  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.
