Minimum error rate detection: An adaptive bayesian approach

Abstract

This paper addresses the thresholding problem which is an important issue in detection theory. A new thresholding methodology is proposed, namely the Minimum Error Rate (MER), related to the minimization of the error probability instead of minimizing only the miss probability for a Constant False Alarm Rate (CFAR). In an adaptive detection scheme, the proposed thresholding technique is combined with Cell Averaging (CA) and Order-Statistics OS estimation methods giving birth to the (CA-MER) and (OS-MER) detectors. Their performance statistics are analyzed for both homogeneous and heterogeneous environments. Moreover, a simplified approximate threshold expression is proposed and its effect on the whole detection process is studied. Theoretical and numerical results show that the MER-based detectors operate better than the classical CFAR-based ones. In particular, the proposed method is shown to be robust w.r.t. estimation errors on the different parameters (priors). Comparative study of MER versus CFAR-based detectors used for the delay detection in multipath context show that OS-MER detector outperforms the OS-CFAR which induces more accurate mobile positioning.