Readout Unit for Wireless SAW Sensors and ID-Tags
Andreas Stelzer, Stefan Schuster, Stefan Scheiblhofer
  Institute for Communications and Information Engineering, Johannes Kepler University Linz,
               Altenberger Str. 69, A-4020 Linz, Austria, E-mail: a.stelzer@ieee.org
   Abstract — Today’s wireless identification (ID) and
sensor systems based on surface acoustic wave (SAW)
technology permit reliable and accurate data acquisition,                             II.   SAW SENSOR
where wired solutions cannot be applied. In this paper we
present an overview of modern concepts for wireless SAW
                                                                 SAW-based sensors generally use two different principles
readout units. Additionally, SAW sensor principles, in           that allow determination of different physical quantities.
particular delay line based temperature sensors and ID-tags      The first type is based on the SAW resonator structure,
are discussed. Different evaluation algorithms are illustrated   whose resonating frequency is influenced by the external
and compared with respect to their performance. Further-         quantity. Such sensors are mainly used for viscometers,
more, temperature measurement and ID determination               gas- and biosensors [2].
results with a realized interrogation unit are shown.
                                                                 In delay-line structures, Fig. 2, the physical measurand
   Index Terms — SAW sensors, SAW reader unit, FMCW,
FSCW, temperature measurement, phase evaluation.                 affects either the velocity of the SAW, or the geometrical
                                                                 dimension of the propagation path, both resulting in a
                                                                 change of the measured round trip delay τ of the readout
                    I.   INTRODUCTION                            signal.
Surface acoustic wave (SAW) based sensors are                    A typical RF interrogable delay line SAW sensor, Fig. 2,
applicable to many industrial processes where wireless           consists of the piezoelectric substrate, an interdigital
sensing, passive operation, and high robustness against          transducer (IDT), several reflectors and an antenna
environmental impacts are fundamental requirements.              structure. In reference to the IDT every reflector can be
These devices use the piezoelectric effect on piezo              characterized by its physical distance L, delay time τ, and
crystals, mainly LiNbO3 or quartz, that convert incoming         phase ϕ.
electromagnetic waves into mechanical waves, propaga-
ting over the surface of the substrate. Due to the relatively
slow propagation velocity of the SAW (~3500 m/s)
compared to the velocity of light, this technology is ideal
for creating delay lines and transversal filters just as high-
Q resonators and several types of sensors [1].
A key feature of wirelessly interrogated SAW sensors is
their completely passive operation. In Fig. 1 a typical
configuration, consisting of interrogation unit and SAW
sensor with attached antenna is shown. The request signal
can be either a short pulse or a continuous wave (CW)            Fig. 2    Arrangement of IDT, reflectors for reference and
which is called time-domain sampling and frequency-              measurement purposes as well as a loaded reflector for use with
                                                                 external sensors.
domain sampling, respectively.
                                                                 The IDT transforms the electromagnetic energy of the RF
                                                                 request signal delivered by the antenna into the surface
                                                                 acoustic wave (SAW) and vice versa. The reflectors
                                                                 partly throw back the acoustic energy towards the IDT
                                                                 which ideally retransmits an overlay of delayed and
                                                                 attenuated versions of the request signal according to the
                                                                 different reflector positions in the propagation track.
                                                                 This provides the following options: First, using only the
                                                                 positions of multiple reflectors in the track one can easily
                                                                 implement numeric codes for identification purposes [3],
                                                                 [4], [5] that benefit from being completely passive and
                                                                 highly temperature stable.
                                                                 Second, this tag structure, with fewer and properly placed
                                                                 reflectors, allows very precise temperature measurements,
Fig. 1    General configuration of wireless SAW sensor           by observing the changes in the round trip delay over
interrogation.                                                   temperature [6].
Especially when measuring temperature, inaccuracies in         generation concepts measurement times down to some
the thermal coefficient of delay (TCD)                         microseconds are feasible at moderate cost. Following is
                                                               a short overview of typical functional blocks for
                            1 ∂τ
                    TCD =    ⋅                          (1)    frequency-domain interrogators [9].
