Random Initial Phase Research Articles

Determining the number of small-sized radars in a network with coherent signal processing for the detection of stealth aerial vehicles

The object of this study is the process of determining the number of small-sized radars in the network when detecting stealth unmanned aerial vehicles. The main hypothesis of the study assumed that determining the optimal number of small-sized radars in the network will make it possible not to waste unnecessary resources of radars to detect stealth unmanned aerial vehicles. The main stages of detection of a stealth unmanned aerial vehicle by a network of small-sized radars are: – reception of the signal reflected from a stealth unmanned aerial vehicle by all small-sized radars of the network; – coordinated filtering of incoming signals in each small-sized radar; – compensation of phase shifts in each matched filter; – coherent addition of output signals from each matched filter at the output of the receivers of each of the N small-sized radars performing reception; – formation of a complex bypass at the output of the corresponding Doppler channel in each small-sized radar of the network; – coherent processing of signals from all elements of the network of small-sized radars; – detection of the output signal from the adder of coherent signals. At the same time, compensation for the random initial phase of signals reflected from a stealth unmanned aerial vehicle is also performed. It has been established that the increase in the elements of the network of small-sized radars increases the value of the conditional probability of correct detection. Such an increase is more significant when the number of elements in the network of small-sized radars is increased to two or three. The gain in the signal/noise ratio when adding elements to the network of small-sized radars was evaluated. It was established that the optimal number of small-sized radars in a network with coherent signal processing when detecting stealth unmanned aerial vehicles is 2‒3 radars

Recovery of Discrete-Time Signal Based on the Moving Average Model and Estimation of the Samples Correlation in Forward and Reverse Forecasting

The article discusses the development of mathematical support for the recovery of the values of discrete-time sequence samples obtained as a result of uniform sampling of a continuous signal. The recovery problem of discrete-time sequence samples is solved for a signal that can be considered stationary or stationary at least in a broad sense (quasi-stationary). The development of mathematical support for the recovery of the values of signal samples was carried out on the basis of constructing a moving average model and estimating the correlation of signal samples over time with forward and reverse forecasting. Estimates of the signal correlation function necessary to recover sample sections with lost values are calculated from samples with known values. Correlation function estimates can be calculated regardless of the location of the recovery area when the condition of stationarity of the signal is met. The obtained estimates of the correlation function samples can be used for both forward and reverse forecasting. Moreover, even if it is necessary to recover several problem sections, it is enough to calculate only once the sample of correlation function estimates necessary for their restoration. The resulting mathematical solution to the problem became the basis for the development of algorithmic support. Test tests and functional checks of the algorithmic support were carried out on the basis of simulation using a signal model representing an additive sum of harmonic components with random initial phases. The simulation results showed that the calculation of estimates of the lost sample values is carried out with a fairly low error, both in forward and reverse forecasting, as well as when they are used together. In practice, the choice of a sequence recovery algorithm based on forward or reverse forecasting will be determined based on the actual conditions of its processing. In particular, if previous samples with known values are not enough to carry out forward forecasting, then the reverse forecasting procedure is implemented and vice versa. The developed algorithmic support can be implemented in the form of metrologically significant software for digital signal processing systems.

Dissimilarity between synchronization processes on networks.

In this study, we present a general framework for comparing two dynamical processes that describe the synchronization of oscillators coupled through networks of the same size. We introduce a measure of dissimilarity defined in terms of a metric on a hypertorus, allowing us to compare the phases of coupled oscillators. In the first part, this formalism is implemented to examine systems of networked identical phase oscillators that evolve with the Kuramoto model. In particular, we analyze the effect of the weight of an edge in the synchronization of two oscillators, the introduction of new sets of edges in interacting cycles, the effect of bias in the couplings, and the addition of a link in a ring. We also compare the synchronization of nonisomorphic graphs with four nodes. Finally, we explore the dissimilarities generated when we contrast the Kuramoto model with its linear approximation for different random initial phases in deterministic and random networks. The approach introduced provides a general tool for comparing synchronization processes on networks, allowing us to understand the dynamics of a complex system as a consequence of the coupling structure and the processes that can occur in it.

