A System-Theoretic View on Breathing Detection using Chirp Sequence Modulated Radar Sensors Tim Poguntke∗ , Davi Duarte de Carvalho Filho∗ and Karlheinz Ochs† ∗ Corporate
Abstract—When charging electric vehicles inductively, living objects must be prevented from being exposed to the magnetic field. Therefore, additional sensors are used to detect endangered objects under the vehicle. This ensures that the charging process can be stopped immediately if endangered objects stay inside the hazardous zone. To prevent the system from unintended charging switch-offs, it is preferable to detect also life-signs for a reliable differentiation between living and non-living objects. In this paper, we propose a method for Doppler-based detection of respiration movements using a chirp sequence modulated radar sensor. We also provide system-theoretical background concerning the identification of linear time-variant systems. This delivers a clear problem statement and facilitates the understanding of the proposed method. Consequently, the theoretical results are applied to measurements for the detection of respiration movements. The results enhance an existing approach for living object protection using a radar sensor on the vehicle side.
I. I NTRODUCTION There is an increasing demand on a suitable sensor technology for the protection of endangered objects when charging electric vehicles (EVs) inductively. Especially in publicly accessible parking areas, it is conceivable that living objects enter the hazardous zone between the charging coils. The guidelines for limiting exposure by the International Commission on Non-Ionizing Radiation Protection (ICNIRP, see [1]) are not met in the hazardous zone between the charging coils. That is why living objects must be prevented from being exposed to the magnetic field. Therefore, additional sensors are used to detect foreign objects such that the charging system can be switched off immediately. In [2], there has been proposed a new approach for monitoring the hazardous zone using an automotive radar sensor on the vehicle side. It can be observed in Fig. 1 that the entire hazardous zone can be monitored using only one sensor on the vehicle side in principle. It is also proposed a method to differentiate between moving and non-moving objects (e.g. wheels or the underbody itself). Nevertheless, there is still the widely discussed use case of sleeping pets under the vehicle. This represents a borderline case between moving and nonmoving objects, since respiration consists only of slight chest movements. That is why this paper is concerned with the detection of respiration movements using an automotive radar sensor.
WIRELESS CHARGING
Sector Research and Advance Engineering, Robert Bosch GmbH, Renningen, Germany Email:
[email protected] † Institute of Digital Communication Systems, Ruhr-Universit¨at Bochum, Bochum, Germany Email:
[email protected]
Fig. 1: Inductive charging pad below an EV that is equipped with a sensor at its underbody to monitor the hazardous zone The radar-based detection of vital signs has been intensively investigated in prior work and there have been published a lot of approaches regarding this topic. For most of them, either Doppler or ultra-wideband (UWB) radars are used to detect vital signs, cf. [3], [4]. Though, existing approaches using automotive radar sensors with carrier frequencies of about 77 GHz are not known to the authors. Assuming respiration relevant radar scatterers on the body surface and considering that the Doppler effect is even intensified for higher carrier frequencies, this approach also seems to be promising. It has been already shown in [5] that a system-theoretical view on radar scenarios is advantageous due to its clear interpretation and its universality. That is why this paper also provides system-theoretical background about the characterization of linear time-variant channels. To analyze a periodically repeated scenario such as respiration movement, a method for short-time linear system identification is proposed in section II. After presenting the automotive radar sensor in section III, measurement results of human respiration movements are presented to verify the provided theoretical results. II. I DENTIFICATION OF L INEAR TIME - VARIANT SYSTEMS This section presents the system-theoretical basis that illustrates the signal processing for detecting respiration movements. It delivers a clear problem statement for the identification of linear time-variant systems. First of all, it is known
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where X(jω) represents the Fourier transform of the input signal x(t). If the system becomes time-variant, i.e. the transfer function shows also a time dependency, this equation is no longer valid. The definition of the time-variant transfer function goes back to Zadeh [6] who defined it in analogy to the time-invariant transfer function H(jω). Similar to the time-invariant case in Eq. (1), the output signal of a timevariant system can be computed with Z ∞ 1 ˆ jω 0 )X(jω 0 )e jω0 t dω 0 . y(t) = H(t, (2) 2π −∞ Note that the frequency variable ω 0 is marked by prime since it does not form a Fourier transform pair with t. The timevariant transfer function plays a key role in network analysis, since it characterizes the channels’ entire behavior in time and frequency domain. A. Double periodic approximation for system identification The system-theoretical contribution of this paper is mainly based on double periodic system functions, see [7]. According to [8], it can be exploited that real-life channels are restricted on duration and bandwidth. Thus, a Fourier series can be used to approximate the time-variant transfer function for a certain bandwidth Ω 0 = 2πB 0 and duration T . This results in m n X X 0 0 ˆ mn (t, jω 0 ) = H hµ,ν e −jω νT e jµΩt , (3) µ=−m ν=−n
