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. This function is chosen so that the output is equal to the false alarm rate of the binary detector, and therefore maps the observation set to a false alarm space corresponding to the false alarm rate, P_FA. An analogous membership function is also developed mapping observations to a detection space which corresponds to the detection rate, P_D. These two spaces allow different detectors to be compared directly with respect to the two important detection performance indices, P_FA and P_D. Comparison of the false alarm space and detection space indicates that the fuzzy CFAR detector and Neyman-Pearson detector detect signals in a different manner and have different detection properties. Nevertheless, performance results illustrate that the fuzzy CFAR detector achieves detection performance comparable to the optimal Neyman-Pearson detector. © 2000 Elsevier Science B.V.