Dependence of the Values of Inter-Component Phase Relations of the Harmonic Components of Vibration on the Displacement of Misaligned Shafts

The analytical dependence of the phases and values of intercomponent phase relations of the harmonic components of vibration displacement of misaligned shafts on their displacement has been presented in the article. Harmonic vibrations of the shafts were modeled using a Lagrangian connecting vibration displacement and forces acting in the system. For ease of derivation, the Lagrangian is rewritten in complex form. The resulting algebraic equations connect the complex amplitudes of vibration components with the amplitudes of periodic forces at the same frequencies and the parameters of the mechanical system (stiffness, damping). The amplitudes of periodic forces are related to the magnitude of the shafts angular and parallel misalignment according to the accepted model. Calculation of intercomponent phase relations values is used to get rid of the random initial phase shift caused by the choice of the timing reference. The magnitude of the effect produced by the misalignment of the shafts on the amplitudes and values of the intercomponent phase relations of the signal components is estimated. The obtained resultcan be used to construct devices for estimation shaft displacements and devices for assessing the condition of equipment based on the analysis of vibration signals.ls.

Protection Against Simulating Interference Based on Coherent Storage and Pulsed Probing Signal with a Random Initial Phase

The confrontation between radar stations and radio electronic countermeasure systems leads to constant advancements on both sides as electronics continue to develop. This multifaceted confrontation determines the success of each side primarily based on the comprehensiveness of analysis and the correctness of the adopted system decisions. Occasionally, decisions are made in pursuit of quality, resulting in success in one aspect but failure in another. One such example is the transition to building radar stations based on true coherence principles. This work highlights the issue of protecting radar stations with true coherence from simulative interference. A method is presented for protecting against “near” simulative interference, which is the most dangerous and is generated between the radar stations and an aerial vehicle equipped with a radio electronic countermeasure systems. The method is based on combining an impulse probing signal with a random initial phase and coherent inter-period accumulation of the received signal.

Unveiling detection probability for multi-Gaussian correlated anomalous vortex modes in maritime atmospheric turbulence

In this study, we employ the Rytov approximation to investigate the detection probability of orbital angular momentum (OAM) in multi-Gaussian correlated anomalous vortex (MGCAV) beams under non-Kolmogorov maritime atmospheric turbulence. Our results demonstrate that the OAM detection probability of a MGCAV beam is influenced by various factors, including beam parameters and the characteristics of maritime atmospheric turbulence. Specifically, an increase in propagation distance, beam order, and beam index, or a decrease in inner scale, spatial coherence width, and non-Kolmogorov parameter, leads to a decrease in the OAM detection probability. The phase characteristics of partially coherent vortex modes are affected by both atmospheric turbulence phase and initial random phase, resulting in reduced robustness compared to fully coherent vortex modes. Furthermore, a comparative analysis between Gaussian–Schell correlated anomalous vortex (GSCAV) beams and MGCAV beams reveals the superior resilience of GSCAV beams in mitigating the impact of maritime atmospheric turbulence. Moreover, specific combinations of beam order, topological charge, and beam waist, or the optimal beam width, yield maximum OAM detection probability or minimum scintillation. These findings provide valuable insights applicable to optical communication, particularly in scenarios above sea and ocean levels.

Influence of cumulative damage on synchronization of Kuramoto oscillators on networks

In this paper, we study the synchronization of identical Kuramoto phase oscillators under cumulative stochastic damage to the edges of networks. We analyze the capacity of coupled oscillators to reach a coherent state from initial random phases. The process of synchronization is a global function performed by a system that gradually changes when the damage weakens individual connections of the network. We explore diverse structures characterized by different topologies. Among these are deterministic networks as a wheel or the lattice formed by the movements of the knight on a chess board, and random networks generated with the Erdős–Rényi and Barabási–Albert algorithms. In addition, we study the synchronization times of 109 non-isomorphic graphs with six nodes. The synchronization times and other introduced quantities are sensitive to the impact of damage, allowing us to measure the reduction of the capacity of synchronization and classify the effect of damage in the systems under study. This approach is general and paves the way for the exploration of the effect of damage accumulation in diverse dynamical processes in complex systems.