                            τ ∂ϑ
                                                               B. Basics of frequency-domain interrogators
of the SAW substrate, that describes both, the change in
SAW velocity and physical dimension over temperature,          Fig. 4 shows a general block diagram of frequency-
becomes the limiting factor for the reachable temperature      domain interrogators. A crucial point is the frequency
accuracy.                                                      synthesis, as nonlinearities in the generated frequency
If only the delay time or phase differences in the received    sweep are directly related to measurement inaccuracies
signal are evaluated, the distance between the                 [10], [11]. The modulation scheme can be frequency
interrogation unit and sensor does not influence the           stepping (FS), linear frequency modulation (LFM) or
measurement results.                                           either arbitrary. Depending on the application and the
Not only the SAW device itself applies for sensory             specific requirements, frequency synthesis can be done
purposes, it can also operate as RF-link for external          with simple voltage controlled oscillators, closed-loop
sensors, such as pressure- [7] or humidity transducers,        control with PLLs and direct digital synthesizers (DDS)
[8]. In that case the reflector on the SAW tag is replaced     or with combinations thereof.
by an IDT, that is connected to the external sensor. Such
a loaded IDT changes its reflectivity due to the sensor
signal and therefore enables RF readout capabilities.
Depending on the readout strategy the matching network
of the physical sensor to the IDT has to maximize either
phase or amplitude changes in the measured S11 over the
sensor impedance variations.
               III. SAW INTERROGATION
A. Frequency-domain versus time-domain sampling
As sketched in Fig. 3, the interrogation unit can operate in
(a) time-domain (TD) or (b) frequency-domain (FD).
Time-domain sampling directly captures the impulse
response, therefore fast analog-to-digital converters are
required.
                                                               Fig. 4. General block diagram of a frequency-domain inter-
                                                               rogator.
                                                               The advantage of continuous wave (CW) signal
                                                               generation in frequency-domain sampling, on the other
                                                               hand is a major drawback, as there is no time gap to
                                                               switch between transmit and receive. Thus, the separation
                                                               of the simultaneously occurring transmit and receive
                                                               signals is a challenging task, and directly influences the
                                                               achievable system dynamic. In low-cost systems a
                                                               homodyne configuration is desirable, which needs only a
                                                               mixer, a filter, an analog-to-digital converter and some
                                                               signal processing.
                                                               B. TX/RX Separation
                                                               In Fig. 5 four common concepts of TX/RX separation
                                                               techniques are sketched. A two antenna concept, as
Fig. 3. (a) Time-domain sampling and (b) frequency-domain      shown in (a), would offer excellent isolation (and is used
sampling of SAW sensors
                                                               e.g. in military radar applications), but is expensive and
                                                               needs a lot of space. Therefore, this topology is quite rare
For low-cost and highly accurate systems, where an
                                                               in industrial sensor applications.
extremely short measurement time is not necessary,
                                                               Configurations using a circulator (also common in
interrogation in frequency-domain with slow sampling is
                                                               military and high-power applications) are a smart solution
a favorable choice. Nevertheless, with advanced signal
                                                               as there are no conceptual losses except for the insertion
loss of the circulator. The limited isolation of the
circulator causes direct coupling of the transmit signal to
the receive path which leads to DC signal components at
the mixer output and hence a reduced dynamic. Another
drawback for low-cost and highly compact solutions is
the difficult realization of the circulator, which requires
gyromagnetic materials and magnetization, both require-
ments that are not compatible with integrated techno-
logies.
                                                               Fig. 6   Open loop configuration with lookup table and
                                                               frequency measurement.
                                                               b) Phase locked loop (PLL) - linearization
                                                               With PLLs both, a good stabilization as well as modula-
                                                               tion like frequency stepping or linear frequency modula-
                                                               tion can be achieved. By rapidly and randomly changing
                                                               the divider values ND the average divider value can be
                                                               fractional and is not limited to integers. With state-of-the-
                                                               art fractional-N PLLs, as shown in Fig. 7, the adjustable
                                                               output frequency steps are much smaller than the refer-
                                                               ence frequency. Therefore, ND can be reduced to smaller
                                                               values, which improves phase noise behavior, as this is
                                                               upconverted proportional to log(ND).
