Cramer-Rao-Bounds for cross-spectrum measurements of oscillator phase noise

The cross-spectrum method is one of the best ways to measure the phase noise of an oscillator. Basically, the phase noise of a device-under-test oscillator is measured using two identical measurement circuits each with a reference oscillator which are synchronized by a phase-locked loop. In this paper, the exact Cramer-Rao-Bounds for the estimation of the oscillator phase noise power spectral density are given and efficient estimators are determined using the maximum-likelihood approach. Furthermore, our measurement system is presented where we discuss crucial points in the practical implementation. Finally, several measured results are shown where we also present a possibility to use an a-priori measurement of the system´s background noise to improve the measurement precision or to reduce the measurement time.