Polarization coherency matrix tomography.

In this paper, a polarization-sensitive optical coherence tomography (PS-OCT) based polarization coherency matrix tomography (PCMT) combining polarization coherency matrix with Mueller matrix is proposed for the determination of complete polarization properties of tissue. PCMT measures the Jones matrix of biological sample based on similar transformation, in which four elements have initial random phase from different polarization states based on traditional PS-OCT. The results indicate that PCMT can eliminate the phase difference of incident lights with different polarization states. In addition, the polarization coherency matrix using three polarization states has complete information of the sample Jones matrix. Finally, the 16 elements of the sample Mueller matrix are applied for deriving fully polarized optical properties of the sample based on the elliptical diattenuator and the elliptical retarder. Thus, the method based on the PCM and Mueller matrix has the advantage over the traditional PS-OCT.

Partial degeneration of finite gap solutions to the Korteweg–de Vries equation: soliton gas and scattering on elliptic backgrounds

We obtain Fredholm type formulas for partial degenerations of theta functions on (irreducible) nodal curves of arbitrary genus, with emphasis on nodal curves of genus one. An application is the study of ‘many-soliton’ solutions on an elliptic (cnoidal) background standing wave for the Korteweg–de Vries (KdV) equation starting from a formula that is reminiscent of the classical Kay–Moses formula for N-solitons. In particular, we represent such a solution as a sum of the following two terms: a ‘shifted’ elliptic (cnoidal) background wave and a Kay–Moses type determinant containing Jacobi theta functions for the solitonic content, which can be viewed as a collection of solitary disturbances on the cnoidal background. The expressions for the travelling (group) speed of these solitary disturbances, as well as for the interaction kernel describing the scattering of pairs of such solitary disturbances, are obtained explicitly in terms of Jacobi theta functions. We also show that genus N + 1 finite gap solutions with random initial phases converge in probability to the deterministic cnoidal wave solution as N bands degenerate to a nodal curve of genus one. Finally, we derive the nonlinear dispersion relations and the equation of states for the KdV soliton gas on the residual elliptic background.

The Metastable State of Fermi–Pasta–Ulam–Tsingou Models

Classical statistical mechanics has long relied on assumptions such as the equipartition theorem to understand the behavior of the complicated systems of many particles. The successes of this approach are well known, but there are also many well-known issues with classical theories. For some of these, the introduction of quantum mechanics is necessary, e.g., the ultraviolet catastrophe. However, more recently, the validity of assumptions such as the equipartition of energy in classical systems was called into question. For instance, a detailed analysis of a simplified model for blackbody radiation was apparently able to deduce the Stefan-Boltzmann law using purely classical statistical mechanics. This novel approach involved a careful analysis of a "metastable" state which greatly delays the approach to equilibrium. In this paper, we perform a broad analysis of such a metastable state in the classical Fermi-Pasta-Ulam-Tsingou (FPUT) models. We treat both the α-FPUT and β-FPUT models, exploring both quantitative and qualitative behavior. After introducing the models, we validate our methodology by reproducing the well-known FPUT recurrences in both models and confirming earlier results on how the strength of the recurrences depends on a single system parameter. We establish that the metastable state in the FPUT models can be defined by using a single degree-of-freedom measure-the spectral entropy (η)-and show that this measure has the power to quantify the distance from equipartition. For the α-FPUT model, a comparison to the integrable Toda lattice allows us to define rather clearly the lifetime of the metastable state for the standard initial conditions. We next devise a method to measure the lifetime of the metastable state tm in the α-FPUT model that reduces the sensitivity to the exact initial conditions. Our procedure involves averaging over random initial phases in the plane of initial conditions, the P1-Q1 plane. Applying this procedure gives us a power-law scaling for tm, with the important result that the power laws for different system sizes collapse down to the same exponent as Eα2→0. We examine the energy spectrum E(k) over time in the α-FPUT model and again compare the results to those of the Toda model. This analysis tentatively supports a method for an irreversible energy dissipation process suggested by Onorato et al.: four-wave and six-wave resonances as described by the "wave turbulence" theory. We next apply a similar approach to the β-FPUT model. Here, we explore in particular the different behavior for the two different signs of β. Finally, we describe a procedure for calculating tm in the β-FPUT model, a very different task than for the α-FPUT model, because the β-FPUT model is not a truncation of an integrable nonlinear model.

