Modeling of range accuracy for a radar system driven by a noisy phase-locked loop

We derive analytical expressions for the standard deviations of distance error and angular error in a radar system due to PLL phase noise. The standard deviation of the distance error σ R is expressed as a function of the target distance R and the PLL phase noise spectrum. If the IF radar signal and noise bandwidth are within the in-band phase noise plateau, the proportionality σ R ∝ R 3/2 is valid. By contrast, if signal and noise bandwidth are in the VCO dominated -6dB/octave region of the PLL spectrum, we obtain σ R ∝ R. The results are compared with measurements on a 61 GHz and a 122 GHz FMCW radar system.