Phase instability induced spectral spread in radar systems

A method for determining the degradation in spectral resolution caused by the phase instability of the system coherent oscillator is presented. Phase instability is modeled as a superposition of a stationary white Gaussian process and a nonstationary random walk (Wiener) process. The model is used to obtain the autocorrelation function and the power spectral density of modulated signals, i.e., signals obtained by modulating the oscillator output signal by some deterministic waveform. For small variances, the variance of the white phase component establishes a lower limit for null depths of the power spectral density for the finite pulse train considered. The variance of the random walk phase component establishes the noise floor roll off rate for the power spectral density for small values of frequency. The number of pulses in the finite pulse train determines the peak main response and peak sidelobe response of the power spectral density.