The use of fuzzy spaces in signal detection

The fuzzy constant false alarm rate (CFAR) detector, which is based on the M-out-of-N binary detector, is characterized and compared with the optimal Neyman-Pearson detector. It replaces the crisp M-out-of-N binary threshold with a soft, continuous threshold, implemented as a membership function. Th is function is chosen so that the output is equal to the false alarm rate o f the binary detector, and therefore maps the observation set to a false al arm space corresponding to the false alarm rate, P-FA. An analogous members hip function is also developed mapping observations to a detection space wh ich corresponds to the detection rate, P-D. These two spaces allow differen t detectors to be compared directly with respect to the two important detec tion performance indices, P-FA and P-D. Comparison of the false alarm space and detection space indicates that the fuzzy CFAR detector and Neyman-Pear son detector detect signals in a different manner and have different detect ion properties. Nevertheless, performance results illustrate that the fuzzy CFAR detector achieves detection performance comparable to the optimal Ney man-Pearson detector. (C) 2000 Elsevier Science B.V. All rights reserved.