Expanding the memory effect in scattering imaging by manipulating photon distributions

Speckle correlation techniques based on the memory effect can recover objects from multiple scattered light without the information of the scattering media. The existing methods, however, are limited by the inherent angular width of the memory effect, and the retrieval algorithms frequently converge to erroneous solutions. In this paper, we propose an autoshrinking algorithm to expand the field of view in scattering imaging. We also develop a pretreatment iteration scheme to achieve high accuracy reconstruction. The autoshrinking method improves the quality of the energy spectrum by adaptively shrinking the speckle autocorrelation to its expanded central peak region and enhancing the ratio of the ballistic photons to the scattered photons. In the pretreatment iteration, the Brenner gradient function of a short testing iteration is employed to select the initial random Fourier phase to ensure the iteration can quickly and accurately converge. Experiments and simulations successfully confirm the effectiveness of our method.

Discrete Time Sequence Reconstruction of a Signal Based on Local Approximation Using a Fourier Series by an Orthogonal System of Trigonometric Functions

The article considers the development of mathematical and algorithmic support for the sample’s reconstruction in problem sections of a discrete sequence of a continuous signal. The work aimed to ensure the reconstruction of lost samples or sections of samples with a non-constant distorted time grid when sampling a signal with a uniform step and at the same time to reduce the computational complexity of digital reconstruction algorithms. The solution to the stated problem is obtained based on the local approximation method. The specific of this method application was the use of two subsequences of samples located symmetrically concerning the reconstructed section of the sequence. The approximating model is a Fourier series on an orthogonal system of trigonometric functions. The optimal solution to the approximation problem is based on the minimum square error criterion. Mathematical equations are obtained for this type of error. They allow us to estimate its value depending on the model order and the samples number in the subsequences used in the reconstruction process. The peculiarity of the mathematical equations obtained in this paper for signal reconstruction is that they do not require the preliminary calculation of the Fourier series coefficients. They provide a direct calculation of the values of reconstructed samples. At the same time, when the number of samples in the subsequences used for reconstruction will be even, it is not necessary to perform multiplication operations. All this made it possible to reduce the computational complexity of the developed algorithm for signal reconstruction. Experimental studies of the algorithm were carried out based on simulation modeling using a signal model that is an additive sum of harmonic components with a random initial phase. Numerical experiments have shown that the developed algorithm provides the reconstruction result of signal samples with a sufficiently low error. The algorithm is implemented as a software module. The operation of the module is carried out on the basis of asynchronous control of the sampling reconstruction process. It can be used as part of metrologically significant software for digital signal processing systems.

Convolutional Neural Network for Phase-Only Hologram Optimization Based on the Point Source Method With the Holographic Viewing-Window

An optimization algorithm for phase-only hologram (POH) based on the point source method (PSM) with the holographic viewing-window (HVW) by using a convolutional neural network (CNN) is proposed. The network training adopts an unsupervised strategy that maps the target image to optimized constant phases (OCPs) corresponding to the wavefront of each point source instead of random constant phases (RCPs), and then the optimized POH can be obtained by wavefront superposition. The simulation and experimental results show that the speckle noise of the reconstruction is significantly suppressed compared with the initial random phase method (RPM), which demonstrates the feasibility of the proposed method and shows a strong generalization ability of the trained CNN. The HVW of a holographic near-eye display (NED) has a continuous observation range of about 6 mm in the horizontal direction without using additional optical expansion elements, and a complete high-quality image can be observed within this range.

