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As the demands on modern radar systems with respect to accuracy, reliability, and availability increase, a detailed assessment of the influence of nonlinear movements has become necessary. In particular, from the point of view of radar, different types of movements, such as any kind of acceleration, braking situation, or vehicle vibration, are essential parts of any traffic scenario. These unavoidable motions, in which the relative velocity changes within one measurement cycle, are called nonlinear movements. These nonlinearities contribute to intermediate frequencies, which are comparable to the extensively described nonlinearities of a frequency ramp. This additional contribution to the intermediate signal has a direct effect on the signal-to-noise ratio and thus on the accuracy and probability of target detection. This paper presents a study of various types of nonlinear motion and a detailed definition of the resulting parameters based on a variety of vehicle-based measurements. An advanced signal model of frequency-modulated continuous wave (FMCW) radar is introduced and verified in addition to a detailed mathematical description of spectral signal behaviour in sinusoidal motions and linear acceleration. The theoretical and experimental results in idealised point targets are transferred to real complex road users. Furthermore, by applying established automotive signal processing steps in the form of an ordered statistical constant false alarm rate (OS CFAR), the consequences of determining the noise level are also shown. In combination with the already introduced signal behaviour, these results enabled general description of the signal-to-noise ratio of nonlinear movements in complex traffic scenarios.

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