On polarity detection schemes with non-gaussian inputs

Abstract

The design of signal detectors which are optimum (in the Neyman-Pearson sense) requires a complete statistical description of the input processes. Certain non-optimum detectors, the “nonparametric detectors,” have the interesting property that their false alarm rates can be fixed for wide classes of inputs. These detectors are often easy to implement and are useful when the input statistics are not completely known. This paper treats two practical nonparametric detectors, the one-input sign detector and the two-input polarity coincidence correlator, both of which utilize only the polarity information about the input. The performance of these nonparametric detectors is evaluated for a wide class of non-gaussian input noises. Their performance is compared to that of their Neyman-Pearson counterparts designed on the assumption of gaussian stationary noises. The comparisons are based on asymptotic relative efficiency (a.r.e.). While the a.r.e. gives a close approximation to the actual relative efficiency for stationary gaussian inputs, significant differences result when considering non-gaussian inputs, particularly of the impulse type. For stationary gaussian inputs the sign detector is 64 per cent as efficient as its Neyman-Pearson counterpart, the mean detector. Under the same conditions the polarity coincidence correlator (PCC) is ,20 per cent as efficient as its Neyman-Pearson counterpart. It is demonstrated in this paper that these known results are relatively insensitive to small changes in the noise statistics. However, as the amplitude density of the noise processes become more sharply peaked and/or more asymmetrical, then the nonparametric detectors become more efficient than the Neyman-Pearson detectors designed for gaussian inputs. These types of noise processes resemble what is commonly called impulse noise.