Amplitude Probability Density Function Research Articles

BER Expression of QAM for Symbol-Level Jamming

In wireless communication systems, quadrature amplitude modulation (QAM) schemes are widely used for high-speed data transmission, and recently, symbol-level jamming (SLJ) is being studied as an effective jamming technique. However, bit error rate (BER) expressions of QAM for SLJ have not been presented in previous studies. In this paper, we derive the exact BER expressions of QAM considering phase coherent and noncoherent scenarios under SLJ. Using the derived expressions, we investigate the SLJ order that maximizes BER of QAM for jamming-to-signal ratio (JSR). Further, we present BER of QAM with tone jamming and show that tone jamming is a special case of noncoherent SLJ. In addition, we use a probability density function of the SLJ amplitude to show that the high order noncoherent SLJ is similar to noise jamming. To increase BER in a low JSR region, we present a BER expression of QAM when SLJ exists in a pulse form. Using the derived expression, we investigate the order and pulse duration ratio to maximize BER for JSR. The derived expressions are verified using computer simulations.

Stochastic transition behaviors in a tri-stable van der Pol oscillator with fractional delayed element subject to Gaussian white noise

The stochastic P-bifurcation behavior of tri stability in a generalized Van der Pol system with fractional derivative under additive Gaussian white noise excitation is investigated. Firstly, based on the minimal mean square error principle, the fractional derivative is found to be equivalent to a linear combination of damping and restoring forces, and the original system is simplified into an equivalent integer order system. Secondly, the stationary probability density function of the system amplitude is obtained by stochastic averaging, and according to the singularity theory, the critical parameters for stochastic P-bifurcation of the system are found. Finally, the nature of stationary probability density function curves of the system amplitude is qualitatively analyzed by choosing the corresponding parameters in each region divided by the transition set curves. The consistency between the analytical solutions and Monte-Carlo simulation results verifies the theoretical results in this paper.

The stationary response of piezoelectric cantilever beam model excited by colored noise

This article provides a method to predict the steady-state response of a piezoelectric cantilever under the excitation of Gaussian colored noise which is a better approximation to the ambient random excitation than the white noise. In this paper, a cantilever energy harvester model, which is fully-paved with piezoelectric ceramic and excited by Gaussian colored noise, is built by the Lagrange’s equations and is nondimensionalized. Then the dynamic equation and piezoelectric equation are transformed into a pair of stochastic differential equations about transient equivalent amplitude and transient phase. After that, the stochastic averaging method is applied to simplify the stochastic differential equations into an Itô type equation about the equivalent amplitude, the drift coefficient and the diffusion coefficient are obtained. This method provides another approach which is different from the stochastic linearization method and moment method. On this basis, some crucial outputs such as the steady-state probability density function (PDF) of the equivalent amplitude, the beam’s displacement, the transient output voltage, the joint probability density function of displacement and velocity as well as the mean square value of output voltage are all obtained. With different noise intensity values and delay factors, the Monte Carlo numerical simulation has verified the correctness of the theoretical prediction.

Distribution Characteristics of Ground Echo Amplitude and Recognition of Signal Grazing Angle.

With the continuous advancement of electronic technology, terahertz technology has gradually been applied on radar. Since short wavelength causes severe ground clutter, this paper studies the amplitude distribution statistical characteristics of the terahertz radar clutter based on the measured data, and provides technical support for the radar clutter suppression. Clutter distribution is the function of the radar glancing angle. In order to achieve targeted suppression, in this paper, selected axial integral bispectrum (selected AIB) feature is selected as deep belief network (DBN)input to complete the radar glancing angle recognition and the network structure, network training method, robustness are analyzed also. The ground clutter amplitude distribution can follow normal distribution at 0~45° grazing angles. The Weibull distribution and G0 distribution can describe the amplitude probability density function of ground clutter at grazing angles 85° and 65°. The recognition rate of different signal grazing angles can reach 91% on three different terrains. At the same time, the wide applicability of the selected AIB feature is verified. The analysis results of ground clutter amplitude characteristics play an important role in the suppression of radar ground clutter.

