Adaptive Threshold Detection of M-ary Signals in Statistically Undefined Noise

Abstract

Much of the effort in the field of signal detection during the past few years has been directed toward the determination of the presence or absence of a given signal, or toward the discrimination between known signals in the presence of additive noise of known statistical form. Due to the long-term nonstationary properties exhibited by many channels it is desirable to design detectors which are independent of the noise distribution in the channel, i.e., nonparametric detectors, or which are capable of adjusting themselves to changing noise situations, adaptive detectors. This paper will present and analyze a particular adaptive detector based on the philosophy of statistical ranking for threshold determination. The detector is designed to discriminate between the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> levels of an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> -ary code. The decision levels are based only upon a knowledge of the a priori probability of occurrence of the various levels. The noise is assumed to be continuous with zero mean and independent of the signal, but no other assumption is made. Threshold determination is based on blocks of signals, received levels, of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> . The system is analyzed for several noise conditions using error probabilities and Delay Asymptotic Relative Efficiency (DARE) relative to the Gaussian optimum detector as criteria. The detector is shown to operate well on a jamming model using Cauchy noise. Finally, block sizes necessary for adequate ranking procedures for threshold settings are determined.