Random Linear Antennas With Controlled Radiation Pattern

Maystrenko, A A; Melnik, S.S.; Pritula, G. M.; Usatenko, O. V.

doi:10.1615/telecomradeng.v73.i4.30

Cited by 2 publications

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“…The other limit, R c goes to infinity, describes totally correlated sequence, K x (r) = 1 and K x (k) = 2πδ(k). All the above-mentioned facts are demonstrated by the following simple example [27]:…”

Section: Introduction To the Convolution Methodsmentioning

confidence: 80%

Bunches of random cross-correlated sequences

Maystrenko¹,

Melnik²,

Pritula³

et al. 2013

J. Phys. A: Math. Theor.

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The statistical properties of random cross-correlated sequences constructed by the convolution method (likewise referred to as the Rice or the inverse Fourier transformation) are examined. We clarify the meaning of the filtering function-the kernel of the convolution operator-and show that it is the value of the cross-correlation function which describes correlations between the initial white noise and constructed correlated sequences. The matrix generalization of this method for constructing a bunch of N cross-correlated sequences is presented. Algorithms for their generation are reduced to solving the problem of decomposition of the Fourier transform of the correlation matrix into a product of two mutually conjugate matrices. Different decompositions are considered. The limits of weak and strong correlations for the one-point probability and pair correlation functions of sequences generated by the method under consideration are studied. Special cases of heavy-tailed distributions of the generated sequences are analyzed. We show that, if the filtering function is rather smooth, the distribution function of generated variables has the Gaussian or Lévy form depending on the analytical properties of the distribution (or characteristic) functions of the initial white noise. Anisotropic properties of statistically homogeneous random sequences related to the asymmetry of a filtering function are revealed and studied. These asymmetry properties are expressed in terms of the third-or fourth-order correlation functions. Several examples of the construction of correlated chains with a predefined correlation matrix are given.

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Section: Introduction To the Convolution Methodsmentioning

confidence: 80%

Bunches of random cross-correlated sequences

Maystrenko¹,

Melnik²,

Pritula³

et al. 2013

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

Bunches of Random Cross-correlated Sequences

Maystrenko,

Melnik,

Pritula

et al. 2013

Preprint

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Statistical properties of random cross-correlated sequences constructed by the convolution method (likewise referred to as the Rice's or the inverse Fourier transformation) are examined. Algorithms for their generation are discussed. They are frequently reduced to solving the problem for decomposition of the Fourier transform of the correlation matrix into a product of two mutually conjugate matrices; different decompositions of the correlation matrix are considered. The limits of weak and strong correlations for the one-point probability and pair correlation functions of the sequences are studied. Special cases of heavy-tailed distributions resulting from the convolution generation are analyzed. Anisotropic properties of statistically homogeneous random sequences related to asymmetry of a filtering function are discussed.

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Random Linear Antennas With Controlled Radiation Pattern

Cited by 2 publications

References 0 publications

Bunches of random cross-correlated sequences

Bunches of random cross-correlated sequences

Bunches of Random Cross-correlated Sequences

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