Performance Evaluation of Algorithms for SAW-Based ... - IEEE Xplore

ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 53, no. 6, june 2006

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Performance Evaluation of Algorithms for SAW-Based Temperature Measurement Stefan Schuster, Student Member, IEEE, Stefan Scheiblhofer, Student Member, IEEE, Leonhard Reindl, Member, IEEE, and Andreas Stelzer, Member, IEEE Abstract—Whenever harsh environmental conditions such as high temperatures, accelerations, radiation, etc., prohibit usage of standard temperature sensors, surface acoustic wave-based temperature sensors are the first choice for highly reliable wireless temperature measurement. Interrogation of these sensors is often based on frequency modulated or frequency stepped continuous wave-based radars (FMCW/FSCW). We investigate known algorithms regarding their achievable temperature accuracy and their applicability in practice. Furthermore, some general rules of thumb for FMCW/FSCW radar-based range estimation by means of the Cramer-Rao lower bound (CRLB) for frequency and phase estimation are provided. The theoretical results are verified on both simulated and measured data.

I. Introduction emperature measurement based on surface acoustic wave (SAW) sensors has received much attention in the past decade. These sensors operate completely passively [1], [2], withstand harsh environmental conditions, and can be interrogated wirelessly [3], [4]. Furthermore, it is possible to equip the sensors with a unique identification number, which can be read out simultaneously with the temperature information. Temperature ranges up to about 400◦ C are achievable [5], depending on the piezoelectric substrate used [6]. Fig. 1 shows the basic arrangement of a SAW tag measurement setup that can be used for remote temperature measurement and identification. The signal transmitted by the interrogation device is converted to a SAW by an interdigital transducer (IDT). Temperature measurement is done by measuring the round trip delay time (RTDT) difference between reflectors placed on the tag, which varies due to both thermal expansion and a temperature-dependent variation of the velocity of the SAW. Having knowledge of the material’s temperature coefficient of delay (TCD), which incorporates both effects, one can determine the temperature [7]. The paper is organized as follows: In Section II, a signal model for the problem at hand is derived. Section III covers general RTDT estimation, and Section IV applies the results to the SAW-based temperature estimation task. In Section V, results for real measurement data are shown.

T

Manuscript received August 2, 2005; accepted February 21, 2006. S. Schuster, S. Scheiblhofer, and A. Stelzer are with the Institute for Communications and Information Engineering, Johannes Kepler University, AT-4040 Linz, Austria (e-mail: [email protected]). L. Reindl is with the Institute for Micro System Technology (IMTEK), Albert-Ludwigs-University of Freiburg, D-79110 Freiburg im Breisgau, Germany.

Fig. 1. Setup for SAW tag-based identification and temperature measurement.

II. Frequency Modulated or Frequency Stepped Continuous Wave (FMCW/FSCW) Signal Model A. FMCW Radar The basic layout of an FMCW/FSCW radar unit is shown in Fig. 2. An FMCW radar transmits a sine wave, generated by the frequency synthesis unit, of amplitude At with linearly increasing frequency f (t) = f0 + kt. The chirp rate k = B/T of the frequency sweep, started at frequency f0 , is determined by the effective bandwidth B and the sweep duration T . The transmitted signal

  k st (t) = At cos 2π f0 + t t + ϕ0 (1) 2 is reflected by a target at distance d, where the target velocity is assumed to be zero (ϕ0 denotes an arbitrary initial phase offset). The received signal sr therefore is time delayed by the RTDT τ = 2d/c, with c denoting the speed of light, and is damped by a factor α1 . sr (t) =


 k α1 At cos 2πf0 (t−τ )+2π (t−τ )2 +ϕ0 −Φref . (2) 2

An additional phase offset Φref (−π ≤ Φref < π) has been included, which is often (falsely) neglected in the literature when information encoded in the phase is used. It is determined by the reflection properties of the target. After

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with n = 0, 1, . . . , N − 1. The transmitted signal takes the form st (t, n) = At cos (2πf [n]t + ϕ0 ) ,

(8)

with nTstep ≤ t < (n+1)Tstep. The received signal becomes (assuming τ  Tstep ) st (t, n) = α1 At cos (2πf [n](t − τ ) − Φref + ϕ0 ) . (9) Mixing, low-pass filtering, and sampling yields s[n] = α2 A2t cos (2πf [n]τ ) .

