Modeling the filtered and sampled continuous-time signal affected by Wiener phase noise

This paper investigates the differences between the symbol-spaced Wiener channel model (SSWCM), used in discrete-time simulations to model the effect of phase noise, and that obtained by symbol-rate sampling the continuous-time received signal affected by continuous-time Wiener phase-noise. In particular, for comparison, we consider some statistical tests to check temporal and distributional properties of the two signals. We show that the mismatch measured is very weak compared to the signal power even with strong phase noise. The main result is that when the standard deviation of the discrete-time Wiener phase noise is below a threshold of approximately 0.1 rad, the SSWCM provides a good approximation, say with a power of the error between the approximated model and the actual signal that is more than 20 dB below the signal level, of the actual symbol-spaced sampled signal. This result suggests that the SSWCM can be adopted for many real-world systems, where, according to experimental results available in the literature, a standard deviation in the order of 0.1 rad is found also when the nonlinearity of the optical channel is deeply stressed.