Том 60, № 12 (2017)

This study investigates algorithms for the estimation of amplitude of the radio signal with rectangular envelope and unknown duration and initial phase. The synthesis and analysis of quasi-likelihood and quasi-coherent estimation algorithm have been performed. This algorithm implies that the unknown duration and initial phase are replaced with certain expected values of these parameters. The loss in accuracy of amplitude estimation owing to the a priori lack of knowledge of the duration and the initial phase is analyzed. The quasi-likelihood noncoherent algorithm for amplitude estimation with the initial phase adaptation is synthesized and its statistical characteristics such as the estimate bias and variance are determined. The relationships of the loss in estimation accuracy owing to the a priori lack of knowledge of signal duration are derived. The maximum likelihood algorithm for amplitude estimation was synthesized and analyzed. This algorithm implies that the unknown duration and the initial phase are replaced with their maximum likelihood estimates. The gain in accuracy of the maximum likelihood estimate as compared to the quasi-likelihood ones was investigated. It is shown that a priori lack of knowledge of the signal duration does not affect asymptotically the accuracy of maximum likelihood estimate of amplitude at large values of signal-to-noise ratio.

As is known, the Nyberg design S-boxes possess the cryptographic properties valuable for practical application. Up to date this construction has been considered only for fields of characteristic 2. This paper presents an extension of the Nyberg construction to the fields of odd characteristic. The notion of nonlinearity distance of p-function is introduced, and the affine ternary code is built. The Nyberg design S-boxes with fields characteristic p = 3 for all lengths N ≤ 243 are built. The nonlinearity distances are calculated, and it is shown that with an increase of S-box length, these distances increase essentially faster as compared to the fields of characteristic p = 2.

A number of features of biconical cavities make them attractive for various applications. Expressions for the calculation of the eigenfrequencies of a biconical cavity with large cone angles can be derived using the overlapping domain decomposition method in combination with the collocation method; however, the expressions reported in the literature involve only a single pair of collocation points, thus giving no way to estimate the eigenfrequency determination accuracy. The aim of this paper is to calculate the biconical cavity eigenfrequencies for an arbitrary number of collocation point pairs. An equation in the biconical cavity eigenfrequencies for an azimuthally symmetric transverse electric field at an arbitrary number of collocation point pairs is derived. The equation reduces to two equations, whose solution requires far less computational effort in comparison with the original equation. The solution of one of the two equations are based on modes symmetric about the cavity symmetry plane, and the solutions of the other are based on antisymmetric modes. The calculated eigenfrequencies converge rapidly with increasing number of collocation point pairs, while the use of only one collocation point pair may introduce noticeable error. The proposed technique may be used in the development of components and units on the basis of biconical cavities.