Investigation of peculiarities of range algorithms and determining opportunities for use in NGN networks

DOI №________________

Abstract

The basic properties of ranks and rank statistics are analyzed. The property of invariance of ranks on the example of a harmonic signal with a random initial phase is considered. An example of signal ranking is considered. It is shown that the distribution of ranks is invariant to the type of initial distribution only if the elements of the ranked samples are statistically homogeneous. In all cases, the elements of the samples are statistically independent, i.e. their distribution does not depend on the element number. The nonlinear transformation characteristic corresponds to the integral impedance distribution function, and the ranking according to the algorithm is equivalent to the actual distribution of the sample, which, depending on the situation, may be a disturbance of the disturbance or mixture of the interference signal. The restrictions on the scope of rank procedures in comparison with optimal invariant transformations are analyzed. First of all, it is necessary that, in the absence of a signal, the ranked sample was statistically homogeneous. This ensures a stabilization of the level of false alarms with an a priori unknown distribution. But it is equally important that the appearance of the signal destabilizes the homogeneity of the sample. Despite the reduction in the number of informative readings, the sensitivity of the distribution of ranks in the presence of a signal not only did not decrease, but even increased, which is an essential principle for organizing the procedure for detecting a signal based on ranks. Flexibility of the ranking procedure provides the possibility of solving a wide range of signal detection tasks under conditions of nonparametric a priori uncertainty.

Keywords: network, NGN, rank, algorithm, function, parameter, signal, quality, sampling, distribution, information, loss, invariance.

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