A Fast Soft Bit Error Rate Estimation Method

We have suggested in a previous publication a method to estimate the Bit Error Rate (BER) of a digital communications system instead of using the famous Monte Carlo (MC) simulation. This method was based on the estimation of the probability density function (pdf) of soft observed samples. The kernel method was used for the pdf estimation. In this paper, we suggest to use a Gaussian Mixture (GM) model. The Expectation Maximisation algorithm is used to estimate the parameters of this mixture. The optimal number of Gaussians is computed by using Mutual Information Theory. The analytical expression of the BER is therefore simply given by using the different estimated parameters of the Gaussian Mixture. Simulation results are presented to compare the three mentioned methods: Monte Carlo, Kernel and Gaussian Mixture. We analyze the performance of the proposed BER estimator in the framework of a multiuser code division multiple access system and show that attractive performance is achieved compared with conventional MC or Kernel aided techniques. The results show that the GM method can drastically reduce the needed number of samples to estimate the BER in order to reduce the required simulation run-time, even at very low BER.