A solution for the problem of estimating the PN (Phase Noise) from the observation of the channel output in burst communications is to establish a state-model for the PN and determine the a posteriori probability density function (pdf) of the state conditioned on all measurement data, thus providing the means to compute an optimal estimate with respect to any criterion, e.g., Minimum Mean-Squared Error (MMSE). However, except in the Gaussian case, it is extremely difficult to determine and propagate this density function. As a result,and since the observation model of the PN is non-linear, the a posteriori pdf becomes non-Gaussian, and a sub-optimal solution for the problem must be found. In this paper we approximate the non-Gaussian pdf by a weighted sum of Gaussians. Additionally, we compare the performance results obtained when modeling the density function by a weighted sum of Gaussians with those obtained with a single Gaussian using a SC-FDE (Single Carrier-Frequency Domain Equalizer) scheme.