Detection performance characteristics of the digital undersampling receiver

Abstract

Multichannel digital receivers based on the signal processing technology involving undersampling are used for the instantaneous wideband analysis of the electronic environment. One of the most common algorithms for measuring input signal’s carrier frequency in such receivers includes unfolding of the signal’s spectrums from the first Nyquist zone of all receiver’s channels to the single frequency axis and searching for the frequency where the spectrum components from all of the receiver’s channels coincided. Performance of the signal detector, which uses this algorithm in its operation, was not studied. In the absence of a mathematical description of such a detector, evaluating the digital undersampling receiver’s sensitivity becomes possible only in the late stages of prototyping when it can be done through experimental study. Additionally, it is impossible to set a detection threshold in the receiver according to the Neyman-Pearson criterion, which hardens building constant false alarm rate (CFAR) systems based on this type's receivers. This paper aims to develop the mathematical description of the digital undersampling receiver's detector and then, using this model, to get expressions and computer models to evaluate the characteristics of such receiver even in early stages of its development. This paper's main result is the developed mathematical tools necessary to evaluate the multichannel digital undersampling receiver’s signal detector performance. It is shown that the false alarm probability in such a detector does not exceed some value no matter how small the detection threshold is. The expression for evaluating the maximum false alarm probability by the receiver’s parameters is also presented in the paper alongside the true positive rate plots as a function of signal-to-noise ratio for the three-channel receiver. These results can be used in evaluating the digital undersampling receiver’s characteristics in the early stages of its development. It allows one to choose optimal values of the receiver’s parameters which are hard and expensive to change after prototyping is done, and there is an opportunity to evaluate the receiver’s characteristics experimentally. Moreover, the obtained mathematical expressions make it possible to set the receiver's detection threshold according to the Neyman-Pearson criterion and build on its base a CFAR-systems widely used for wideband signal analysis.