A Class of Distribution-Free Detectors for Pulse Amplitude Modulated Signals

A class of distribution-free detectors for
M
-ary pulse amplitude modulated digital signals in the presence of certain signal dependent interference and additive noise of unknown distribution is formulated, evaluated in terms of probability of error and compared to a matched filter detector in Gaussian noise. The noise distribution is unknown except that it satisfies certain broad assumptions and that its value at the median is known. A decision method based on the value of a test statistic is developed. An analytical expression for the average probability of error and a method of calculating the optimum decision thresholds that minimize this probability of error are presented. The probability of error is independent of the form of the noise distribution but depends on the value of the noise density function at the median. An example of a ternary signal set in white Gaussian noise is worked out for illustration. The optimum decision thresholds are calculated and the resulting average probability of error is plotted as a function of signal-to-noise ratio. Average probability of error of a matched filter detector is also evaluated under similar conditions and a comparison is made with that of the proposed detector.