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Application of the Monte-Carlo method for synthesis of sequential coherent algorithm of signals detection


A. G. Aganin, M. Yu. Mozgonov

Development of sequential coherent multi-channel adaptive algorithms of the detection for perspective multipurpose aviation impulse Doppler radar stations with the active phased antenna lattices is actual, allowing to find out a weak signal against clutter from a steady background for minimum time of viewing of space. Application of algorithm with sequential decision-making will give an essential time reduction for signals detection in those directions of space where the targets are not present. Large time of coherent accumulation will raise detection range and Doppler frequency resolution. Synthesis of sequential coherent multi-channel adaptive algorithms of the detection was not considered in the existing literature, concerning the account of the changing sizes of elements of the Doppler frequency resolution, statistical influence between channels, and also weight processing. Offered algorithm is close to suboptimal algorithm of signals detection for impulse Doppler radar stations in which the combined solving statistics and constant thresholds are used. Its lack is that arrangement of thresholds are carried out on Wald that for the truncated multi-channel procedures is not optimum. Variable arrangement of filters on Doppler frequency is not useful for processing of signals and leads to additional losses of energy of a signal. Besides, constant intervals of time at sequential detection are not obligatory. It is not possible to execute analytical calculation of characteristics of offered algorithm and to find optimum of thresholds and observation time intervals on each step, therefore taking into account high speed of modern computers it is expedient to use a method of Monte-Carlo which is the most universal. The work purpose was application of a method of Monte-Carlo to optimize of parameters of sequential coherent multi-channel adaptive algorithm of signals detection. In work, as an example, the algorithm with unique thresholds on each step on the extreme statistics is synthesized. Constant arrangement of filters on Doppler frequency, corresponding to the maximum time of coherent accumulation for convenience and the concerted processing of a signal on all time of accumulation was used. Because it is analytically impossible to find multidimensional function of distribution density of probabilities of solving statistic in practically interesting cases. By means of modeling N-dimensional histograms of their joint distribution (N – a maximum quantity of steps of decision-making) have been received. As criterion of optimality the maximum of probability of correct detection (PCD) has been chosen at the set characteristics: prob-abilities of a false alarm (PFA) and average quantity of time intervals of acceptance of the terminal decision at the validity of zero hypothesis H0 (the target is not present). Varied parameters: thresholds and the size of time intervals on all steps of observation. The method of casual local search was used for optimization. The choice of a method of optimization is connected with features of calculation PCD as functions of parameters. Characteristics and parameters for 4 steps algorithms without adaptation and with adaptation to noise level are received. The given method allows to synthesis sequential algorithms for comprehensible time at quantity of steps of detection no more than 5 and quantity of channels of an order 10000 with accuracy ±0,005 on value PCD and ±15 % on PFA. As a result of research it is established, that the found optimum values of time intervals of observation remained invariable for all considered sets of parameters of algorithm; the relation a signal/noise (RSN) on power for full time of observation should be in 1,1 … 1,3 times more than RSN single-step algorithm of Neumann-Pirson.
June 24, 2020
May 29, 2020

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