A Nonparametric Sinusoid Detector with CFAR in White Noise

Abstract

A nonparametric detector called SFCD (segments frequency checking detector), the P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fa</sub> (false alarm probability) of which is constant and can be easily calculated, is put forward for the problem of detecting a sinusoid of unknown amplitude, frequency and phase in complex white Gaussian or non-Gaussian noise of unknown variance and probability distribution. The decision will be made on the basis of a statistical hypothesis test vector that is composed of a group of discrete frequency bins, which are scaled coarse frequency estimations of hypothetical sinusoid in all length-equal and non-overlapping segments of signal samples. A sinusoid is believed to exist in the received signal if all the absolute values of the difference between the first element and the others of the vector equal zero or one. The basic principle of the proposed algorithm in this paper introduced on condition of white Gaussian noise. The P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fa</sub> and P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> (detecting probability) are proved independent of the probability distribution of white noise by Monte Carlo simulation, although the performance of P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> is shown to deteriorate less than 4 dB compared with optimal parametric detector as far as samples length of 256 and P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fa</sub> of 1e-4 is concerned