Numerical model of the analytical estimating and selection of signals ensembles in the asynchronous address telecommunication systems

Аuthors

Mikhaylov V. Y.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: mihvj@yandex.ru

Abstract

Cross-correlation properties of M-sequences ensembles are completely determined by the Galois field structure, from which they mapped to the binary symbols. This dependence is very complicated. In the case expandable M-sequences lengths and, especially, expandable polynomials degrees some important properties of cross-correlation function can reveal by the numerical methods. One of these methods for even values of polynomials degrees proposed in this paper. Feature of the method and based on it the techniques for reviewing the characteristics of their cross-correlation function is analytical in nature, which certainly expands the boundaries of knowledge about the properties of these widely used encoded sequences. Discussed in the article examples of estimating methods show high accuracy of the analytical results. The results obtained can also be viewed as a starting point for further method development and further detail the properties of M-sequences cross-correlation function. In addition the proposed method can be successfully applied to estimate the correlation properties of the composite encoded sequences that are algebraically related to the M-sequences, in particular, the Gold codes. The proposed method and the cross-correlation function estimation technique may be useful in selecting ensembles of complex encoded signals in the asynchronous address and command control airspace communications systems.

Keywords:

analytical estimating, signal ensembles, asynchronous address systems, telecommunications, cross-correlation functions.

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