The method of synthesis of multistage coherent detection algorithm on the base of extremal statistic

Researches of the so-called k-stages procedures of detection have shown that they provide rather appreciable prize on the average time of detection in comparison with one-stages procedures (at equality of other characteristics of detection) in radio engineering systems with greater number of channels (> 1000). Offered methods of synthesis of such detectors are based on direct mathematical modelling which main advantages are simplicity and universality. However for systems with greater number of channels or small demanded probability of a false alarm (FAL) computing expenses grow on so much that complicate synthesis of this algorithm. For certain detector types it is possible to reduce essentially computing expenses by a combination of calculations of characteristics of an algorithm (one values are defined numerically, and others are modelled). In particular such approach is to be applied for detectors with independent solutions in channels. It is of interest to expand the list of detector types for which are possible a combination of calculation of characteristics, algorithms with dependent solutions in channels (extremal statistic) as it is known that they possess greater efficiency. In the present work, the method of synthesis multistage coherent algorithm of detection on the basis of extremal statistic is considered, its characteristics are obtained, and comparison with algorithm of independent solutions in channels is carried out. The radio engineering system needs to detect a coherent signal which structure generally can be any and known (except for amplitude and an initial phase), and channels can be formed on some information parameter (time delay, Doppler frequency, etc.). The decision on detection can be accepted on N stages on which all time of detection shares. As solving statistic value the maximum likelihood ratio logarithm in all channels is chosen. The method of parametrical synthesis of algorithms is reduced to search of a maximum of function which value is equal to detection probability (DP), in space of arguments (parameters of algorithm: stage durations and thresholds) at restrictions on FAL and average solution time (AST) at a zero hypothesis (H0). Values of thresholds are connected with characteristics of algorithm at H0 by procedure which does not demand greater computing expenses (at use of some approximations). DP is estimated by direct modelling of a signal in one channel and imitation (with the use of calculated conditional probabilities) of overcoming by the statistics of thresholds in other channels. The offered synthesis method of detection algorithm is approximate because of approximation of solving statistic distribution is applied and that is more important, statistical dependences of solving statistic not the next steps are ignored. Calculations have shown that the method provides accuracy of parameters DP and AST in units of percent. The worst accuracy is available for FAL parameter which at N = 3, 4, 5 turn out accordingly 20, 50, 100 %. However, this parameter can be easily corrected by the value of the last threshold. Speed of this method of synthesis is two orders greater, than that in a method on the basis of direct modelling. Calculations have shown, that the algorithm on extremal statistic appears more effectively on the average on 10 % of algorithm with independent solutions in channels.