where ΩT = Ω T = 2π. Inside of the approximation area depicted in Fig. 2a, this Fourier series approximates the timeˆ jω 0 ). Outside of this rectangle, variant transfer function H(t, it is periodically repeated. That is why the system is called to be double periodic. The corresponding Fourier coefficients hµ,ν are determined with an integral in time and frequency domain each. These 0
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will be provided separately, since the interim results will be taken up in the following calculations. Evaluating the integral in frequency domain first, it results the time-varying Fourier coefficients 0 Z ωref+ ˆ ν (t) = 1 ˆ jω 0 ) e jω0 νT 0 dω 0 . h H(t, (4) 0 0 Ω ωref− If the integral in time domain is evaluated afterwards, this leads to the two-dimensional Fourier coefficients Z 1 Tˆ hν (t)e −jµΩt dt. (5) hµ,ν = T 0 Besides the approximation area, which is determined with bandwidth Ω 0 and duration T , these Fourier coefficients contain all information for the characterization of radio channels inside of the approximation rectangle. To derive the input-output relation, the double periodic timevariant transfer function from Eq. (3) is inserted in Eq. (2). It can be observed that the resulting output signal y(t) =
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is represented by a sum of delayed and then Doppler-shifted versions of the input signal x(t), having a scattering amplitude hµ,ν . Thus, the Fourier coefficients can be recognized as a sampled version of the original Delay-Doppler-Spread Function introduced by Bello [8]. For radar radio channels, the targets’ distance can be computed from the delay (i.e. timeof-flight) and its velocity can be computed from the Doppler frequency. In [5], it has been already shown how these Fourier coefficients can be determined using an FMCW radar system with a chirp sequence modulated transmit signal. B. Short-time linear system identification The previous section presents how linear time-variant systems can be approximated using a two-dimensional Fourier series. The system-theoretical view for the detection of vital signs is particularly interesting, since the movements are periodic. Thus, the sensor needs to detect Doppler frequencies
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where Tm denotes the entire measurement time and the window is nonzero only for the duration of one approximation interval T . This integral shows great similarities to the shorttime Fourier transform. Thus, this principle for continuous determination of the Fourier coefficients can be regarded as a short-time linear system identification. The measurement principle with a sliding approximation rectangle is illustrated in Fig. 2b, when determining the Fourier coefficients at certain measurement times τκ = κTx . For each approximation rectangle, the Fourier coefficients are recomputed delivering delays and Doppler frequencies corresponding to the time of measurement τκ . If the update interval Tx is chosen smaller than the approximation interval (Tx < T ), the Fourier coefficients contain redundant information. In return, the update rate of the Fourier coefficients can be increased when the approximation rectangles overlap. In Fig. 2b, this can be obtained for overlapping approximation rectangles. Consequently, the system-theoretical approach delivers a clear problem statement revealing that the solution is equivalent to the computation of a short-time Fourier transform, cf. 2 [4]. Accordingly, the squared amplitude |hµ,ν (τ )| can also be regarded as the spectrogram of linear double periodic systems. III. P ROTOTYPICAL AUTOMOTIVE RADAR SENSOR The RF front-end of the automotive radar is depicted in Fig. 3a. This prototypical sensor uses the MMICs (Monolithic Microwave Integrated Circuits) that are also used for the 4th generation Bosch MRR (Mid Range Radar). Their technology
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Fig. 3: Respiration movement detection using the automotive radar RF front-end in (a) for the measurement setup in (b)
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caused by chest movements that are periodically changing with time. It can be observed in Eq. (5) that this time dependency vanishes when the Fourier coefficients with respect to µ (i.e. the Doppler frequency µΩ) are computed. Thus, this type of approximation is not sufficient for detecting periodically repeated Doppler frequencies. Fortunately, this time dependency can be reestablished by introducing a window w(t) such that Z 1 Tm ˆ hν (t) w(t − τ )e −jµΩt dt, (7) hµ,ν (τ ) = T 0
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Fig. 4: Fourier coefficients determined during the respiration phase with chest movement towards the sensor (inhaling) and in the opposite direction (exhaling) in (a) and (b), respectively is described in [9]. The radar sensor is equipped with four receive and two transmit antennas, allowing measurements of distance, velocity, and an estimation of the Angle-of-Arrival. IV. D ETECTION OF RESPIRATION MOVEMENTS The previous sections provided system-theoretical principles of short-time linear system identification that are used for the determination of Fourier coefficients as a function of time. The Doppler-based detection of respiration movement proposed in this paper utilizes these principles. Due to practical reasons, the measurements provided in this section are not carried out with real pets. Instead, human respiration movements have been used to verify the theoretical results, which does not affect the detection principle. According to Fig. 3b, the radar sensor is placed approximately 30 cm away from a test person who sits on a chair and remains stationary. The stationarity ensures that the respiration movements do not overlap with other body movements. As a high Doppler frequency resolution contradicts to small values of T and the Doppler frequency varies periodically with time, T has to be appropriately chosen. It turns out that T = 880 ms represents a good compromise for the detection of respiration movements. The chirp sequence modulated radar
