This paper considers the modeling of oscillator phase instability and the resulting spectral dispersion. A phase covariance matrix method is developed for determining the autocorrelation function and the power spectral density of the oscillator sinusoidal RF signal when corrupted by a superposition of a white phase random process and a random walk phase random process. By limiting the discussion to phase covariance matrices, it is shown that the direct use of a certain class of nonstationary phase random processes leads to stationary RF signal autocorrelation functions and associated power spectral densities. This is so despite the nonstationary phase driving force. The procedures provided here are also applied towards the determination of the average autocorrelation function and the average spectrum when the cisoidal oscillator signal undergoes modulation. Modulating waveforms used as examples include the CW, the infinite pulse train, and the finite pulse train.

Abstract : This dissertation considers the problem of characterization and stochastic properties of oscillator phase instabilities. Spectral dispersion caused by such instabilities is also determined. The instabilities are modeled using white phase, random walk phase, random walk frequency random processes as well as drift phase and frequency terms. Auto-correlation functions and power spectral densities are derived for the oscillator rf output signal containing such instabilities. Furthermore, a procedure is proposed which involves the covariance matrix of the phase random process in conjunction with the characteristic function for determining the higher order moments of the rf signal. Stationarity and ergodicity properties of the rf signals containing phase instabilities are discussed. In each case, conditions for ergodicity are established for the mean, auto-correlation function, and the power spectral density. The spectral dispersion generated by oscillator phase instabilities imposes limits on dynamic range and Doppler resolution in radar signal processing. This spectral dispersion is determined for the phase instability models considered in this dissertation. Modulating waveforms considered as examples include the cw, the infinite pulse train and the finite pulse train.