(10)

Combining (10) and (7) yields s[n] = α2 A2t cos (2πψn + Φ + Φref ) . Fig. 2. Block diagram of an FMCW/FSCW interrogation unit.

reception, the two signals are mixed (i.e., multiplied) and low-pass filtered (see Fig. 2), resulting in an intermediate frequency (IF) signal at the mixer output (with an amplitude factor α2 containing the mixer’s conversion loss, etc.): s(t) = α2 A2t cos (2πktτ + 2πf0 τ + Φref ) .

(3)

Quadratic terms of τ are neglected because f0  kτ in practical radar systems. If p targets are present, the signal at the output of the mixer is a sum of cosines. Sampling of (3) at t = nTs yields s[n] =

p 

Ai cos (2πψi n + Φi + Φref,i )

This is the same result as for the FMCW case (4). Therefore, the same signal model is valid for both radar types, with similar limitations for the single as well as for the multiple targets case. Henceforth, the signal model (4) will be used in the following discussion. Furthermore, as the RTDT contains the range information d, we focus on estimation of τ rather than estimation of d.

III. DFT-Based Signal Processing A. Achievable RTDT Estimation Accuracies To calculate the achievable accuracies for general FMCW/FSCW radar-based range estimation, we have to account for the unavoidable measurement noise. Therefore, the discrete data are modeled as

(4)

i=1

x[n] =

p 

Ai cos (2πψi n + Φi + Φref,i ) + v[n], (12)

i=1

with Φi = 2πf0 τi

(5)

and ψi = kTs τi =

B τi , N

(6)

where N is the number of samples. The RTDT information is encoded in the normalized frequency ψi (0 ≤ ψi < 1/2) as well as in the phase Φi . Therefore, if only the information encoded in the frequency is used (6), the problem at hand is a classical frequency estimation problem and can be solved by means of a discrete Fourier transform (DFT). B. FSCW Radar As in the case of an FMCW radar, an FSCW radar uses a frequency ramp as transmit signal, but the frequency is increased in steps of duration Tstep rather than continuously: f [n] = f0 +

B n, N

(7)

(11)

with v[n] assumed additive white Gaussian noise (AWGN), zero mean, and variance σ2 . A justification for the AWGN assumption is given later. As already indicated, the frequency as well as the phase in (12) contain the desired RTDT information. Therefore, we split the following discussion into algorithms based on frequency estimation and algorithms based on phase estimation. 1. RTDT Estimation Based on Frequency Estimation: Here we focus on classical Fourier transform-based methods to estimate ψi . This is mainly because frequency estimation based on the DFT magnitude spectrum turns out to be an excellent frequency estimator and appropriate for the SAW-based temperature measurement problem. When estimating ψi in (12) for the single target case (p = 1), a lower bound for the minimum achievable variance is given ˆ CRLB by the CRLB derived in [8]. Shown in Fig. 3 is std{ψ} as a function of ψ and N . An approximate (asymptotic) Cramer-Rao lower bound (CRLB) [8] can be found: ˆ CRLB ≈ var{ψ}

12 , (2π)2 ηN (N 2 − 1)

(13)

schuster et al.: algorithms for saw-based temperature measurement

Fig. 3. Exact CRLB for the single target case as a function of the normalized frequency and number of samples with A = 1, σ2 = 1, and Φ = 0. The CRLB “flattens out” for rising N and merges into the asymptotic CRLB.