Effect of Nonlinear Detection Response Characteristics of Electric Field Probe on LTE Signal Measurement and Statistical Evaluation of Its Detection Response

To improve the calibration accuracy of an electric field (E-field) probe loaded with a diode detector for digital wireless communication signals with complex waveforms, the effect of the nonlinear characteristics of the E-field probe on the detection response of a long-term evolution (LTE) signal is investigated. In this article, we focused on single-carrier frequency division multiple access (SC-FDMA) and orthogonal frequency-division multiplexing access (OFDMA) signals used for LTE uplink and downlink, respectively. First, we investigated the effect of the nonlinear characteristics of the E-field probe on the detection response of continuous SC-FDMA and OFDMA signals simulating frequency division duplexing LTE. Then, intermittent SC-FDMA and OFDMA signals simulating time-division LTE were also investigated. Furthermore, we proposed a method of estimating the detection response of SC-FDMA and OFDMA signals using the probability density function of the envelope amplitude. When the envelope variation of the LTE signal is fully covered within the response time of the E-field probe, the estimated detection response agrees well with the measured result. In addition, the detection response of an intermittent LTE signal with a typical repetition period can be calculated with the proposed approximation formula by separately considering the probability density functions of the envelope amplitude for the burst and nonburst periods.

Improving IGM temperature constraints using wavelet analysis on high-redshift quasars

ABSTRACT The thermal state of the intergalactic medium contains vital information about the epoch of reionization, one of the most transformative yet poorly understood periods in the young Universe. This thermal state is encoded in the small-scale structure of Lyman-α (Ly α) absorption in quasar spectra. The 1D flux power spectrum measures the average small-scale structure along quasar sightlines. At high redshifts, where the opacity is large, averaging mixes high signal-to-noise ratio transmission spikes with noisy absorption troughs. Wavelet amplitudes are an alternate statistic that maintains spatial information while quantifying fluctuations at the same spatial frequencies as the power spectrum, giving them the potential to more sensitively measure the small-scale structure. Previous Ly α forest studies using wavelet amplitude probability density functions (PDFs) used limited spatial frequencies and neglected strong correlations between PDF bins and across wavelets scales, resulting in suboptimal and unreliable parameter inference. Here we present a novel method for performing statistical inference using wavelet amplitude PDFs that spans the full range of spatial frequencies probed by the power spectrum and that fully accounts for these correlations. We applied this procedure to realistic mock data drawn from a simple thermal model parametrized by the temperature at mean density, T0, and find that wavelets deliver 1σ constraints on T0 that are on average 7 per cent more sensitive at z = 5 (12 per cent at z = 6) than those from the power spectrum. We consider the possibility of combing wavelet PDFs with the power, but find that this does not lead to improved sensitivity.

Strong Quarterdiurnal Tides in the Mesosphere and Lower Thermosphere During the 2019 Arctic Sudden Stratospheric Warming Over Mohe, China

AbstractWe present an analysis of a quarterdiurnal tide (QDT) during the 2019 Arctic sudden stratospheric warming (SSW) event. The analysis is based on data obtained from a meteor radar located at Mohe (MH, 53.5°N, 122.3°E), China. The enhancement of the QDT amplitude is observed during the SSW and the maximum QDT amplitude is about 10 m/s in both neutral wind components. Using the meter radar measurements at MH in the period from August 2011 to April 2019, a probability density function of the QDT amplitude is estimated. The probability of the QDT amplitude larger than 8 m/s is less than 1% at MH. A clear seasonal variability of the QDT amplitude is apparent with the maximum amplitudes that appeared in winter. Based on our analysis, the seasonal variability of the QDT is not the main reason that amplified the QDT. According to the bispectral and bicoherence analyses, nonlinear interaction between tidal waves may contribute to the enhancement of the ODTs. The nonlinear interaction between two semidiurnal tides (SDTs) is important, while the effect of the nonlinear interaction between the diurnal tide and the terdiurnal tide is secondary. It may be possible that the effect of the 2019 SSW amplifies the SDT first and then the QDT is generated via nonlinear interaction of SDTs.