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Fig. 5: Spectrogram of the radar channel evaluated at a distance of 30 cm showing the movements of respiration and heart beat sensor uses K = 16 chirps per sequence resulting in a ramp repetition interval of Trri = T /K = 55 ms. Further, the Fourier coefficients are recomputed after each single measurement such that Tx = Trri . The modulation parameters are completed with a bandwidth of B 0 = 4.375 GHz and L = 152 samples per chirp with a center frequency of fc = 75 GHz. The sampled beat signals of each chirp sequence are saved in a measurement matrix of size K × L. According to [5], the Fourier coefficients can be computed by applying a twodimensional DFT. Two sets of Fourier coefficients determined at different times of measurement are depicted in Fig. 4. Both figures show a strong reflection at a range of approximately 30 cm corresponding to the distance between sensor and test person. Looking carefully at the main focus of the reflection peak, differences in velocity can be observed. The Fourier coefficients in Fig. 4a correspond to a measurement during the inhalation phase (i.e. positive velocity). In contrast, the Fourier coefficients depicted in Fig. 4b correspond to a measurement during the exhalation phase, since the chest movement goes into the opposite direction. Utilizing the principle of short-time identification, the spectrogram of linear double periodic systems can be evaluated. As the distance between radar and test person is known, it is evaluated for ν = 85. This corresponds to a distance of 30 cm (i.e. a delay νT 0 ≈ 19.4 ns). Thus, the Fourier coefficients with respect to µ can be applied to the measurement time. It can be observed in Fig. 5 that the periodic respiration movement can be directly obtained from the spectrogram without further signal processing. Between measurement times of 25 s and 35 s, there can be obtained four breathing periods corresponding to a respiration rate of approximately 0.4 Hz. Furthermore, the test person holds the breath between measurement times of approximately 10 s and 20 s. During this phase, even the heart beat of the test person can be observed. The detected 13 periods correspond to a heart beat rate of 78 beats per minute. Though the heart beat detection may be not expedient in context of inductive charging, the differentiation between living and non-living objects is feasible using the Dopplerbased detection of respiration movements. Consequently, the spectrogram of linear systems can be used to characterize radio channels instantaneously. The dimension
of approximation rectangles and the Fourier coefficient update rate are dependent on specific purposes and have to be chosen suitably. In this section, the operating principle is demonstrated for the detection of human vital signs. V. C ONCLUSION In this paper, we present system-theoretical background that is used to characterize linear time-variant channels. In particular, it is proposed a method for short-time characterization of linear systems. This allows an introduction of a system-specific spectrogram that both delivers a clear problem statement and enhances the approximation using regular double periodic system functions. The theoretical results are applied to a Dopplerbased detection of respiration movements using an automotive radar sensor. The provided measurements prove that a sensitive differentiation of non-moving objects and sleeping pets under the vehicle is feasible in context of inductive charging systems. R EFERENCES [1] International Commission on Non-Ionizing Radiation Protection, “Guidelines for limiting exposure to time-varying electric, magnetic and electromagnetic fields (up to 300 GHz),” Health Physics, vol. 74, no. 4, pp. 494–522, 1998. [2] T. Poguntke, P. Schumann, and K. Ochs, “Radar-based living object protection for inductive charging of electric vehicles using two-dimensional signal processing,” Wireless Power Transfer, 2017, to be published. [3] C. Li, V. M. Lubecke, O. Boric-Lubecke, and J. Lin, “A review on recent advances in doppler radar sensors for noncontact healthcare monitoring,” IEEE Transactions on Microwave Theory and Techniques, vol. 61, no. 5, pp. 2046–2060, 2013. [4] J. A. Nanzer, “A review of microwave wireless techniques for human presence detection and classification,” IEEE Transactions on Microwave Theory and Techniques, vol. 65, no. 5, pp. 1780–1794, 2017. [5] T. Poguntke and K. Ochs, “Linear time-variant system identification using fmcw radar systems,” in Midwest Symposium on Circuits and Systems (MWSCAS), Oct. 2016, pp. 324–329. [6] L. A. Zadeh, “Frequency analysis of variable networks,” Proceedings of the IRE, vol. 38, no. 3, pp. 291–299, Mar. 1950. ¨ [7] K. Ochs, Theorie zeitvarianter linearer Ubertragungssysteme, ser. Kommunikationstechnik. Shaker Verlag GmbH, 2012. [8] P. Bello, “Characterization of randomly time-variant linear channels,” IEEE Transactions on Communications Systems, vol. 11, no. 4, pp. 360– 393, Dec. 1963. [9] J. Hasch, E. Topak, R. Schnabel, T. Zwick, R. Weigel, and C. Waldschmidt, “Millimeter-wave technology for automotive radar sensors in the 77 ghz frequency band,” IEEE Transactions on Microwave Theory and Techniques, vol. 60, no. 3, pp. 845–860, Mar. 2012.