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Fig. 4. Evaluation of the achievable minimum RTDT estimation RMSE vs. RTDT difference for two nearby targets via the exact CRLB. Also shown is the CRLB for a single target. N = 1601, B = 100.0625 MHz, η = 10 dB, and A = 1 (for both targets) were used.

where the signal-to-noise ratio (SNR) η is defined as η=

or

A2 . 2σ2

(14)

A hat denotes an estimated value and var{·} denotes the variance operator. Eq. (13) is valid for large N and for ψ not near 0 and 1/2 [8] (as can be seen from Fig. 3). This is fulfilled in the SAW-based temperature measurement problem. Henceforth, only (13) will be used in the following calculations and will be referred to as CRLB. Combining (6) and (13) with var{aX} = a2 var{X} for a constant a and a random process X, we obtain var{ˆ τ }CRLB ≈

12 (2π)2 ηN B 2

(15)

for large N . This shows that the variance of the RTDT estimation decreases linearly with η and N , but quadratically with B. Therefore, one should use the maximum allowed bandwidth in order to achieve the best possible range estimates. Furthermore, it can be shown that (13) is also approximately valid for the multiple targets case when the cosines are of similar amplitudes Ai and the frequencies ψi are spaced far apart (or equivalently, the targets are spaced far apart) [9], that is, |ψi − ψj | 

1 for i = j N

(16a)

1 for i = j. B

(16b)

or equivalently from (6) |τi − τj | 

This condition is called the Rayleigh resolution limit [10]. Otherwise, the exact CRLB for the multiple cosinusoids case [9] must be used. In practice, |ψi − ψj | >

4 for i = j N

(17a)

|τi − τj | >

4 for i = j B

(17b)

is often used as a rule of thumb for approximate fulfillment of (16). Fig. 4 shows a Monte Carlo simulation for two nearby frequencies (i.e., targets) (p = 2), where the exact CRLB for different target RTDT differences is plotted. Due to the symmetry of the problem, the CRLBs for both targets are nearly equal (the RTDT of the two targets has been chosen large so that the influence of the mirrored targets at negative RTDTs caused by the real valued signal model are negligible). It can be seen that (17b) is a conservative approximation and gives some margin for the commonly used additional weighting with windowing functions. On the other hand, windowing increases the variance of the RTDT estimation and this must be incorporated by a correction factor to yield accurate predictions [11], [12]. Note that the exact CRLB for two nearby targets is strongly dependent on the absolute phase difference and RTDT difference [9] of the individual cosines. Therefore, Fig. 4 is an example to show that the influencing effect becomes more and more negligible and independent of the phase and RTDT differences at about 40 ns RTDT difference, in agreement with (17b). It can be shown that maximization of the Schuster periodogram (or periodogram, for short) [9], [13] 1 periodogram = N

 2 −1 N    x[n] exp(−j2πψn)    n=0

(18)

as the maximum likelihood frequency estimator achieves (13) for large N and above a certain level of SNR and is

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Fig. 5. Evaluation of the periodogram’s threshold level for the estimation of ψ vs. SNR and number of samples for a single cosinusoid (p = 1) in (12), with ψ = 0.25, Φ = 0, Φref = 0, and zero-padding to 217 . No additional windowing function was applied to the data.

therefore the optimum frequency estimator. Furthermore, the frequency estimates can be shown to be asymptotically Gaussian distributed. Rife and Boorstyn showed that the maximization of (18) can be implemented efficiently using a fast Fourier transform (FFT) with zero padding to decrease errors due to the frequency quantization [14]. Simulation results indicate that the periodogram attains the CRLB at very low SNRs, depending on N (e.g., about −17 dB SNR at N = 2048; see Fig. 5). A closed-form expression for this threshold behavior is available in the literature [15]. The above results explain the widespread use of the periodogram [and equivalently the DFT magnitude spectrum, as obvious from (18)] as the first choice in frequency estimation problems for well separated targets. Because (16) is fulfilled for commonly used SAW tags [5] (although some coding schemes exist that do not [1]), all of the above formulas can be directly applied to the SAW-based temperature measurement task. To prove the above equations, we have performed numerous Monte Carlo simulations with simulated data as well as measured data. Figs. 6, 7, and 8 show simulation results of the root mean square error (RMSE) of RTDT estimation achieved for a single target. These results clearly validate (15). Fig. 6 also shows the results from real measurement data, where the measurements have been done with an interrogator and a SAW tag as described in [5], [16]. The different SNRs were simulated by inserting damping elements in the RF path of the interrogator. A hanning window was applied to the data prior to computation to reduce influence of the strong low frequency components (see Fig. 9 for a typical magnitude spectrum) on the measurement results. Furthermore, the influence of additional windowing on the estimation variance can be seen. Measurements with different bandwidth B and/or different number of samples N were not possible due to some technical limitations of the interrogation

