This thesis is related to the Bit Error Rate (BER) estimation for any digital communication system. In many designs of communication systems, the BER is a Key Performance Indicator (KPI). The popular Monte-Carlo (MC) simulation technique is well suited to any system but at the expense of long time simulations when dealing with very low error rates. In this thesis, we propose to estimate the BER by using the Probability Density Function (PDF) estimation of the soft observations of the received bits. First, we have studied a non-parametric PDF estimation technique named the Kernel method. Simulation results in the context of several digital communication systems are proposed. Compared with the conventional MC method, the proposed Kernel-based estimator provides good precision even for high SNR with very limited number of data samples. Second, the Gaussian Mixture Model (GMM), which is a semi-parametric PDF estimation technique, is used to estimate the BER. Compared with the Kernel-based estimator, the GMM method provides better performance in the sense of minimum variance of the estimator. Finally, we have investigated the blind estimation of the BER, which is the estimation when the sent data are unknown. We denote this case as unsupervised BER estimation. The Stochastic Expectation-Maximization (SEM) algorithm combined with the Kernel or GMM PDF estimation methods has been used to solve this issue. By analyzing the simulation results, we show that the obtained BER estimate can be very close to the real values. This is quite promising since it could enable real-time BER estimation on the receiver side without decreasing the user bit rate with pilot symbols for example.
