### Identification of Linear Time Invariant Systems Using FMCW Signals and Stretch Processing Receivers

#### Abstract

The paper deals with the identification of linear time invariant (LTI) systems by a special observer. An observer emitting an frequency modulated continuous wave (FMCW) signal and having a stretch processor as receiver will be considered for system identification. A thorough derivation of the gathered baseband signal for arbitrary LTI systems will be given. It is shown, that the received signal is approximately given by the transfer function of the LTI system over the frequency sweep of the FMCW signal. The proof relies on an infinite large time-bandwidth product of the transmit signal, such that errors remain in practical applications with a finite time-bandwidth product. Monte–Carlo simulations are conducted to verify the approximation and to quantify its accuracy and remaining errors. The findings are important for e.g. calibration or derivation of a device model in FMCW radar applications.

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L. Ljung, System Identification: Theory for the User, ser. Prentice-Hall Information and System Sciences Series. Prentice-Hall, 1987.

T. Söderström and P. Stoica, Eds., System Identification. Prentice-Hall, Inc., 1989.

R. Pintelon and J. Schoukens, System Identification: A Frequency Domain Approach. IEEE Press, 2001.

R. Zetik, J. Sachs, and R. S. Thomä, “UWB Short-Range Radar Sensing - The Architecture of a Baseband, Pseudo-Noise UWB Radar Sensor,” IEEE Instrum. Meas. Mag., vol. 10, no. 2, pp. 39–45, April 2007.

S. Häfner, A. Dürr, R. Thomä, C. Waldschmidt, and G. D. Galdo, “High-Resolution Parameter Estimation for Chirp-Sequence Radar Considering Hardware Impairments,” in 11th German Microw. Conf. (GeMiC), March 2018, pp. 355–358.

R. S. Thomä, D. Hampicke, A. Richter, G. Sommerkorn, A. Schneider, U. Trautwein, and W. Wirnitzer, “Identification of Time-Variant Directional Mobile Radio Channels,” IEEE Trans. Instrum. Meas., vol. 49, no. 2, pp. 357–364, April 2000.

R. Müller, S. Häfner, D. Dupleich, R. S. Thomä, G. Steinböck, J. Luo, E. Schulz, Xiaofeng Lu, and Guangjian Wang, “Simultaneous Multi-Band Channel Sounding at mm-Wave Frequencies,” in 10th Eur. Conf. Antennas and Propag. (EuCAP), April 2016, pp. 1–5.

P. B. Papazian, C. Gentile, K. A. Remley, J. Senic, and N. Golmie, “A Radio Channel Sounder for Mobile Millimeter-Wave Communications: System Implementation and Measurement Assessment,” IEEE Trans. Microw. Theory Techn., vol. 64, no. 9, pp. 2924–2932, Sep. 2016.

R. Zetik, M. Kmec, J. Sachs, and R. S. Thomä, “Real-Time MIMO Channel Sounder for Emulation of Distributed Ultrawideband Systems,” Int. J. Antennas and Propag., vol. 2014, p. 16, 2014.

F. Bao, L. Arend, S. Bertl, and J. Detlefsen, “Application of FMCW Radar Principle for fast Inhomogeneity Identification on Transmission Lines,” in 6th German Microw. Conf. (GeMiC), March 2011, pp. 1–4.

T. Poguntke and K. Ochs, “Linear Time-Variant System Identification using FMCW Radar Systems,” in IEEE 59th Int. Midwest Symp. Circuits Syst. (MWSCAS), Oct 2016, pp. 1–4.

C. E. Cook and M. Bernfeld, Radar Signals: An Introduction to Theory and Application, ser. Artech House Radar Library. Artech House, 1993.

M. A. Richards, Fundamentals of Radar Signal Processing, 2nd ed. Madison: McGraw Hill Professional, 2013.

T. Hauschild and R. Knochel, “Calibration of Short Range FMCW-Radars with Network Analyzer Calibration Techniques,” in IEEE MTT-S Int. Microw. Symp. Digest, vol. 2, June 1998, pp. 969–972.

S. O. Piper, “Receiver Frequency Resolution for Range Resolution in Homodyne FMCW Radar,” in Proc. Nat. Telesyst. Conf., 6 1993, pp. 169–173.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables, ser. Applied mathematics series. Dover Publications, 1972, vol. 9.

J. L. López and P. J. Pagola, “A Simplification of the Stationary Phase Method: Application to the Anger and Weber Functions,” Electron. Trans. Numer. Anal. (ETNA), vol. 46, pp. 148–161, 2017.

DOI: http://dx.doi.org/10.11601/ijates.v8i2.276

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