Mixture distribution model for extreme mooring tension and mooring fatigue analysis due to snap loads

Three hybrid moorings are proposed for the station keeping of wave energy converters. The hybrid mooring leg consists of top synthetic fibre rope (nylon or polyester), intermediate buoy and bottom chain (with or without clumped weights attached). The dynamic responses of the point absorber wave energy converter-mooring system are experimentally studied in three irregular sea states. A mixture Rayleigh-Gamma-Weibull distribution is proposed for extreme mooring tension and mooring fatigue damage analysis, and the parameters of this mixture model are estimated by the Expectation Maximization algorithm. The performance of this mixture model is studied by comparing its results with that of the other commonly used distributions. A large number of snap loads are found in survival wave conditions, and a de-clustering procedure is used for the extreme tension analysis. The influence of de-clustering procedure settings on predicted extreme tension is investigated. The rainflow counting approach is applied to calculate mooring fatigue damage and the results are acted as reference values. The Rayleigh, Weibull, Gamma and mixture model are applied to fit the probability density function of rainflow counting tension amplitude for mooring fatigue damage analysis. The accuracy of these models is evaluated by comparing corresponding estimated mooring fatigue damage with the reference values.

Prediction of vortex precession in the draft tube of a model hydro turbine using mean field stability theory and stochastic modelling

In this work we employ mean field stability theory (MFST) to predict the onset of the precessing vortex core (PVC) in the draft tube of Francis turbines. MFST is based on the linear stability analysis of the mean field of turbulent flows. Recent work shows that MFST very accurately predicts the formation of coherent structures in turbulent shear flows, such as the PVC. MFST may further reveal the flow regions that are most susceptible to flow actuation to suppress the PVC, which is of great practical relevance. In this work, MFST is accompanied by a data-driven approach to predict the linear growth rate of the PVC based on pointwise wall pressure measurements. The method is based on statistical evaluation of the probability density function of the PVC amplitude at limit cycle. It makes use of the intense noise induced by the background turbulence, which is expected to be a major driver of hydrodynamic instabilities. The empirical and analytic results are compared to phase-locked LDV measurements conducted inside the draft tube at various operating conditions, to assess the quantitative accuracy of the approach. The methodologies outlined in this work will be of relevance for future design of hydro turbines to run stable over a wide range of operating conditions.

Theoretical determination of asymmetric rolling amplitude in irregular beam seas

A methodology for predicting the probability density function of roll motion for irregular beam seas is developed in the author’s previous research. In this paper, two methods for the prediction of the probability density function (PDF) of the rolling amplitude are examined. One of these methods is an approach based on a non-Gaussian PDF with the use of the equivalent linearization and the moment method, which has been used by Maki in the field of naval architecture. In the framework of this method, the instantaneous joint PDF of the roll and roll rate can be calculated. Thereby, the transformation from the joint PDF to the PDF of the total energy H is necessary. In this paper, the transformation from the joint PDF of instantaneous roll and rate to the PDF of H was conducted. The other method is the energy-based stochastic averaging method, whereby the PDF of the total energy H is determined from which the roll amplitude is calculated. It is noteworthy that the proposed theory aims to predict the PDF of the amplitude of the vessel due to wind or flooding. For such conditions, the restoring curve (GZ curve) has asymmetricity. To take into account this asymmetricity, a new theory for the transform of the PDF of the total energy H to the PDFof amplitude is proposed. The obtained theoretical results show almost complete agreement, and both of the two theoretical methods i.e., the energy-based stochastic averaging method and the non-Gaussian PDF method with the use of the equivalent linearization and moment method, show equivalent prediction performance even in the asymmetric condition.

Evidence for non-Rayleigh characteristics in ship underwater acoustic signatures.

This work examines ship underwater acoustic signature amplitude statistics and statistical distributions and explores the hypothesis that ship signatures exhibit amplitude fluctuations that are different from Rayleigh-distributed ambient ocean noise. Signature measurements from a small oceanographic ship conducting a variety of maneuvers are examined, focusing on those conditions where propeller cavitation and broadband signal modulation occur, specifically during maximum speed runs and turning maneuvers. A key difference for a ship signature is the amplitude modulation generated by propeller cavitation, and this is found to be associated with super-Rayleigh signal characteristics. Cyclostationary processing techniques are used to estimate propeller shaft- and blade-rate modulation. Under conditions of clearly observable propeller modulation, time-series statistics scintillation index and skewness showed values significantly in excess of Rayleigh-distributed values. Ship signature amplitude probability density functions were found to be better matched by a K-distribution model with small shape factor, indicating clearly non-Rayleigh behavior. Evidence for a secondary, high-amplitude, lognormally distributed sound generation mechanism was observed during maximum helm turns.

