A Novel Non-Parametric Iterative Soft Bit Error Rate Estimation Technique for Digital Communications Systems

This paper addresses the problem of unsupervised soft BER estimation for digital communications systems, where no prior knowledge about transmitted information bits is available. We show that the problem of BER estimation is equivalent to estimating the conditional probability density functions (pdf)s of soft channel/receiver outputs. We also propose a non parametric Gaussian Kernel-based pdf estimation technique. Then, we introduce an iterative stochastic expectation maximization (EM) 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 procedure used for the estimation of conditional pdfs. We analyze the performance of the proposed BER estimator and show that is asymptotically unbiased and point-wise consistent. We also provide numerical results in the case of CDMA systems and show that attractive performance is achieved compared with conventional Monte Carlo (MC)-aided techniques.