In this paper, we perform Bit Error Rate (BER) estimation in a low-voltage indoor power line communication channel. This is done over power line channels impaired with bursty impulsive noise in the broadband frequency range of 1-30 MHz. This method is based on the estimation of the Probability Density Function(PDF) of the soft observed samples. We first of all use the Gaussian Mixture Method (GMM) distribution model to motivate the Expectation-Maximization (EM) algorithm in a fairly informal way. GMM is a simple linear superposition of Gaussian components, aimed at providing a richer class of density models than the single Gaussian. The optimal number of Gaussians is computed by using Mutual Information theory. Simulation results are presented for the proposed BER estimator in the frame work of a multiuser Binary Phase Shift Keying (BPSK) system and shows that attractive performance is achieved. These results show that GMM technique provides a good fit to our data samples and thus provides better performance in the sense of minimum variance of the estimator. This drastically reduces the needed number of samples required to estimate the BER in order to reduce the required simulation run-time, even at low BER.