Fig. 5   Four variants for transmit-signal (TX) and receive-
signal (RX) separation in continuous wave (CW) sensor
systems with frequency-domain sampling.
A directional coupler as sketched in (c) has limitations in
its directivity and a conceptual loss of at least 3 dB, when
using small ceramic packages mostly 6 dB ore more.
With a 90°-hybrid, as drawn in (d), half of the transmit
and receive signal can be split off simultaneously and fed
to the mixer. Similar to the coupler, the limited isolation
capabilities of the hybrid cause large DC-offsets at the
mixer output, which can often be filtered out when using
a large lead time from the IDT to the first reflector on the
SAW device.
C. Signal generation concepts for CW systems                   Fig. 7.   Fractional-N PLL block diagram.
a) Free running VCO with lookup table                          The whole system is controlled by the arbitrary divider
                                                               values, and it is possible to generate a sequence which
The cheapest configuration for signal generation consists
                                                               produces a linear frequency chirp at the output with a
of a free running VCO only, that is controlled by a ramp
                                                               resulting phase error in the RF signal of a fraction of a
generator. As the voltage-frequency (U/f ) characteristic
                                                               radian [12], [13], [14].
of a VCO is mostly quite nonlinear, a lookup table in
                                                               By characterizing the whole loop dynamics and
conjunction with a digital-to-analog converter, as shown
                                                               adaptively controlling the frequency divider, the sharp
in Fig. 6, can be used to improve linearity. The generation
                                                               transitions from upchirp to downchirp can be reproduced
of the voltage-values requires a frequency measurement.
                                                               very precisely. All in all, PLL-based concepts are very
With an in-system frequency measurement the lookup
                                                               attractive for industrial applications due to their high
table can be regularly updated during operation cycles to
                                                               accuracy, low cost, modulation capabilities, and simple
keep the frequency linearity of the generated chirp high,
                                                               RF-signal generation without the need for any further
despite temperature drifts and other variations in the U/f-
                                                               upconversion components. State-of-the-art PLL control-
characteristic.
                                                               led frequency chirps can range down to a length of some
                                                               tens of microseconds with a bandwidth of greater than
                                                               100 MHz.
c) Direct digital synthesizer (DDS) with upconversion
Direct digital synthesizers are very attractive when
highest ramp linearity and fast and digital control is
required. As the RF signal is digitally generated by means
of an digital-to-analog converter, frequency and phase as
well as chirp-rates can be controlled with high accuracy
(mostly 32-bit registers or wider). Although there are
low-power DDS available, these chips generally require a
lot of power, keeping in mind mobile applications and
output frequencies are limited to some hundred MHz
[15]. Therefore, upconversion to the RF-band is neces-
sary. This can be accomplished e.g. by using a single
sideband (SSB) upconverter as shown in Fig. 9, which
can easily be done with the DDS supplies I and Q signals.
                                                             Fig. 10. Linearization concept of an FMCW interrogator with
                                                             SAW delay line.
                                                             e) Chirp linearization with SAW device
                                                             In [16] a linearization concept was introduced, that uses a
                                                             SAW delay line for linearization purposes. As can be
                                                             seen in Fig. 10, the delay line forms a second target at a
                                                             virtual but constant distance. In the IF signal the zero-
                                                             crossings correspond to equally spaced frequency points
Fig. 8.   DDS with single sideband upconversion to the RF    of the transmit signal. Using this information the
                                                             sampling is shifted to non-equidistant sampling in time,
                                                             but equidistant sampling in frequency, which virtually
d) Direct digital synthesizer (DDS) with PLL
                                                             linearizes the oscillator characteristics.
