Relationship of Supervised and Unsupervised Criteria for Minimum BER Filtering

In this paper we present a relationship between supervised and unsupervised criteria for minimum bit error rate (BER) filtering. A criterion based on the probability density function (pdf) estimation is used to link the minimum mean square error (MMSE) criterion and the maximum a posteriori one in order to obtain a linear filter that minimize the BER. An important analytical relationship of the three criteria is presented and analyzed showing that is not possible to achieve minimum BER without training sequences when the pdf estimation-based criterion is considered.