Fig. 6. Monte Carlo simulation of the RTDT estimation of a single target with periodogram vs. the SNR. There were an average of 200 runs at each SNR with N = 1601, B = 100.0625 MHz, and zero-padding to 220 . No additional windowing function was applied to simulated data, whereas a hanning window was applied to the measured data. Shown are the results for the first reflector.

Fig. 7. Monte Carlo simulation of the RTDT estimation problem vs. B (for a single target). There were an average of 200 runs at each bandwidth, with N = 1601, η = 10 dB, and zero padding to 220 . No additional windowing function was applied to the data.

system used. The above results also confirm the AWGN assumption in (12) as well as the adequateness of (12) for the SAW-based temperature measurement task. It seems that the finite width of the reflectors, multiple reflections in between the reflectors, etc., do not significantly lower the measurement variance. The SNR in this case was estimated according to the method described in Section III-B. 2. RTDT Estimation Based on Phase Estimation: Because the RTDT information is also contained in the IF phase, it is natural to ask whether RTDT estimation via phase estimation delivers more accurate estimation re-

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Therefore, the resulting RTDT accuracy when combining (19) and (20) is var{ˆ τ }CRLB =

2(2N − 1) 4 1 ≈ 2 ηN ηN (N + 1) (2πf0 ) (2πf0 ) (21) 1

2

for large N . To compare the achievable accuracies, we can compare the variances of the phase-based RTDT estimation (21) and the frequency-based RTDT estimation, resulting in 1 4 2 ηN var{ˆ τ }CRLB,phase B2 (2πf0 ) = = . 12 var{ˆ τ }CRLB,frequency 3f02 (2π)2 ηN B 2 Fig. 8. Monte Carlo simulation of the RTDT estimation problem vs. N (single target case). There were an average of 200 runs at each number of samples with B = 100.0625 MHz, η = 10 dB, and zero padding to 220 . No additional windowing function was applied to the data.

(22)

In typical FMCW/FSCW radar systems, the ratio B/f0  1. Therefore, the variance of the phase-based RTDT can reach much lower values than that based on frequency estimation. Further, note that the resulting ratio is independent of N and η. Consider as a simple example a typical SAW interrogation system [16] with f0 = 820 MHz and B = 100.0625 MHz. Evaluation of (22) yields  2 100.0625 · 106 s−1 var{ˆ τ }phase 1 = 2 = 201.5 . 6 −1 var{ˆ τ }frequency 3 · (820 · 10 s ) (23) This means that the achievable variance of the phase-based RTDT estimate is about a factor of 201.5 lower (or equivalently, a factor of 14.2 in standard deviation). However, direct estimation of the Φi is difficult due to the 2π periodicity. In [7] an algorithm gives solution to this 2π ambiguity problem. Phase estimation with the DFT phase spectrum achieves the CRLB of (20) under the same condition (17) as the periodogram for frequency estimation (Fig. 10) [8]. Also, for phase estimation it is true that windowing increases the variance and must be taken into account to achieve accurate predictions of the achievable variance [11], [12].