With a combination of DDS and PLL as shown in Fig. 9,
we can combine the advantages of digital signal genera-
                                                                              IV. SIGNAL PROCESSING
tion with a higher bandwidth obtained by the frequency
multiplication behavior of the PLL and the simple
generation of the RF signal without upconversion mixer       A. Derivation of Evaluation Algorithm
and additional local oscillator.                             According the CW radar principle, the following signal
                                                             model describes the (digitised) signal at the output of the
                                                             mixer in Fig. 4,
                                                                                    p
                                                                      s IF [n] =          Ai cos(2πf i n + 2π f 0τ i ) ,   (2)
                                                                                   i =1
                                                             if the transmitted signal is of the form
                                                                                                     k
Fig. 9. Chirp signal generation with DDS and PLL to obtain              sT (t ) = AT ⋅ cos 2π ( f 0 + ) t .                (3)
                                                                                                     2
higher bandwidth and frequency.
                                                             Here, τ = 2d/c is the round trip delay caused by a target in
Especially for higher output frequencies and fast ramps an   distance d, c denoting the speed of light. f0 is the starting
additional IF stage with PLL-techniques is used, whereas     frequency of the frequency ramp (chirp) with bandwidth
the second stage uses conventional upconversion.             B. Basically, the signal model describes a sum of
                                                             sinusoidal waves. The desired distance information is
                                                             encoded in the frequency f=kτ of a particular wave, where
                                                             k =B/Tsweep is the steepness of the chirp, as well as in the
                                                             phase Φ =2π f0τ. A first approach for determining τ
                                                             (which is equivalent to getting d ) is to estimate the
                                                             frequencies of the cosines of (2) by the FFT (fast Fourier
transform). To ensure resolution of individual targets as                                                                             N
well as keeping the sidelobe level low, a proper                                                                      b=       N −1
                                                                                                                                                 .                        (10)
windowing function (Hanning window) should be applied                                                                                        2
                                                                                                                                      w[n]
to the raw data. Since frequency discretisation is quite                                                                       n =0
coarse using only the usually relatively low number of
samples, zero padding increases the accuracy of the                                     Other methods to obtain the frequency information are the
estimated frequencies. After transforming, a peak search                                adoption of parametric spectral estimation methods (AR,
algorithm can be used to determine the location of the                                  ARMA models) for frequency estimation as well as state
strongest peaks which correspond to the target                                          space algorithms [18], such as MUSIC [19], [20], [21]
frequencies fi in (2). For SAW ID purposes as an                                        ESPRIT [22], TAM [23], DDA [18]. These algorithms
example, one can compare these locations to an                                          yield higher frequency resolution [24] than conventional
imaginary grid defined in a pulse position coding scheme.                               Fourier transform based methods, especially at high SNRs
Temperature measurement is possible by measuring the                                    [25], [26], [27].
distance between the first an the last target which is rising                           A more sophisticated and accurate way for getting the
nearly linear with rising temperature, according to the                                 distance information is the so called phase evaluation
TCD as described in (1).                                                                algorithm, which exploits the fact that the distance
When measurement of the amplitude of the reflected                                      information is also encoded in the phase of the used
sinusoidal waves is of interest (e.g. delay line applications                           signal model, as can be seen in (2). Applying the DTFT
as described in Section II), the usage of a particular                                  (discrete time Fourier transform) to (2), the resulting
windowing function (excepting the rectangular window)                                   spectrum (magnitude and phase) is
decreases the measured amplitude. To overcome this, a                                                             p
signal power compensation algorithm can be used [17].                                           S( f ) =
                                                                                                                       Ai
                                                                                                                          (δ ( f − f i ) + δ ( f + f i ))                 (11)
Let s[n] denote measured data according to the signal                                                         i =1
                                                                                                                       2
model of (2). Before applying the FFT to the discrete
data, one multiplies it with a particular windowing                                                               arg(S ( f ) ) = 2π f 0τ i                               (12)
function w[n], which results in a loss of signal power.
