V.M. Artyushenko1, V.I. Volovach2

1 Technological University named after twice Hero of the Soviet Union Cosmonaut A.A. Leonov (Moscow, Russia)

2 Volga Region State University of Service (Tolyatti, Russia); Voronezh State University (Voronezh, Russia)

1 artuschenko@mail.ru; 2 volovach.vi@mail.ru

Bayesian algorithms for classifying signals with random parameters are based on statistics of the likelihood ratio averaged over the probability distribution of the values of random signal parameters. However, it is not always possible to determine the values of these statistics. Approximate calculation methods are used to solve the problem, the most common of which is the method of the special principle of asymptotic optimality and the hypothesis of high-precision measurements. These methods are also not without limitations. The article suggests combining these approaches, which makes it possible to overcome these limitations.

Under the given conditions, it is necessary to find an approximation for the average likelihood ratio that allows a simple implementation. An expression is defined for conditional estimates of the maximum likelihood of the vector of random parameters of the active signal, as well as an expression for asymptotically sufficient statistics characteristic of radio technical problems. A block diagram of a computer implementing the named statistics is proposed. Simplified expressions for asymptotically sufficient statistics are obtained, which are typical, for example, for radar applications. The corresponding block diagrams of the calculators are also proposed. It is noted that the type of transformation of the input data is determined both by the distribution of interference and the way they interact with the signal. The developed algorithms can be successfully used in classification devices operating in non-stationary conditions. At the same time, the structure of the classifier remains unchanged, only the parameters of its individual nodes change.

The quality of the obtained optimal algorithms is evaluated, which is characterized by a limiting value of the total probability of classifier error. It is shown that the value of the probability of error in the classification of algorithms depends on the type of probability density distributions of the values of the vector of random parameters only for those cases when the type of these distributions is specified. It is noted that the probability distribution of Yl(Xn) values under the action of any of the possible signals is described by the b-dimensional normal law. In this case, the values of Ll(Xn) obey a non-central c2-distribution. The limiting expression for the conditional probability of classification error is determined, provided that the condition of asymptotic orthogonality is usually fulfilled for radio signals. An upper bound can also be calculated for the full probability of classification error.

The study was supported by a grant from the Russian Science Foundation № 23-21-00452, https://rscf.ru/pro-ject/23-21-00452/.

Artyushenko V.M., Volovach V.I. Synthesis of the algorithms for classification of the quasi-deterministic signals. Radiotekhnika. 2025. V. 89. № 1. P. 50−57. DOI: https://doi.org/10.18127/j00338486-202501-04 (In Russian)

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