Fig. 9. Typical magnitude spectrum obtained from an interrogation of a SAW tag with eight reflectors placed on the tag with B = 100.0625 MHz and N = 1601. A hanning window was applied to the data prior to computation.

B. SNR Estimation

sults. Suppose, for a moment, that Φref,i is zero and that we can estimate the Φi from (12) and not only the modulo 2π value. Then, the RTDT information can be calculated as

In most real measurement setups, the SNR as defined in (14) is unknown and must be estimated to be able to predict the RTDT estimator’s performance used. Amplitude estimation can be easily accomplished by using the DFT magnitude spectrum. However, σ2 is unknown. A common approach for the estimation is

ˆi Φ τˆi = . 2πf0

N −1 1  2 σˆ2 = (x[n] − sˆ[n]) , N n=0

(19)

The CRLB for phase estimation is given by [8] ˆ CRLB = var{Φ}

2(2N − 1) . ηN (N + 1)

(20)

(24)

where the estimated signal model sˆ[n] is calculated by first estimating frequencies, phases, and amplitudes and then inserting these estimated values into (4). However, this method performs poorly in our case because the signal model s[n] does not consider the reflections in between the

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Fig. 11. SAW tag setup for temperature measurement.

IV. Temperature Estimation A. Definition of the TCD Fig. 10. Evaluation of the achievable minimum phase estimation RMSE vs. target difference for two nearby targets via the exact CRLB. Also shown is the CRLB for a single target case with N = 1601, B = 100.0625 MHz, η = 10 dB, and A = 1 (for both targets).

The TCD is defined as the following Taylor series expansion [17]: T CDm =

reflectors, etc. Instead of taking these effects into account (which would result in a very complicated signal model), the idea is to use a region of the spectrum that does not contain any deterministic signal. That is, we use N1 1  2 ˆ 2 σ = |X[k]| , b

Tˆ = T0 +

with a constant b yet to be determined, N0 and N1 as the indices of the limits of the “noise-only” region of the spectrum (see Fig. 9, 5.5 µs to 8 µs), and X[k] =


 2π x[n] exp −j kn , N n=0

N −1 

(28)

This can be achieved by setting b = N (N1 − N0 + 1) .

(29)

Thereafter, the estimated amplitudes and noise variance can be used to estimate the SNR of the i-th target signal: ηˆi =

Aˆ2i . 2σˆ2

Hereby, τˆ is the RTDT estimate and τ0 is the RTDT at temperature T0 . Higher-order terms (m = 2) are often neglected because they are usually very small [7]. B. DFT-Based Temperature Estimation

N1   1 1  2 E |X[k]| = N σ2 (N1 − N0 + 1) . b b (27) k=N0

To make (27) unbiased, we require that   E σˆ2 = σ2 .

1 1 2 (ˆ τ − τ0 ) + (ˆ τ − τ0 ) + · · · . T CD1 τ0 2T CD2 τ0 (32)

(26)

that is, the DFT spectrum. If a windowing function is used, it must be incorporated into the derivation. The constant b must be chosen properly in order to make (25) unbiased. This can be achieved [8] by recognizing that E{σˆ2 } =

(31)

To estimate the TCD for a given material, it is necessary to perform a reference measurement and estimate the coefficients, e.g., using a least squares approach. Knowledge of the TCD enables an estimate of the actual material’s temperature by evaluation of

(25)

k=N0

1 ∂mτ · . τ m! ∂T m

(30)

The formulas derived in Section III-A can be directly applied to the SAW-based temperature estimation problem. A first commonly used approach [7] is to determine the actual RTDT difference ∆τp−1,T at the unknown temperature T between the last and the first reflector (Rp and R1 , respectively; see Fig. 11) and (higher-order TCD coefficients are neglected) to estimate the temperature by evaluation of Tˆ = T0 +

1 (∆ˆ τp−1,T − ∆τp−1,T0 ) . T CD1 ∆τp−1,T0

(33)