This can be corrected by multiplying a constant b to                                    where δ ( f ) denotes the Dirac Delta function. To obtain
obtain the corrected signal x[n]                                                        very accurate distance (i.e. round trip delay) information,
                  x[n] = b ⋅ w[n] ⋅ s[n] .                                        (4)   the magnitude spectrum is used to obtain a coarse round
                                                                                        trip delay estimate, as well as the phase spectrum for a
To determine b, the variance (i.e. the power) of both the                               finer determination. This approach can be formulated as
original as well as the windowed signal must be
calculated. Assuming that s[n] has zero mean and let E{⋅}                                 τˆPhase =
                                                                                                      (Φˆ   FFT   (τˆFFT ) + 2π m )                  Φ
                                                                                                                                                     ˆ
                                                                                                                                                       FFT ∈ [ −π , π ]   (13)
define the expectation-operator, the variance of x[n] as                                                              2π f 0
well as s[n], is given by
                                                                                        with
                           {
                          E s[n]        2
                                            }   = σ s2                            (5)
                                                                                                             2π f 0 ⋅τˆ FFT
                                                                                                  m=                                      = f 0 ⋅τˆ FFT .                 (14)
                                                                                                                  2π
                                    {
              E{x[n]} = E b w[n] s[n]       2        2            2
                                                                      }           (6)
                                                                                        Here all terms annotated with “^” denote estimates de-
Since s[n] and w[n] are independent and b is a deter-                                   rived from FFT magnitude spectrum (subscript “FFT”) or
ministic variable, (6) can be written as                                                phase evaluation (subscript “Phase”).
   {      }       {             }{
 E x[n]2 = b 2 E w[n]2 E s[n]2 = b 2 E w[n]2 σ s2 .  }                {       }   (7)
                                                                                        A problem when using the phase information is caused by
                                                                                        the 2π phase ambiguity when evaluating m in (14).
To restore signal power, the relation                                                   Although not within the scope of this paper, this can be
                                                                                        solved with properly placed targets whose round trip
                      {         } { !
                  E s[n]2 = E x[n]2 .                        }                    (8)   delay ratios on the SAW tag are known.
                                                                                        B. Accuracy Comparison
has to be satisfied. This leads to
                                                                                        To determine and compare the achievable accuracies with
                                                                                        both traditional Fourier based methods and the phase
                      1                                  1
          b2 =                      =                                     ,       (9)   evaluation algorithm, one can utilize the Cramer Rao
                  {
                 E w[n]     2
                                }       (1 / N )
                                                     N −1
                                                                 w[n]2
                                                                                        Lower Bound (CRLB) [28]. Consider the following
                                                                                        signal model
                                                     n=0
where N is the number of discrete data points.                                                          x[n] = cos(2πf1n + Φ ) + v[n]                                     (15)
Rearranging (9) yields                                                                  with v[n] additive, white Gaussian noise with zero mean.
This corresponds to the signal model of a SAW tag with a                                 results. Assuming a B=100 MHz sweep at f0=820 MHz,
single reflector. Round trip delay estimation using the                                  (21) yields
                                                                                                           std{τˆPhase }CRLB
magnitude spectrum calculated via Fourier transformation
yields                                                                                                                       ≈ 0.07 .          (22)
                                                                                                           std{τˆFFT }CRLB
                                        fˆ1,FFT
                         τˆFFT =                      .                           (16)   This means that the achievable accuracy with the phase
                                            k
                                                                                         evaluation method is about 14 times higher than round
On the other hand, round trip delay estimation via the                                   trip delay estimation via the magnitude spectrum.
phase evaluation algorithm leads to
                   τˆPhase ≈
                                  (Φˆ   FFT+ 2πm              )                   (17)
                                                                                           V.      FSCW INTERROGATION UNIT FOR ID-TAGS AND
                                         2πf 0                                                           TEMPERATURE MEASUREMENT
                                                                                         Designing a low cost interrogation unit requires the right
neglecting phase estimation errors due to errors in the
                                                                                         trade-off between system performance and costs.
coarse round trip delay estimation. Using
                                                                                         The implemented system is based on the frequency
   var{ aX } = a 2 ⋅ var{X }                std{ aX } = a ⋅ std{ X }              (18)   stepped continuous wave (FSCW) radar principle, that
                                                                                         measures a target’s round trip delay evaluating the phase
with a a constant and X a random process as well as                                      difference between transmitted and received signal in a
                                                                                         homodyne (zero IF) receiver, Fig. 11. Although being
                                                2(2 N − 1)
                  {
              std Φ
                  ˆ
                    FFT      }   CRLB   =
                                                ηN (N + 1)
                                                                                  (19)   relatively slow due to the stepped frequency ramp and
                                                                                         therefore not applicable to fast moving targets, this
                                                                                         concept offers the advantage of SNR enhancement using
and                                                                                      averaging on every frequency step.
