are considered in Section III, proposing the optimal ID threshold. In Section IV, we find optimal thresholds for two SAW RFID-tags commercially available. Finally, concluding remarks are drawn in Section V. II. MEASUREMENT SIGNAL MODEL AND ROBLEM FORMULATION To read out all the sensor responses with similar SNRs, the best way is to interrogate it with a linear frequency modulated (LFM) RF impulse request signal [10] (Fig. 1 a, c), as shown in [6], where 2S and µ0 are the peak-power and initial phase, respectively, f 0 is the initial carrier frequency, and t is the current time. In order to overlap all responses of the tag without large violations in the magnitude, the LFM pulse must have a near rectangular normalized waveform a(t) of duration T such that α = Δω / T, where Δω is a required angular frequency deviation [10]. At the IDT, the request signal appears with the environmental echoes (Fig. 1b), although noise does not perturb it here substantially. (1) /10 $ IEEE DOI /SENSORDEVICES /SENSORDEVICES

3 Figure 1. Operation principle of identification of wireless SAW ID-tags: (a) interrogator, (b) SAW RFID-tag label coded, (c) transmitted request signal, (d) received request signal with environmental echoes [7], and (e) response of the RFID-tag at the receiver detector [2]. At the receiver, each of the RF pulses sk in (2) is contaminated by the zero-mean additive stationary narrowband Gaussian noise n(t) with a known variance σ2, so that we have a mixture in which V k (t) > 0 is the positive valued envelope representing either the On-pulse or the Off-pulse in the K- bit burst and θ k is the modulo 2π random phase that does not play any substantial role in coding with ASK, unlike the SK case [10], and will further be omitted. The received pulse-burst can thus be modeled as (2) where y k (t) is specified with (6). The received pulse burst (6) is measured for the reader local timescale to find the responses at exact time instances specified by encoding. In the virtual slots at the receiver, we thus have harmonic On- or Off-signals as shown in Fig. 1b with amplitudes affected by energy of the readout signal, design imperfections, and problems with propagation. The reader induces Gaussian noise allowing us to use the narrowband model (5) for each of the pulses. Following Rice [17], the instantaneous envelope Vk in (2) is distributed at t = t d + τ k with the probability density function (pdf) (3)

4 where the normalized envelope is given by the instantaneous SNR in the kth pulse is calculated as (4) (5) (6) For the Off-pulses, we respectively have O(M+1) (), O(M+2) (),..., OK () and O(M+1) () = 1 O(M+1) (), O(M+2) () = 1 O(M+2) (),..., OK () = 1 OK (). The tag cannot be identified correctly if at least one of the On- or Off-pulses fails. Because all of the pulses appear independently, the identification error probability E () can thus be specified by the probability of the mutually exclusive failures in each of the pulses. Following [18], [19], E () for the independent pulses can hence be written as and (7) E M 1= 1 K [ 1 ( )] 1 ( ) [ O j ] = 1 I i (8) j= M + 1 is the modified Bessel function of the first kind and zeroth order. The measurement shown in (1e) suggests that the pdf (7) is conditional on the given variable γ k playing a substantial role in choosing the identification threshold depicted in Fig. 1e. If this threshold is chosen at the point where the identification error probability reaches a minimum, the SAW ID-tag reader can be said to be designed in an optimum way providing the identification with minimum slips. The problem now formulates as follows. Allowing zk and γk to be random with supposedly known distributions, we would like to find an optimal threshold for the K-bit pulse-burst (6) with time position encoding in order to provide the minimum error probability of the SAW ID-tag identification. III. IDENTIFICATION ERRORS While identifying the pulse-bursts coded with time position encoding, a threshold can logically be located equidistantly between the amplitudes of the sets of Onand Off-pulses. Owing to noise, such a strategy does not allow for a minimum identification error, although it gives a reliable effect when the SNR is large. Otherwise, the threshold must be specified optimally, corresponding to the minimum identification error probability. A. ID Error robability The identification error probability for the SAW RFIDtag with time position encoding having K-bits can be specified as in the following. It has been shown in [16] that the time location of On- and Off-pulses in slots does not play any role in the determination of the error probability. If we now introduce a separating (detection) threshold between the On- and Off-pulses, we then can denote the probability of each of the On-pulses as I1 (), I2 (),..., IM () and the relevant error probabilities as I1() = 1 I1() I2() = 1 I2() IM() = 1 IM() Given (4), the error probability in the ith On-pulse and jth Off-pulse can be calculated as, respectively, I i O i ( γ ) = 1 p( x ˆ γ ) ˆ (9) i ( γ ) = p( x γ ) j j i dx dx (10) Referring to (8) and referring to (9) and (10), the generic conditional error probability of the SAW ID-tag identification becomes (11a) (11b) If to substitute (4) to (11b), it will attain its most compact form of