Equivalent Spectral Method to Estimate the Fatigue Life of Composite Laminates Under Random Vibration Loadings

The power spectral density (PSD) of an equivalent stress is proposed to analyze the fatigue life of composite laminates under random vibration loadings using the Tsai–Hill criterion. The vibration fatigue life can be estimated based on the rainflow amplitude probability density function p(S) of the equivalent stress, which is obtained from this PSD, combined with the S-N curve of the materials. The fatigue life analysis of a random vibration fatigue experiment of composite laminates was carried out, and the calculation results were in accordance with experimental data, which indicates that the fatigue life analysis model proposed gives a satisfactory prediction accuracy.

Fatigue life prediction of train wheel shaft based on load spectrum characteristics

Based on the analysis of load spectrum data, the loading sequence and the interaction between loads are considered, a fatigue life prediction model based on load spectrum is proposed. The load spectrum is preprocessed and the probability density function of mean and amplitude are fitted. The running condition of the train is analyzed, the one-dimensional program load spectrum of wheel and axle load is constructed by extrapolating the load spectrum. According to the modified fatigue cumulative damage method, the fatigue life of the axle is predicted with the one-dimensional program load spectrum. The relevant factors that affect the strength of the part are fully considers in the model. It more accurately reflects the objective facts of the component fatigue process. The result has more engineering reference significance and it provides a theoretical basis for the design and manufacture of train axles and ensuring safe operation.

Adjustable Nonlinear Companding Transform Based on Scaling of Probability Density Function for PAPR Reduction in OFDM Systems

Orthogonal frequency division multiplexing (OFDM) systems suffer from the inherent problem of high peak-to-average power ratio (PAPR). In this article, a novel adjustable nonlinear companding transform is proposed, which is based on scaling of original probability density function (PDF) of OFDM signal amplitudes. The target PDF consists of two parts. The first part with amplitudes no more than the transition point is same to that of original PDF. The second part with amplitudes larger than the transition point and smaller than the cutoff point is obtained by scaling original PDF in dimensions of ordinate and abscissa concurrently, for guaranteeing the constant average power. Companding and decompanding functions are derived, and constraint equation for solving parameters is formulated. Parameters of the proposed algorithm can be adjusted flexibly to achieve desired tradeoffs among algorithmic complexity, bit error rate (BER), out-of-band (OOB) rejection and PAPR reduction performance. Some key properties of the proposed algorithm are theoretically analyzed and proved, which may be much instructive for practical implementations. To further reduce algorithmic complexity, a piecewise curve fitting scheme employing quadratic polynomials is first proposed to simplify companding and decompanding functions. Simulation results confirm analysis results and verify the superiorities of proposed algorithms to other existing algorithms.

Effects of Combined Feedbacks and Recycling Noise on a Birhythmic Self-sustained Oscillator

Numerous studies have demonstrated the important role of noise in the dynamical behavior of a complex system. This work is devoted to investigating the constructive role of combined feedbacks and recycling random excitation on stochastic bifurcations and its regularization in a birhythmic oscillator. This possesses a bistability mode with the coexistence of two stable limit cycles in the deterministic case. However, so far, these combining effects on the birhythmic dynamic system have not been reported. Relying on the approximate methods, the harmonic approximation is adopted to drive the delay self-control feedback to state variables without delay noise. The dynamical behavior of the model is analyzed analytically using Hopf bifurcation theorem and numerically such as two-dimensional bifurcation diagrams with respect to two feedback parameters are obtained. Then, Fokker–Planck–Kolmogorov (FPK) equation and stationary probability density function (PDF) for amplitude are obtained by applying the stochastic averaging method. Based on these results, the influence of related parameters of recycling noise and damping coefficient on the stochastic P-bifurcation is studied.

Stochastic averaging on a nonlinear oscillator with coordinate-dependent mass excited by Gaussian white noises

In this paper, a new stochastic averaging procedure is presented in detail to illustrate the improvement which develops the former stochastic averaging methods which can only deal with randomly excited oscillators without the coordinate-dependent mass (also called as inertia nonlinearity in many literature) into a new method which can handle nonlinear oscillators with both coordinate-dependent mass and stiffness nonlinearity terms. The crucial issue of this method is balancing the input and the dissipation of the Hamiltonian energy of the oscillator. After the oscillator has been simplified to be an I t ^ o type stochastic differential equation, the stationary probability density function (PDF) of transient equivalent amplitude, as well as the joint PDF of the displacement and velocity is studied. Numerical simulations are carried out to verify the theoretical anticipations. The numerical results coincide with the theoretical results perfectly.

