Quasi-deterministic Signals Research Articles

Зависимость стохастического резонанса в нелинейной системе от характеристик каждого слагаемого аддитивной смеси

A nonlinear system was investigated using a modeling approach, constructed based on the scheme of a digital filter using the Lyapunov characteristic function. The phenomenon of stochastic resonance was observed in the nonlinear system when there was an additive mixture of a quasi-deterministic signal and noise at the system input. Stochastic resonance improves the signal-to-noise ratio at the system output by more than 15400 times compared to its value at the system input. The recorded number may vary and represents the main characteristic of the resonance. The dependence of the stochastic resonance characteristic on the variations of the probabilistic characteristics of the quasi-deterministic signal and noise was studied. An analysis of experimental data describing the values of the characteristic and the peculiarities of the stochastic resonance effect in the nonlinear system was performed. Additionally, a connection between the value of the resonance characteristic and the total energy of the periodic signal was discovered for the first time.

Зависимость стохастического резонанса в нелинейной системе от характеристик каждого слагаемого аддитивной смеси

A nonlinear system was investigated using a modeling approach, constructed based on the scheme of a digital filter using the Lyapunov characteristic function. The phenomenon of stochastic resonance was observed in the nonlinear system when there was an additive mixture of a quasi-deterministic signal and noise at the system input. Stochastic resonance improves the signal-to-noise ratio at the system output by more than 15400 times compared to its value at the system input. The recorded number may vary and represents the main characteristic of the resonance. The dependence of the stochastic resonance characteristic on the variations of the probabilistic characteristics of the quasi-deterministic signal and noise was studied. An analysis of experimental data describing the values of the characteristic and the peculiarities of the stochastic resonance effect in the nonlinear system was performed. Additionally, a connection between the value of the resonance characteristic and the total energy of the periodic signal was discovered for the first time.

CORRELATION FUNCTIONS AND QUASI-DETERMINISTIC SIGNALS

When processing data on random functions, they are most often limited to constructing an empirical correlation function. In this regard, the problem arises of constructing a random function (a quasi-deterministic signal) determined by a finite set of random variables and having a given correlation function. Moreover, a random function can often be considered Gaussian, since in many cases a random signal is obtained at the output of the system, which is fairly well approximated by a Gaussian. For stationary random processes and for random fields, this problem has been considered. For random sequences and discrete random fields, as well as for non-stationary random signals, the problem remained open. The article considers the problem of restoring a random sequence from known mathematical expectation and correlation function. Such a model random sequence is constructed, in which the mathematical expectation and correlation function coincide with the given ones. The mathematical expectation and the correlation function are the simplest probabilistic numerical characteristics, but they do not uniquely determine the corresponding set of probability distribution densities that satisfy the conditions of normalization and consistency, provided that for each fixed integer value of the parameter, the random sequence is a continuous random variable. The article considers the restoration of a quasi-deterministic signal in stationary and non-stationary cases. For the stationary case, three examples are given for constructing a quasi-deterministic discrete signal EMBED Equation.DSMT4 , provided that the spectral density has three different forms. For the non-stationary case, the corresponding quasi-deterministic signal was obtained for various cases of the spectrum. The use of a random function model determined by a finite number of parameters makes it possible to significantly simplify the analysis of applied problems, the solution of which is associated with differential equations with random coefficients, which are such quasi-deterministic signals. In this case, there is no need to use a complex apparatus of stochastic differential equations, since the solution of such an equation simply depends on random variables as on parameters.

Стохастический резонанс в цифровом фильтре на основе характеристической функции Ляпунова

The phenomenon of stochastic resonance in a radio engineering system, similar in structure to a digital filter based on the Lyapunov characteristic function, is considered. The physical meaning of stochastic resonance is revealed and the hypothesis of its existence in a radio engineering system is confirmed. In the process of modeling a digital filter, the effect and indicators of stochastic resonance were established when filtering an additive mixture of a quasi-deterministic signal and "white" noise. An improvement in the signal-to-noise ratio at the output of the system by a factor of 634 compared to the signal-to-noise ratio at its input was obtained when filtering an additive mixture of a centered quasi-deterministic signal and "white" noise. When filtering an additive mixture of a non-centered quasi-deterministic signal and "white" noise, the indicated stochastic resonance index is lower and amounts to 174 times. It is proposed to consolidate the phenomenon of stochastic resonance for a radio engineering system with such new definitions as the band and bandwidth of the resonance. Noise immunity increases noticeably in the resonance band in a digital modem with a circuit similar to a digital filter based on the Lyapunov characteristic function. The purpose of this work is to present a hypothesis with a future perspective, revealing the possibility of using a new effect in the construction of radio engineering systems.