5 where 2 2 x + a 2 ( a b) = xe I ( ax) Q 0 b (12), dx (13) with respecto to = In the particular case represented with (16), the optimum threshold can be ascertained by solving the following equation is the generalized Marcum Q-function of first order commonly used in radar signal detection [20]. A particular situation may occur when the SNRs in the On-pulses and Off-pulses are near equal; that is, for all i for all j One can also substitute them with their average value (14) (15) in order to find E approximately. In both cases (12) attains the form of (16) The Q-function cannot be expressed in simple functions and it is usually recommended to use asymptotic formulas [20]. We, however, still do not know exact criteria for the approximations in the SAW ID-tags and postpone these investigations to further studies preferring in this paper non asymptotic numerical estimates. B. Optimal Threshold The optimal threshold can be found if we minimize (12) by equating to zero the gradient of Ei ( γ ˆ γ γ γ γ γ ) p( x γ ) ˆ dx with M M + ˆ 1 K M M + 1 K = respect to. That means solving the equation j (18) For the Q-function (13), exact analytical solutions of (17) and (18) are commonly not available even in simple particular cases and numerical solutions are preferable. IV. ALICATIONS Based upon the above-given analysis, below we consider two applications for the identification error probability (12) and optimal threshold obtained by solving (17) The noise standard deviation in the absence of signal is determined here by the noise envelope level to be σ z Then the measured peak envelope V of the On- or Offpulse allows computing the SNR with 2 V γ = (19) 2 2σ We consider below the most typical case of = 30 db and σ = assuming all Off-pulses zeroth and all Onpulses unities [16]. Basically, (12) gives us the error probability for any code, if we take M and K with the values according to any scheme used in commercial products. Case 1: SAW ID-tag with time position encoding, 4 groups, 10 slots per group, 1 On-bit per group. If we take M=4 and K=36, which are the values for this case; numerically calculated, this error is exhibited in (2). For E 1%, thre threshold region will be any value between < < To achieve E 0.1% (1 slip per 1000 readings) the minimum SNR must be γ = 32 db. Case 2: SAW ID-tag with time position encoding, 10 groups 5 slots per group, 1 bit per group. We take M=10 and K=40, which are the values for this case;. numerically calculated, this error is exhibited in (3). For E 1%, thre threshold region will be any value between < < To achieve E 0.1% (1 slip per 1000 readings) the minimum SNR must be γ = db. These results allows the following generalizations: The optimal threshold ranges between 0.55 and 0.6, although it varies for different codes. Beyond, the error probability rises dramatically with the slope of about two decades per unity. Fixed the error probability, the region of the allowed thresholds is narrowed, similarly to (4) and (5), by (17)

6 increasing the number of groups, with one On-bit per group in the time position encoding. Figure 2. Optimal and allowed thresholds for 4 slots, 10 bits per group with different error probabilities (in %) as a function of the SNR. V. CONCLUDING REMARKS In this paper, we discussed the optimal thresholds for the identification of passive wireless SAW ID-tags with timeposition encoding in the sense of the minimum error probability. A generic relationship for the identification error probability has been represented via the Marcum Q- function of first order widely used in radar signal detection. A special feature of such tags is that the SNR in the On-pulse is affected by the technological factors. The SNRs in both the On- and Off-pulses are also affected, often strongly, by the interrogating signal echoes. Therefore, the results have been presented for arbitrary SNRs in the time position encoding pulse-burst. In applications, we estimated the optimal threshold for two encoding schemes found in commercial products. The main problem with using the exact relationships, (9), (10) and (11), is in their still poor engineering features, because the Marcum Q-function cannot be represented in simple ones. On the other hand, the optimum threshold does not depend on the code structure, being coupled only with the number of On- and Off-pulses in the burst. That gives a chance of finding reasonably accurate approximations for the K-slots SAW IDtags with M Onpulses that is currently under investigation. ACKNOWLEDGMENT G. Cerda-Villafana thanks CONCYTEG for funding part of this project. Figure 3. Optimal and allowed thresholds for 4 slots, 10 bits per group with different error probabilities (in %) as a function of the SNR. The identification threshold should not obligatorily be optimum, if E is limited with some value. In fact, allowed E = 1% for γ = 50, for the first case the region for is For the second case it is < < sketches the relevant allowed regions as functions of the SNR, assuming E = 5%, E = 1%, and E = 0.5%. REFERENCES [1] V. lessky, Review on SAW RFID tags, in roc. Joint Mtg. Europ. Freq. and Time Forum and IEEE Freq. Contr. Symp., Besancon, France, 2009, pp [2] F. Schmidt, O. Sczesny, C. Ruppel, and V. Mágoni, Wireless interrogator system for SAW-Identification-Marks and SAW- Sensor components, in: roc. IEEE Freq. Contr. Symp., Honolulu, USA, 1996, pp [3] L. M. Reindl and I. M. Shrena, Wireless measurement of temperature using surface acoustic waves sensors, IEEE Trans. Ultrason. Ferroel. Freq. Contr., 51 (11), 2004), pp [4] Q.-L. Li, X.-J. Ji, T. Han, and W.-K. Shi, Walsh threshold matched-filtering based anti-collision for surface acoustic wafe tags, J. Shanghai Jiaotong Univ., 14 (6), 2009, pp [5] A. Stelzer, M. ichler, S. Scheiblhofer, and S. Schuster, Identification of SAW ID-tags using an DSCW interrogation unit and model-based evaluation, IEEE Trans. Ultrason. Ferroel. Freq. Contr. 51 (11) 2004, pp [6] S. Scheiblhofer, S. Schuster, and A. Stelzer, Modeling and performance analysis of SAW reader systems for delay-line sensors, IEEE Trans. Ultrason. Ferroel. Freq. Contr. 56 (10) 2009, pp [7] L. Reindl, G. Scholl, T. Ostertag, H. Scherr, U. Wolff, and F. Schmidt, Theory and application of passive SAW radio transponders as sensors, IEEE Trans. Ultrason. Ferroel. Freq. Contr. 45 (5) 1998, pp [8] W.-E. Bulst, G. Fischerauer, and L. Reindl, State of the Art in wireless sensing with surface acoustic waves, IEEE Trans. Industr. Electron. 48 (2) 2001, pp [9] D. uccio, D. C. Malocha, N. Saldanha, D. R. Gallagher, and J. H. Hines, Orthogonal frequency coding for SAW tagging and sensors, IEEE Trans. Ultrason. Ferroel. Freq. Contr. 53 (2) 2006, pp

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