A Fourier analysis method has been employed deriving both the phase and group velocities of the atmospheric and ionospheric waves observed by various radar instruments. In this paper, a simulation is conducted to estimate errors of the two velocities resulted from the noises of natural background and radar system. The two noises with various amplification factors are placed into both synthetic data and observations of the MU (Middle- and Upper-atmosphere) radar for further investigations and validations. It is found that the errors of the phase and group velocities caused by the system noise are approximately constants, while those by the natural background noise are generally proportional to the amplification factors. The results confirm that the method can sustain the influences from natural background and system noises.