The minimum variance of the temperature estimate can be calculated to   1 var Tˆ = τp−1,T } . 2 var {∆ˆ (T CD1 ∆τp−1,T0 ) (34) But now we use the formulas derived for the general RTDT estimation case from the preceding section. The variance

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of the RTDT difference can be calculated assuming uncorrelated estimates (which is fulfilled when using the DFT magnitude spectrum [8]), that is, τp,T } + var {ˆ τ1,T } , var {∆ˆ τp−1,T } = var {ˆ

(35)

and using (15) var {∆ˆ τp−1,T } =

12 (2π)2 N B 2




1 1 + ηp η1

 ,

(36)

where ηi denotes the SNR of the i-th target signal as defined in (30). Combining (34) and (36) results in the minimum achievable variance of the temperature estimate   var Tˆ =
 1 12 1 1 + . (37) 2 η1 (T CD1 ∆τp−1,T0 ) (2π)2 N B 2 ηp Eq. (37) can be used together with (30) to calculate the variance of a particular temperature estimate. If necessary, higher-order TCDs can be easily incorporated into above derivation.

Fig. 12. Plot of periodogram-based temperature estimation results from a temperature ramp and comparison to a PT100 reference measurement.

TABLE I Measurement Results for Periodogram-Based Estimates.

C. Phase Evaluation Method The RTDT time information (which incorporates the temperature information) is also included in the phase of the IF signal. To calculate the variance in this case, we combine (34) with (21):   var Tˆ =
 4 1 1 1 + . (38) 2 2 η1 (T CD1 ∆τp−1,T0 ) (2π)2 N f0 ηp The ratio of temperature variances can be calculated from (37) and (38) to   var Tˆ B2   phase = , (39) 3f02 var Tˆ frequency

as expected from (22). Therefore, we expect the same ratio of variances as in the RTDT estimation case given in (23).

PT100 temperature (◦ C)

Std.-dev. predicted from estimated SNR (◦ C)

Std.-dev. of periodogrambased estimates (◦ C)

50.5 142.5

0.4 0.44

0.538 0.596

measurement cycle of 200 measurements. This was done to be able to determine the statistics of temperature estimates at nearly constant temperature and therefore constant SNR (the SNR may vary with temperature due to damping effects of the material) to correctly prove (37) and (38), using the TCD estimated before. Estimation results are given in Tables I and II. Figs. 13 to 16 show the estimated temperature curves. For all measurements, B = 100.0625 MHz, N = 1601, and f0 = 820 MHz have been used. A hanning window was applied to the data prior to computation. The measurement results are in good agreement with the theoretically achievable temperature standard devia-

V. Measurement Results To prove (37), (38), and (39), we have performed numerous temperature measurements with a SAW interrogation system, as described in [16]. First, the temperature estimation results from the DFT magnitude spectrum of a temperature ramp (see Fig. 12) were compared to a PT100 temperature sensor reference measurement. This measurement was primarily done for the estimation of the TCD, resulting in T CD1 = 89.8 ppm. Thereafter, we performed measurements at two different temperatures, where the temperature was held constant during a

TABLE II Measurement Results for Phased-Based Estimates.

PT100 temperature (◦ C)

Std.-dev. predicted from estimated SNR (◦ C)

Std. dev. of phased-based estimates (◦ C)

Std.-dev. ratios (periodogram to phased-based)

50.5 142.5

0.027 0.03

0.042 0.053

12.81 11.25

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Fig. 13. Plot of periodogram-based temperature estimation results at nearly constant temperature of about 50◦ C.

Fig. 14. Plot of phase-based temperature estimation results at nearly constant temperature (same measurement data as Fig. 13) of about 50◦ C.

