Identifying linear time-variant (LTV) systems has been of great interest for many decades already and an important problem in many engineering applications. This paper proposes to use a double periodic system approximation for the characterization of LTV radar channels. Hereby, a two-dimensional Fourier series is used to approximate the time-variant transfer function in both time and frequency domain. By observing the system's response corresponding to an appropriate input signal, this paper presents a mathematical derivation of how to determine the Fourier coefficients. In practice, these Fourier coefficients are often approximated by assuming the LTV system to be piecewise constant in time domain. This paper establishes an analytical relationship between the original Fourier coefficients and the approximated ones and it investigates how the Fourier coefficients get distorted due to this assumption. Further, this paper provides practical measures to evaluate and control the degree of distortion in advance by adjusting the input signal modulation. This is illustrated by simulation results that are carried out for a double periodic system model with fictitious Fourier coefficients. Consequently, it is shown how the provided results are applied to chirp sequence modulated radar systems and how the radar signals can be interpreted from a system-theoretical perspective.
Automotive radar sensors have been used for measurements of time-varying scenarios for several years and the demands on their performance are increasing continuously. For the development of future signal processing algorithms, it is useful to investigate the problem of linear system identification as a generalized radar scenario. This paper provides a method for the approximation of a wireless transmission channel and derives how such a linear time-variant system can be identified using an FMCW radar. This universal approach enables the introduction of system functions, each characterizing the system's behavior in different time and frequency representation. These system functions of a wireless transmission channel are illustrated by radar measurements of a radially approaching cyclist, which deliver a profound interpretation of the wireless channel.
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.
As battery capacities become suitable for the mass market, there is an increasing demand on technologies to charge electric vehicles. Wireless charging is regarded as the most promising technique for automatic and convenient charging. Especially in publicly accessible parking spaces, foreign objects are able to enter the large air gap between the charging coils easily. Since the evoked magnetic field does not meet regulations, wireless charging systems are demanded to take further precautions related to the protection of endangered objects. Thus, additional sensors are required to protect primarily living objects by preventing them from being exposed to the magnetic field. In this paper, we propose a new approach for monitoring the air gap under the vehicle underbody using an automotive radar sensor on the vehicle side. The concept feasibility is evaluated with the help of a prototypical implementation. Further, two-dimensional signal processing techniques are applied to meet the requirements of inductive charging systems. Consequently, this paper provides measurement data for relevant use cases frequently discussed in the community of inductive charging.
Optimal Wiener filtering is a popular method for the estimation of stationary processes which can be completely derived system-theoretically. Although there exist several optimal filtering concepts for non-stationary processes, there is still a lack of fundamental time-variant system theory that describes the problem statement for non-stationary process estimation. This paper provides an intuitively understandable theory for the fundamental optimal filtering concept. By interpreting cross- and autocorrelations as a time-variant impulse response of a linear system, the problem statement can be illustrated with a network of linear systems. This paper introduces a double periodic system model that approximates a time-variant transfer function in both time and frequency domain which leads to an analytic solution for the optimal time-variant filter. The presented results are generally applicable and degenerate for simplified process properties (e.g. stationarity) to the well known results. We also present how the problem statement can easily be extended due to the fundamental and uniform theoretical approach.