Joint Maximum Likelihood and Expectation Maximization Methods for Unsupervised Iterative Soft Bit Error Rate Estimation

This paper addresses the problem of unsupervised soft bit error rate (BER) estimation for any communications system, where no prior knowledge either about transmitted information bits, or the transceiver scheme is available. We show that the problem of BER estimation is equivalent to estimating the conditional probability density functions (pdf)s of soft receiver outputs. Assuming that the receiver has no analytical model of soft observations, we propose a non parametric Kernel-based pdf estimation technique, with Maximum Likelihood based smoothing parameter computation. We then introduce an iterative Stochastic Expectation Maximization algorithm for the estimation of both a priori and a posteriori probabilities of transmitted information bits, and the classification of soft observations according to transmitted bit values. These inputs serve in the iterative Kernel-based estimation procedure of conditional pdfs. We analyze the performance of the proposed unsupervised BER estimator in the framework of a multiuser code division multiple access (CDMA) system with single user detection, and show that attractive performance are achieved compared with conventional Monte Carlo-aided techniques.