Fig. 16. Plot of phase-based temperature estimation results at (nearly) constant temperature (same measurement data as Fig. 15) of about 142.5◦ C.

tions (see Table I). However, as can be seen in Fig. 13, it is difficult to make statements of the achievable absolute temperature accuracy due to the following reasons. First, the accuracy of the PT100 reference measurement is not high enough (especially at higher temperatures), so it makes no sense to compare the results, especially from the phase-based algorithm, to it. Also, it is difficult to keep the temperature at a constant level with variations in the 10 mK region for the measurement time of about 10 minutes. Second, the TCD is generally unknown and must be estimated. Furthermore, we have neglected higher-order coefficients of the TCD which may enable more accurate results, particularly at higher temperatures. Third, the algorithm described in [7] implies a calibration of every sensor. This serves to eliminate the phase offset shown in (2) as well as accounts for biased frequency and phase estimates (e.g., in Fig. 13, a small bias of about 0.5◦ C is visible), which may occur due to reflections in between the reflectors; see Fig. 9. However, calibration might not be possible in all practical applications. VI. Conclusions In this paper, we have presented some closed-form expressions for assessing the accuracy of SAW-based temperature measurement. Furthermore, the general problem of RTDT estimation and SNR estimation is discussed and the results provided can be used not only for the SAW-based temperature estimation task, but also in general continuous wave radar applications. The results from simulations as well as from measurement data are in good agreement with the theory. References

Fig. 15. Plot of periodogram-based temperature estimation results at nearly constant temperature of about 142.5◦ C.

[1] C. S. Hartmann, “A global SAW ID tag with large data capacity,” in Proc. IEEE Ultrason. Symp., vol. 1, Oct. 2002, pp. 65–69.

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[2] R. Peter and C. S. Hartmann, “Passive long range and high temperature ID systems based on SAW technology,” in Proc. Sensor Conf., Nuremberg, Germany, vol. 1, May 2003, pp. 335– 340. [3] A. Pohl, “A review of wireless SAW sensors,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 47, no. 2, pp. 317–332, Mar. 2000. [4] F. Schmidt and G. Scholl, “Wireless SAW identification and sensor systems,” in Advances in Surface Acoustic Wave Technology, Systems and Applications. vol. 2, T. Fjeldly and C. Ruppel, Eds. London: World Scientific Publ., 2001, pp. 277–325. [5] R. Hauser and G. Bruckner, “A high-temperature stable SAW identification tag for a pressure sensor and a low-cost interrogation unit,” in Proc. Sensor Conf., Nuremberg, Germany, vol. 2, May 2003, pp. 467–472. [6] J. Hornsteiner, E. Born, G. Fischerauer, and E. Riha, “Surface acoustic wave sensors for high-temperature applications,” in Proc. IEEE Freq. Contr. Symp., May 1998, pp. 615–620. [7] L. M. Reindl and I. M. Shrena, “Wireless measurement of temperature using surface acoustic wave sensors,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 51, no. 11, pp. 1457–1463, Nov. 2004. [8] S. M. Kay, Fundamentals of Statistical Signal Processing Estimation Theory. Englewood Cliffs, NJ: Prentice-Hall, 1993. [9] S. M. Kay, Modern Spectral Estimation Theory and Application. Englewood Cliffs, NJ: Prentice-Hall, 1988. [10] L. L. Scharf, Statistical Signal Processing. Reading, MA: Addison-Wesley, 1991. [11] F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE, vol. 66, no. 1, pp. 51–83, Jan. 1978. [12] C. Offeli and D. Petri, “The influence of windowing on the accuracy of multifrequency signal parameter estimation,” IEEE Trans. Instrum. Meas., vol. 41, no. 2, pp. 256–261, Apr. 1992. [13] A. Schuster, “On the investigation of hidden periodicities with applications to a supposed 26 day period of meteorological phenomena,” Terr. Magn., vol. 3, pp. 13–41, Mar. 1989. [14] D. C. Rife and R. R. Boorstyn, “Multiple tone parameter estimation from discrete-time observations,” Bell Syst. Tech. J., vol. 55, pp. 1389–1410, Nov. 1976. [15] B. G. Quinn and P. J. Kootsookos, “Threshold behavior of the maximum likelihood estimator of frequency,” IEEE Trans. Signal Processing, vol. 42, no. 11, pp. 3291–3294, Nov. 1994. [16] S. Scheiblhofer, S. Schuster, A. Stelzer, and R. Hauser, “SFSCW-radar based high resolution temperature measurement with SAW sensors,” in Int. Symp. Signals, Systems, Electronics (ISSSE’04), Aug. 2004, pp. 128–131. [17] K. Hashimoto, Surface Acoustic Wave Devices in Telecommunications. Berlin, Heidelberg, New York: Springer-Verlag, 2000.