Mean‐based reciprocity calibration in TDD massive MIMO system

Non-reciprocity limits the potential of time division duplexing (TDD) massive multiple-input and multiple-output (MIMO) systems. Due to the reciprocal channel, there is no need for downlink (DL) pilot transmission implies computational complexity reduction and saving precious time resources. In this study, the DL channel matrix is estimated using the uplink channel matrix by a novel reciprocity calibration technique. Non-reciprocity arises due to the hardware mismatch (HM) across the base station (BS) and the user terminal (UT)/both. Its detrimental effect causes amplitude and phase impairment in the downlink signal transmission. Since a massive MIMO network has a large number of antenna elements across the BS, hence the instantaneous HM coefficient cannot be determined accurately. For solving such a problem, the authors use the statistical response of the hardware unit. Considering a complex Gaussian hardware response across each antenna terminal, the probability density function (PDF) of amplitude and phase mismatch is derived. They also derive the joint PDF of amplitude and phase mismatch, considering the HM. Simulation results address the sensitivity and complexity for evaluating the sum-rate capacity under three linear precoders (matched filter, regularized zero-forcing, and zero-forcing), which validate their effectiveness in this scenario.

System identification and early warning detection of thermoacoustic oscillations in a turbulent combustor using its noise-induced dynamics

Despite significant research, self-excited thermoacoustic oscillations continue to hinder the development of lean-premixed gas turbines, making the early detection of such oscillations a key priority. We perform output-only system identification of a turbulent lean-premixed combustor near a Hopf bifurcation using the noise-induced dynamics generated by inherent turbulence in the fixed-point regime, prior to the Hopf point itself. We model the pressure fluctuations in the combustor with a van der Pol-type equation and its corresponding Stuart–Landau equation. We extract the drift and diffusion terms of the equivalent Fokker–Planck equation via the transitional probability density function of the pressure amplitude. We then optimize the extracted terms with the adjoint Fokker–Planck equation. Through comparisons with experimental data, we show that this approach can enable prediction of (i) the location of the Hopf point and (ii) the limit-cycle amplitude after the Hopf point. This study shows that output-only system identification can be performed on a turbulent combustor using only pre-bifurcation data, opening up new pathways to the development of early warning indicators of thermoacoustic instability in practical combustion systems.

A new nonlinear companding algorithm based on tangent linearization processing for PAPR reduction in OFDM systems

In this paper, a novel nonlinear companding transform (NCT) is proposed to reduce the Peak-to-Average Power Ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals. The companding function is designed based on continuously differentiable reshaping of the probability density function (PDF) of signal amplitudes. The original PDF is cut off for PAPR reduction, and lower and medium segments of original PDF are scaled and linearized respectively, for maintaining power and cumulative distribution constraints. The linearized segment is set to be the tangent of the scaled version at the inflexion point, so as to reduce the out-of-band (OOB) radiation as much as possible. Parameters of the proposed scheme are solved under joint constraints of constant power and unity cumulative distribution. A new receiving method is also proposed to improve the bit error rate (BER) performance of OFDM systems. Simulation results indicate the proposed scheme can achieve better OOB radiation and BER performance at same PAPR levels, compared with existing similar companding algorithms.

Fourier amplitude distribution and intermittency in mechanically generated surface gravity waves.

We examine and discuss the spatial evolution of the statistical properties of mechanically generated surface gravity wave fields, initialized with unidirectional spectral energy distributions, uniformly distributed phases, and Rayleigh distributed amplitudes. We demonstrate that nonlinear interactions produce an energy cascade towards high frequency modes with a directional spread and trigger localized intermittent bursts. By analyzing the probability density function of Fourier mode amplitudes in the high frequency range of the wave energy spectrum, we show that a heavy-tailed distribution emerges with distance from the wave generator as a result of these intermittent bursts, departing from the originally imposed Rayleigh distribution, even under relatively weak nonlinear conditions.