ОБОБЩЕНИЕ ТЕОРИИ НОВОГО МЕТОДА МОДУЛЯЦИИ И ДЕМОДУЛЯЦИИ СЛУЧАЙНОГО СИГНАЛА

A new method of modulation and demodulation of a quasi-deterministic signal is investigated, which in the future opens up great opportunities for improving the efficiency of digital systems. The method contains new technical solutions for transforming a random signal, including the modulation of the characteristic function and the measurement of estimates of the real and imaginary parts of this function. The purpose of this work is the development of optimal algorithms and generalization of the theory of the new modulation and demodulation method by using new elements (algorithms) when transforming a random signal using the arcsine distribution law. Single-channel and dual-channel modems are considered for operation in a radio channel and in a wired channel respectively. The comparison of characteristics of the modems with optimal and non-optimal modulation algorithms is performed, wherein the characteristics of the first modem turn out to be an order of magnitude better than the second modem. It has been established that the modems have different noise immunity in a channel with «white» noise and in this indicator surpass the known modems by at least ten orders of magnitude. The energy efficiency of the modems is high and exceeds the efficiency of QPSK (Quadrature Phase Shift Keying) signal modems by 10 dB at the error probability level of 1∙10-10.

Determination of probabilistic characteristics of random values of estimates of the Lyapunov function when describing a physical process

The applied application of the Lyapunov characteristic function is determined by the properties of its estimates. Probabilistic characteristics of estimates of the Lyapunov characteristic function are described for the first time. The probabilistic characteristics of random values of estimates of the Lyapunov function are empirically estimated using statistical methods. The Matlab package has developed a model of a special device for obtaining estimates of the characteristic function by a direct method. A quasi-deterministic signal is fed to the input of the model, the instantaneous values of which are distributed according to the arcsine law, and an array of values of estimates of the Lyapunov function is obtained at the output, which is used to estimate the probabilistic characteristics of these estimates. Statistical estimation was performed by an indirect method. It is established that the values of the estimates of the Lyapunov characteristic function are distributed according to the normal law. The results of the research will be useful in engineering calculations, for example, when detecting message transmission errors in modems with a modulated characteristic function.

Detection Efficiency of Signal with Unknown Non-Power Parameter Using Algorithms Based on the Compressive Sensing Theory

The problem of detecting quasi-deterministic signals against the background of noise during the digital processing has been considered. In this case, at the specified detection efficiency, the minimum criterion of required arithmetic operations was used as a synthesis criterion for such algorithms. To this end, such algorithms were synthesized based on concepts of the compressive sensing theory. The computer simulation was used to check the efficiency of developed algorithms making it possible to determine the manner in which the total probability of detection errors depends on the signal-to-noise ratio and the compression ratio (ratio of the number of elements in the sufficient statistic vectors before and after “compression”). The detection efficiency losses of proposed algorithms were determined in comparison with the classical optimal algorithm in accordance with the maximum likelihood method at different values of signal-to-noise ratio and compression ratio. At the same time, the paper indicates the gain in the number of used arithmetic operations of proposed algorithms as compared to the classical one. The presented results allow us to make a sound choice of detection algorithm depending on the available hardware resources and admissible degradation of the detection efficiency.

Adaptive energy detection of quasi-deterministic signals in the presence of the non-Gaussian noise

Analytical expressions for the parameters of the adaptive energy detection of the quasi-deterministic radio signals in the presence of the Lichter noise are derived. The effect of the random amplitude distribution of radio signals on the decision statistics of detection is analyzed.

Bayesian estimate of the doppler frequency shift with reduction of the data dimensionality

The paper considers the possibility of reducing the amount of calculations of the Bayesian estimate of the Doppler frequency shift and the initial phase of a quasi-deterministic signal observed in the presence of white-noise distortions due to introduction of the stage of reduction of the dimensionality of the observed data. The minimization of the loss of the Fisher information on the estimated parameter is used to control the correctness of the dimensionality reduction procedure; the estimation accuracy depends on this procedure. The computer simulation using test signals proves the possibility of a considerable reduction in the amount of calculations upon realization of Bayesian procedures for the same estimation accuracy.

Recognition of gravitation impulses on a correlated non-Gaussian noise background

We consider the problem of gravitation-wave impulse recognition against the background of correlated noise produced by resonance gravitational antennas. A new algorithm for the joint processing of data recorded by spatially separated gravitational detectors is obtained. The algorithm is an alternative to the coincidence scheme, which is traditionally used in gravitation-wave experiments. It is based on the principles, well known in statistical radiophysics, of joint detection and parameter estimation in quasi-deterministic signals.

Characteristics of Energy Detection of Quasi-Deterministic Radio Signals with a Non-Rayleigh Distribution of Amplitude Fluctuations

We find the distribution of the decision statistic of a discrete energy detector in the case of reception of the superposition of white noise and a quasideterministic signal with a non-Rayleigh distribution of amplitude fluctuations. An expression for the true-detection probability is derived.

Characteristics of Energy Detection of Quasideterministic Radio Signals

We determine the decision-statistic distribution of an energy detector for the case of receiving an additive mixture of the Gaussian quasi-deterministic signal and Gaussian white noise. Exact and approximate expressions for true detection probability are obtained.

Causality and conservation of energy : their implications for prediction of receiver performance

The paper is concerned with the analysis of receiver performance in range-dependent waveguides. The problem is shown to be amenable to a simple theoretical treatment. The necessary analytical technique is based on the application of the principle of causality and the low of conservation of energy. The focus of the analysis is on prediction of limiting capabilities of an optimum detector of quasi-deterministic signals in irregular multi-mode channels. Explicit analytical formulae are derived for the probability of detection, the far-field directivity function and the Cramer-Rao bound for mean-root-square errors in estimates of signal parameters. The theory presented reveals clear physical limits on capabilities of signal processing technique in non-uniform oceanic environment