Stefan Scheiblhofer (S’03) was born in Linz, Austria, in 1979. He received the M.Sc. degree in mechatronics in 2003 from the Johannes Kepler University, Linz, Austria, where he is currently pursuing the Ph.D. degree at the Institute for Communications and Information Engineering. His primary research interests concern advanced radar system concepts, the development of the associated signal processing algorithms, statistical signal processing, and their application to surface acoustic wave devices for ID and temperature measurement purposes.

Stefan Schuster (S’03) was born in Linz, Austria, in 1978. He received the Dipl.Ing. (M.Sc.) degree in mechatronics from Johannes Kepler University, Linz, Austria. He is currently with the Department of Information and Communications Engineering (ICIE), University of Linz, Austria, as a Ph.D. student. His research interests include all kinds of signal processing, especially focused on radar signal processing and RF system design.

Andreas Stelzer (M’00) was born in Haslach an der M¨ uhl, Austria, in 1968. He received the Diploma Engineer degree in electrical engineering from the Technical University of Vienna, Austria, in 1994. In 2000 he received the Dr.Techn. degree (Ph.D.) in mechatronics with honors “sub auspiciis praesidentis rei publicae” from the Johannes Kepler University, Linz, Austria. In 2003 he finished his habilitation thesis and became an associate professor at the Johannes Kepler University, Linz. He joined the Johannes Kepler University as an university assistant in 1994. Since 2000 he has been with the Institute for Communications and Information Engineering. His research work focuses on microwave sensor systems for industrial applications, RF- and microwave subsystems, SAW sensor systems and applications, and digital signal processing for sensor signals. He has authored or coauthored more than 100 journal and conference papers. Dr. Stelzer is a member of the Austrian OVE and a member of the Microwave Theory and Techniques, Circuits and Systems, and Instrumentation and Measurement Societies within the IEEE. He served as an associate editor for the IEEE Microwave and Wireless Components Letters.

Leonhard Reindl (M’93) received the Dipl. Phys. degree from the Technical University of Munich, Germany, in 1985 and the Dr.Sc.Techn. degree from the University of Technology, Vienna, Austria, in 1997. From 1985 to 1999 he was a member of the micro acoustics group of the Siemens Corporate Technology department, Munich, Germany, where he was engaged in research and development on SAW convolvers, dispersive and tapped delay lines, ID-tags, and wireless passive SAW sensors. In winter 1998/99 and in summer 2000 he was guest professor for spread spectrum technologies and sensor techniques at the University of Linz, Austria. From 1999–2003 he was university lecturer for communication and microwave techniques at the Institute of Electrical Information Technology, Clausthal University of Technology. In May 2003 he accepted a full professor position at the laboratory for electrical instrumentation at the Institute for Micro System Technology (IMTEK), AlbertLudwigs-University of Freiburg, Germany. His research interests include wireless sensor and identification systems, surface acoustic wave devices and materials, and microwave communication systems based on SAW devices. He holds 35 patents on SAW devices and wireless passive sensor systems and has authored or co-authored approximately 130 papers in this field. Leonhard Reindl is Elected Administrative Committee (AdCom) member of the IEEE Ultrasonics, Ferroelectrics, and Frequency Control Society and also a member of the Microwave Theory and Techniques Society. Since 2000 he has been a member of the Technical Program Committee of the IEEE Frequency Control Symposium. He is also engaged in technical committees of the German VDE/ITG Association.