Phase noise in communication systems: from measures to models

We consider the phase noise affecting communication systems, where local oscillators are employed to obtain a reference signal for frequency and timing synchronizations. We try to fill the gap between measurements and analytical models, in case of free-running and phase-locked oscillators. In particular, we propose a closed form expression for the power spectral density of the phase noise described by few parameters that are explicitly linked to the oscillator measurements. We also propose an analytical model for the oscillator power spectral density. We then consider the discrete-time domain, and analyse the most common discrete-time phase noise channel model with reference to the measurements parameters and to the system bandwidth. In this context, we show that the proposed models for power spectral densities lead to analytical models for the discrete-time phase noise signal, that can be used for the design of estimation/detection algorithms, for performance evaluation, or simply for fast simulations.