Speed Interference Suppression for PD Radar Based on Adaptive Dictionary

Random pulse initial phase (RPIP) signal is a kind of agility waveform which is commonly used in pulse Doppler (PD) radar. Although RPIP has the merit of restraining velocity deception jamming effectively, its efficiency is restricted under the condition of strong interference. To make the RPIP signal fully play the anti-jamming performance, this paper proposed a speed interference suppression method based on adaptive dictionar that separates the target echo from the strong jamming signal with good sparsity. First, the prior knowledge of strong interference signal is obtained by the technique of peak detection which is combined with the dual channel processing. Second, the quasi-Karhunen-Loeve transform (Q-KLT) basis of interference signal is constructed based on the prior knowledge, and the approximate Q-KLT basis of target signal is constructed by the way of dictionary learning, and those signals can be obtained from the adaptive dictionary by the algorithm of base tracking (BP). Finally, the effectiveness of the proposed method is verified by numerical simulation, which proves that the method can ensure a lower Doppler sidelobe in the strong interference scene, which confirmed that it has a good anti-velocity deception performance.

Effects of High-Order Nonlinearities on Freak Wave Generation in Random Sea States

High-order nonlinearities may be an important cause of freak wave generation; however, it is still unclear how to stimulate the generation of freak waves in deep-water random waves. This study employs the modified fourth-order nonlinear Schrӧdinger equation (mNLSE) to simulate the occurrence of freak waves and analyses the influence of high-order nonlinearities on the evolution of random wave trains described initially by the JONSWAP spectrum. In the evolution of freak wave generation, variations in the linear and nonlinear terms of the mNLSE are displayed with the nonlinear growth of surface elevations. For comparison, the corresponding results from the cubic nonlinear Schrӧdinger equation (CSE) and the linear Schrӧdinger equation (LSE) are also obtained. Power spectra and spectral peakedness curves in the evolution of the wave train are also given to analyze the potential mechanism of freak wave formation. Additionally, the probabilities of freak wave appearances are estimated for different initial parameters and different governing equations. The results show that the fourth-order nonlinearity plays an important role in the generation of freak waves, but this single factor is not enough to generate freak waves, and freak wave occurrence is the contribution of multiple factors to the unstable evolution of the wave train. The higher-order nonlinearity, concentrated initial random phases, larger wave steepness, narrower initial spectral width, and smaller sideband instability parameter can increase the probability of freak wave generation.

ALGORITHM OF RANDOM START PHASE CORRECTION AND FREQUENCY OFFSET IN THE COMMUNICATION SYSTEM WITH THE QUADRATURE MODULATION

The goal of the work is to find a solution, realization, and modelling of the algorithm for the compensation of a start random phase error of a quadrature signal, which began at the input of the receiver’s digital part. This algorithm also solves the problem of carrier frequency error offset. These errors have enough values for the lock-band of Costas PLL using minimum hardware resources. To complete this task, the realization and modelling algorithm problems of phase and frequency offset error corrections in Matlab Simulink IDE, arising from Costas PLL, were solved. This algorithm sets values errors for Costas PLL work stability. From the results of calculation and modelling obtained in the article, it follows that the developed model of the receiving path completely eliminates the probability of the error of a random initial phase and frequency offset in the receiver model of a QPSK signal, before the PLL loop is switched on, which significantly reduces the time of readiness for operation of this model.

Reconstructed quality improvement with a stochastic gradient descent optimization algorithm for a spherical hologram.

The spherical holography is a promising technology to realize a true three-dimensional (3D) display. Compared to plane holography and cylindrical holography, it has an unlimited field of view, which can be observed from all perspectives. However, so far, the reconstructed images from computer-generated spherical holograms (CGSHs) are not of high quality, especially phase-only holograms, which will seriously affect its application. In this paper, an optimization algorithm for a CGSH based on stochastic gradient descent (SGD) is proposed to improve the quality of the reconstructed image. First, a new, to the best of our knowledge, diffraction model used in the process of optimization is proposed by considering the obliquity factor and occlusion culling. Based on our proposed diffraction model, the optimization process includes diffracting the initial random phase to another sphere, calculating the loss between the reconstructed image and the original image, and optimizing the initial phase through the SGD optimization algorithm. Both the correctness of the proposed diffraction model and the effectiveness of the SGD optimization for spherical holograms are verified well by numerical simulations. Through SGD, a high-quality reconstructed image can be achieved, which is 18 dB higher in the PSNR than that of spherical self-diffraction iteration. Meaningfully, our method has broad application prospects in 3D and omnidirectional displays. The SGD optimization algorithm is brought into the CGSH, and remarkable results have been achieved.

