Single-channel doppler frequency detector of coherent synchronously fluctuating signal packets under gaussian noise

The need to further simplify the systems for detecting useful signals against a background of complex noises calls for the development of simple algorithms subject to certain restrictions on the detector structure and the type of input signal.This article presents the developed optimal detection algorithm invariant to Doppler phase shifts of the signal for the class of single-channel Doppler frequency detectors of a Gaussian signal against the background of an additive mixture of uncorrelated and correlated Gaussian noises and under restrictions on synchronous fluctuations of pulses in a packet. The authors prove that the synthesized algorithm is optimal according to the criterion of the likelihood ratio averaged over the signal phase φс , as well as according to the criterion of the maximum of the “detection quality indicator” averaged over φс when solving the problem of detecting a Gaussian signal that fluctuates synchronously under Gaussian noise. The authors prove that the synthesised algorithm is optimal according to the criterion of the signal phase-averaged likelihood ratio,A comparative analysis of the efficiency of the developed algorithm with the efficiency of the optimal multi-channel algorithm for a completely defined signal and with the potential efficiency of the algorithm forming the Hotelling statistics for various spectral-correlation parameters of the additive mixture of correlated and uncorrelated noise, both in terms of probabilistic characteristics — the probability of correct detection at a given probability of false alarm depending on the signal / uncorrelated noise ratio at the input of the system, and in terms of the "improvement index", which is the fraction of the signal/noise ratio at the output of the nonlinear system to the signal/noise ratio at its input, averaged over all possible radial velocities of the target. The research established the parameters of the signal and the additive mixture of uncorrelated and correlated noise for which the potential efficiency of the developed algorithm turns out to be higher than the efficiency of the algorithm implementing the known Hotelling statistics.The obtained results allow us to determine the theoretical limit of improvement of real systems of this class and directions of search for new systems for practical application. In particular, they can be used to analyse the efficiency in designing coherent-pulse radar systems for detecting signals of moving targets against the background of an additive mixture of uncorrelated and correlated noises.