                                                                                         As the presented system is a specialized solution for a
             {
          std fˆ1, FFT   }        =
                                                          12                             industrial sensor identification system employing the
                                                              (       )
                                                                                  (20)
                         CRLB
                                         (2π )    2
                                                      ηN N 2 − 1                         existing sensor cable for the ID-readout sequence, the
                                                                                         SAW-ID tag mounted in the sensor housing is
where η is the SNR and N is the number of sampled data                                   interrogated mainly via capacitive coupling. The ID-tag
points [28], the theoretical achievable accuracies can be                                cannot be matched properly, as the existing capacitance
compared:                                                                                of the physical sensor causes a strong perturbing
                                                                                         reflection at low frequencies, respectively delay times. In
   std{τˆ Phase }CRLB            B       2 N 2 − 3N + 1               B Rel              conjunction with the signal windowing this results in
                             =                                    ≈
      std{τˆ FFT }CRLB                                    2                   .   (21)
                                 f0             6N                        3              leakage effects that have to be reduced by appropriate
                                                                                         filtering.
Brel=B/f0 denotes the relative system bandwidth. The                                     Fig. 11 shows the realized 900 MHz readout unit, which
resulting ratio is nearly independent of N. Furthermore, it                              is based on the block diagram of Fig. 12. It uses an RF
can be shown that the FFT approximately achieves the                                     switch that enables the system to read out multiple
calculated CRLB for a single target and even for multiple                                sensors sequentially.
targets if they are well separated in frequency [24]. So
above results are directly applicable to measurement
                 signal generation                                channel switching             amplification                   power supply
                      power amplifier                             receiver                   AD-conversion         controller
                                              Fig. 11. 4-layer multichannel readout-unit for SAW-ID-tags
                                                               (dashed line) with the results from a phase evaluation
                                                               (solid line) is plotted. The achieved resolution is about
                                                               ±0.3 K whereas the simple FFT approach is only as
                                                               accurate as ±5 K at the given readout distance.
Fig. 12. Block diagram of the combined ID / temperature
readout unit.
                                                               Fig. 14. Comparison of temperature measurement results with
              VI. MEASUREMENT RESULTS                          FFT magnitude and phase based evaluation.
A. ID-tag evaluation                                           From verifications with a PT100 temperature sensor as
                                                               shown in Fig. 15, it is expected that the temperature
Fig. 13 shows a typical readout result after inverse
                                                               accuracy can be in the same magnitude of order, but rely
Fourier transform. The highlighted 5-digit code
                                                               on accurate calibration or the availability of accurate
information is embedded between a start and a stop digit
                                                               SAW device parameters.
that serve as defined references for the utilized coding
scheme.
                                                               Fig. 15. Typical temperature readout during a heating and
                                                               cooling cycle with a resolution down to 0.3°C.
Fig. 13. Typical identification readout result with the code
‘03909’.
                                                                                   VII. CONCLUSION
To suppress the leakage of the dominant reflection from
the existing physical sensor mismatch the window               We have presented an overview of state-of-the-art
function has to be chosen properly e.g. with Kaiser-           interrogation concepts for SAW sensors and ID-tags in
Bessel windows.                                                frequency domain. Beside the commonly used delay time
                                                               evaluation based on the FFT magnitude spectrum a
B. Temperature measurement
                                                               method employing the phase information is described in
Employing the advanced signal processing based on the          detail. The comparison of these two methods for
phase evaluation algorithm described in section IV, the        statistical data as well as the analysis of real measured
very small relative reflector displacement caused by           data shows the superior performance of the phase
temperature variation can be evaluated with high               accounting algorithm. Results are shown on a prototype
accuracy. In Fig. 14 a comparison of the measured              board for wireless ID and temperature measurement.
temperature obtained from FFT magnitude evaluation
                      ACKNOWLEDGMENT
                                                                       [14] T. Musch , “A High Precision 24-GHz FMCW Radar
The authors would like to thank Prof. Leonhard Reindl of                    Based on a Fractional-N Ramp-PLL,” IEEE Trans. on
the Institute for Microsystem Technology at the                             Instrumentation and Measurements, IM-52, No. 2, pp.
