APPLICATION OF BLIND SIGNAL SEPARATION TECHNIQUES FOR DETECTION OF PHASE-SHIFTED RADIO SIGNALS

Целью данной работы является исследование эффективности алгоритма слепого разделения сигналов (СРСв задаче обнаружения цифровых фазоманипулированных радиосигналов. Рассмотрены классические методы СРС и критерии независимости сигналов. Исследована модель алгоритма СРС, основанного на вычислении размешивающей матрицы, которая приводит совместные кумулянты второго и четвертого порядков к нулю. Для исключения тривиального решения накладываются дополнительные ограничения на дисперсии сигналов. Приводится система уравнений для нахождения коэффициентов размешивающей матрицы. Показан вид коэффициентов размешивающей матрицы, приводящей сигналы к некоррелированному виду. Доказана возможность аналитического решения уравнения, связанного с равенством совместного кумулянта четвертого порядка к нулю. По результатам моделирования алгоритма СРС показано, что предложенный алгоритм позволяет обеспечить прием ФМ-2 радиосигнала на фоне гауссовой помехи. Выигрыш в отношении сигнал-помеха составляет не менее 2 дБ. The purpose of this work is to study the effectiveness of the blind signal separation algorithm in the problem of detecting digital PSK radio signals. Classical methods of blind signal separation and criteria of signal independence are considered. A model of a blind signal separation algorithm based on the calculation of a mixing matrix that reduces the joint cumulants of the second and fourth orders to zero is investigated. To eliminate the trivial solution, additional restrictions are imposed on the signal variances. A system of equations for finding the coefficients of the mixing matrix is given. The view of the coefficients of the mixing matrix, which leads the signals to an uncorrelated form, is shown. The possibility of an analytical solution of the equation associated with the equality of the joint cumulant of the fourth order to zero is proved. Based on the results of the simulation of the blind signal separation algorithm, it is shown that the proposed algorithm allows receiving the PSK-2 radio signal against the background of Gaussian interference. The gain in the signal-to-noise ratio is at least 2 dB.

Limit theorems for iterated random functions

We study geometric moment contracting properties of nonlinear time series that are expressed in terms of iterated random functions. Under a Dini-continuity condition, a central limit theorem for additive functionals of such systems is established. The empirical processes of sample paths are shown to converge to Gaussian processes in the Skorokhod space. An exponential inequality is established. We present a bound for joint cumulants, which ensures the applicability of several asymptotic results in spectral analysis of time series. Our results provide a vehicle for statistical inferences for fractals and many nonlinear time series models.

Limit theorems for iterated random functions

We study geometric moment contracting properties of nonlinear time series that are expressed in terms of iterated random functions. Under a Dini-continuity condition, a central limit theorem for additive functionals of such systems is established. The empirical processes of sample paths are shown to converge to Gaussian processes in the Skorokhod space. An exponential inequality is established. We present a bound for joint cumulants, which ensures the applicability of several asymptotic results in spectral analysis of time series. Our results provide a vehicle for statistical inferences for fractals and many nonlinear time series models.

Cumulants and partition lattices II: generalised k-statistics

The role played by the Möbius function of the lattice of all partitions of a set in the theory of k-statistics and their generalisations is pointer out and the main results conscerning these statistics are drived. The definitions and formulae for the expansion of products of generalished k-statistics are presented from this viewpoint and applied to arrays of random variables whos moments satisfy stitable symmentry constraints. Applications of the theory are given including the calculation of (joint) cumulants of k-statistics, the minimum variace estimation of (generalised) moments and the asymptotic behaviour of generalised k-statistics viewed as (reversed) martingales.