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The demand for autonomous cruise control and collision warning/avoidance systems has increased in recent years. Many systems based on frequency-modulated continuous-wave (FMCW) radar have emerged and are still in development. Due to the high complexity of such systems, the accurate evaluation of the noise spectra in the transmitter chain driven by complex modulated signals is today a severe drawback due to the limitation of simulation tools. In this paper, a method is proposed to compute easily with any commercially available nonlinear simulator, the amplitude and phase modulated signal distortion introduced by the nonlinearities of the transmitter on an FMCW signal. First, the amplitude modulation (AM) and phase modulation (PM) noise spectra of the driving FMCW signal is derived from the knowledge of the continuous wave (CW) AM and PM noise spectra of the voltage-controlled oscillator (VCO), and the modulating saw-tooth signal applied. Using the narrow band envelope concept and a first-order expansion of the nonlinear transfer function of the transmitter, the transfer of the AM and PM noise spectra of the driving FMCW signal through the nonlinear transmitter chain and the resulting output distortion are then computed. This novel approach allows to compute with reduced computation time and very good accuracy the AM/AM, AM/PM, PM/PM, and PM/AM conversion terms in any nonlinear system driven by CW or FMCW signals. This new method has been applied to the characterization of a whole car radar transmitter operating at 77 GHz driven by an FMCW signal issuing from a VCO. A successful comparison between measured and simulated PM-to-AM conversion coefficients of this transmitter is shown, validating the proposed method.