Real-time reconstruction of high energy, ultrafast laser pulses using deep learning

We report a method for the phase reconstruction of an ultrashort laser pulse based on the deep learning of the nonlinear spectral changes induce by self-phase modulation. The neural networks were trained on simulated pulses with random initial phases and spectra, with pulse durations between 8.5 and 65 fs. The reconstruction is valid with moderate spectral resolution, and is robust to noise. The method was validated on experimental data produced from an ultrafast laser system, where near real-time phase reconstructions were performed. This method can be used in systems with known linear and nonlinear responses, even when the fluence is not known, making this method ideal for difficult to measure beams such as the high energy, large aperture beams produced in petawatt systems.

Optimal nonlinear filtering of M-PSK signals against a background of harmonic interference with a random initial phase

Objectives. The widespread use of radio data transmission systems using signals with multiposition phase shift keying (MPSK) is due to their high noise immunity and the simplicity of constructing the transmitting and receiving parts of the equipment. The conducted studies have shown that the presence of non-fluctuation interference, in particular, harmonic interference, in the radio channel significantly reduces the noise immunity of receiving discrete information. The energy loss in this case, depending on the interference intensity, can range from fractions of dB to 10 db or more. Therefore, interference suppression is an important task for such radio systems. The aim of the work is to synthesize and analyze an algorithm for optimal nonlinear filtering of MPSK signals against a background of harmonic interference with a random initial phase.Methods. The provisions of the theory of optimal nonlinear signal filtering and methods of statistical radio engineering are used.Results. The synthesis and analysis of the algorithm of optimal nonlinear filtering of MPSK signals against the background of harmonic interference with a random initial phase are carried out. The synthesized receiver contains a discrete symbol evaluation unit, two phase-locked frequency circuits of reference generators that form evaluation copies of the signal and interference, and cross-links between them. Analytical expressions are obtained that allow calculating the dependences of the bit error probability on the signal-to-noise ratio and the interference intensity µ. It is established that uncompensated fluctuations of the initial phase of the useful signal have a greater effect on the receiver noise immunity than similar fluctuations of the phase of harmonic interference, especially with low positional signals.Conclusions. Comparison of the obtained results with the results obtained in the case when there are no harmonic interference compensation circuits shows that the use of the obtained phase filtering algorithms allows for almost complete suppression of harmonic interference. Thus, if µ = 0.5 and the probability of error is 10−2, the energy gain at M = 2 is about 2.5 dB, at M = 4 – about 6 dB, at M = 8 and M = 16 – at least 10 dB.

An Adaptive Filtering Algorithm in Pulse-Doppler Radar for Counteracting Range-Velocity Jamming

In this paper, an anti-jamming scheme based on transmitted multiple pulses through random initial phases and adaptive iterative filtering algorithm is considered for counteracting range-velocity deceptive jamming in Pulse-Doppler (PD) radar system. This anti-jamming scheme relies on the fact that the digital radio frequency memory (DRFM) repeated jammer needs more than one pulse repetition interval PRI (at least one PRI) to identify the radar transmitted pulses, and therefore uses the captured pulses of the lag PRIs to reproduce multiple false targets. As a consequence, an adaptive-iterative algorithm to estimate the range-Doppler plane of the real targets in range dimension processing and Doppler dimension processing can appropriately suppress the deceptive false targets, which employed the lagged PRIs for the radar deception. Firstly, the proposed method achieves the optimal estimation of the true targets and false targets in the range dimension. Then, with the estimation information in the range dimension, the presented method estimates the range-Doppler plane of the true targets and false targets. Based on these estimations the deceptive jamming can be easily suppressed with few numbers of iterations and outstanding suppression performance. Finally, we evaluate the performance of the proposed method as well as achieving a good trade-off between anti-jamming performance and computational complexity via numerical simulations.