University of Freiburg for many stimulating discussions                     324–327, April, 2003.
as well as Dr. Robert Hauser of the Carinthian Tech                    [15] AD9858, 1 GSPS Direct Digital Synthesizer, Analog
Research for the supply of SAW sensor prototypes.                           Devices Inc., Norwood, MA, 2002.
                                                                            available: www.analog.com
                                                                       [16] M. Vossiek, P. Heide, M. Nalezinski, V. Màgori, “Novel
                          REFERENCES                                        FMCW radar system concept with adaptive compensation
                                                                            of phase errors”, Proc. 26th European Microwave
[1]    A. Pohl, “A Review of Wireless SAW Sensors,” IEEE                    Conference EUMC, Sept. 9–12, 1996, Prague, Czech
       Trans. on Ultrasonics, Ferroelectrics, and Frequency                 Republic, pp. 135–139, 1996.
       Control, vol. 47, no.2, pp. 317-332, March 2000.                [17] E. C. Ifeachor, B. W. Jervis, Digital Signal Processing, A
[2]    J. D. Sternhagen et al., “A Novel Integrated Acoustic Gas            practical Approach, Harlow, Pearson Education Limited,
       and Temperature Sensor,” IEEE Sensors Journal, vol. 2,               Second Edition 2002.
       no.4, pp. 301-306, August 2002.                                 [18] B. D. Rao and K. S. Arun, "Model Based Processing of
[3]    C. S. Hartmann, “A Global SAW ID Tag with Large Data                 Signals: A State Space Approach", Proceedings of the
       Capacity” in Proc. 2002 IEEE Ultrasonics Symposium,                  IEEE, Vol. 80, No. 2, pp. 283-309, 1992.
       Munich, Germany, October 2002.                                  [19] P. Stoica and A. Nehorai, "MUSIC, Maximum Likeli-
[4]    SOFIS – Siemens Surface Acoustic Wave Identification                 hood, and Cramer-Rao Bound", IEEE Transactions on
       System, Automatic Vehicle Identification and Locating,               Acoustics, Speech and Signal Processing, vol. 37, no. 5,
       Siemens AG, Transprotation Systems, Rail Automation,                 pp. 720-741, 1989.
       Braunschweig,         Germany,        2003,        available:   [20] B. D. Rao and K. V. S. Hari, "Performance analysis of
       http://www.siemens.com                                               Root-Music", IEEE Transactions on Acoustics, Speech
[5]    A. Stelzer, G. Bruckner, L. Maurer, L. Reindl, R. Teich-             and Signal Processing, vol. 37, no. 12, pp. 1939-1949,
       mann, R. Hauser: “A Low-Cost Interrogation Unit and                  1989.
       Signal Processing for a SAW-Identification Tag for a            [21] D. W. Tufts and R. Kumaresan, "Estimation of Frequen-
       Pressure Sensor“, XVII International Measurement Con-                cies of Multiple Sinusoids: Making Linear Prediction
       federation World Congress, IMEKO 2003, Dubrovnik,                    Perform Like Maximum Likelihood", Proceedings of the
       Croatia, June 22–27, 4 pages on CD-ROM, 2003.                        IEEE, Vol. 70, No. 9, pp. 975-989, 1982.
[6]    L. Reindl, I. Shrena, H. Richter, R. Peter. “High Precision     [22] C. Yuan Hwang and C. Chao Hung, "An alternative
       Wireless Measurement of Temperature by Using Surface                 algorithm based on subspace rotation invariance techni-
       Acoustic Waves Sensors,” Proc. Sensor, Nuremberg,                    ques for directions-of-arrival estimation using the com-
       Germany, May 13–15, 2003. Vol. II, pp. 103–108, 2003.                pressed data pencil", Journal of the Acoustical Society of
[7]    G. Schimetta, F. Dollinger, R. Weigel, “A Wireless Pres-             America, Vol. 92, No. 4, Pt.1, pp. 1962-5, 1992.
       sure Measurement System Using a SAW Hybrid Sensor”,             [23] S. Y. Kung, K. S. Arun, and D. V. Bhaskar-Rao, “State-
       IEEE Trans. on Microwave Theory and Techniques, vol.                 space and singular-value decomposition-based approxi-
       MTT-48, No. 12, pp. 2730–2735, 2000.                                 mation methods for the harmonic retrieval problem,” J.
[8]    L. Reindl, C. W. Ruppel, A. Kirmayr, N. Stockhausen,                 Opt. Soc. Amer., vol. 73, pp. 1799–1811, Dec. 1983.
       M. A. Hilhorst, J. Balendonck, “Radio-Requestable Pas-          [24] S. M. Kay, Modern spectral estimation theory and
       sive SAW Water-Content Sensor,” IEEE Trans. Micro-                   application, Englewood Cliffs, N.J.: Prentice Hall, 1988.
       wave Theory and Techniques, MTT-49, No. 4, pp. 803–             [25] P. Gulden, M. Vossiek, E. Storck, and P. Heide, "Appli-
       808, 2001.                                                           cation of state space frequency estimation techniques to
[9]    M. I. Skolnik, Introduction to Radar Systems, 3rd ed.                radar systems", Proceedings of the 2001 IEEE Inter-
       Boston: McGraw-Hill, 2001.                                           national Conference on Acoustics, Speech, and Signal
[10]   S. O. Piper, “Homodyne FMCW Radar Range Resolution                   Processing, Salt Lake City, UT, USA, vol. 5, pp. 2870-
       Effects with Sinusoidal Nonlinearites in the frequency               2880, 2001.
       Sweep”, Proc. IEEE International Radar Conference               [26] A. Stelzer, M. Pichler, “Resolution Enhancement with
       1995, pp. 563–567, 1995.                                             Model-Based Frequency Estimation Algorithms in Radar
[11]   M. Pichler, A. Stelzer, P. Gulden, M. Vossiek, “Influence            Signal Processing“, Subsurface Sensing Technologies and
       of Systematic Frequency-Sweep Non-Linearity on Object                Applications, SSTA-Vol. 4, No. 3, July 2003, Kluwer
       Distance Estimation in FMCW/FSCW Radar Systems”,                     Academic / Plenum Publishers, pp. 241–261.
       Proc. 33rd European Microwave Conference EUMC, Oct              [27] P. Gulden, M. Vossiek, M. Pichler, A. Stelzer, “Appli-
       7–9, 2003, Munich, Germany, pp. 1203– 1206, 2003.                    cation of State-Space Frequency Estimation to a 24-GHz
[12]   A. Stelzer, K. Ettinger, J. Höftberger, J. Fenk, R. Weigel,          FMCW Tank Level Gauging System”, 33rd European
       “Fast and Accurate Ramp Generation with PLL-Stabilized               Microwave Conference EUMC-2003, Oct 7–9, 2003,
       24-GHz SiGe VCO for FMCW and FSCW Applications”,                     Munich, Germany, pp. 995–998.
       IEEE International Microwave Symposium 2003, June 8–            [28] S. M. Kay, Fundamentals of Statistical Signal Processing
       13, 2003, Philadelphia, USA, vol. 2, pp. 893–896, 2003.              Estimation Theory, Englewood Cliffs, Upper Saddle
[13]   A. Stelzer, J. Höftberger, K. Ettinger, R. Weigel, “Highly           River, N.J.: Prentice Hall, 1993
       Linear Ramp Generation in the 24-GHz band for
       LFMCW Microwave Sensor Systems” Asia Pacific
       Microwave Conference, Nov. 4–7, 2003, Seoul, Korea,
       vol. 3, pp. 1652–1655, 2003.