Time-varying Plasma Sheath Research Articles

A Multi-Cycle Echo Energy Concentration Method for High-Mobility Targets Enveloped by Time-Varying Plasma Sheath

When a target moves at hypersonic speed, the aerodynamic thermal effect will cause air molecules to form a plasma sheath that envelopes the outer surface of the target, which consists of a large number of charged particles. The plasma sheath imposes a complicated modulation effect on the radar echo signal in terms of amplitude, phase, and frequency. When the plasma sheath is time-varying, the inter-pulse coherence of the multi-cycle echo signals is severely disrupted, resulting in the failure of coherent accumulation. To address the problem of abnormal inter-pulse energy accumulation in targets covered with time-varying plasma sheaths, we analyzed the dynamic modulation effects of time-varying plasma sheaths on echo signals and constructed a radar echo model enveloped with time-varying plasma sheaths. Based on this, we propose a method for inter-pulse energy concentration of multi-cycle echo signals based on range-frequency inversion, second-order Wigner–Ville distribution (WVD), and slow-time symmetric auto-correlation. The proposed method is capable of realizing energy concentration for targets enveloped with time-varying plasma sheaths and can accurately estimate the motion parameters of the target. The effectiveness of our proposed method has been verified via simulation analysis of multi-cycle echo signals from targets enveloped with time-varying plasma sheaths, and the reliability of the method has been further validated through statistical experimental analysis.

Spatial Selectivity of Plasma Sheath Channel at Millimeter Wave Band for Hypersonic Vehicle

Millimeter wave is a potential way to overcome the blackout problem. However, the plasma sheath is axially nonuniform, and it has different effects on millimeter wave at different axial positions. In this article, the influences of the spatially inhomogeneous time-varying plasma sheath on millimeter waves are investigated. The electron density model is established, the time-domain sequence of the random channel is calculated, and the channel statistical parameters at different axial positions are extracted. The results show that the millimeter wave channel is spatially selective. Millimeter waves can transmit through the plasma sheath with less attenuation, multiplicative interference, and nonlinear effects at any position of the vehicle except the nose. When the antenna position is properly selected, the attenuation and multiplicative interference intensity can be further reduced. This indicates that millimeter wave communication technology is the most promising way to overcome the blackout problem and accomplish diverse communication tasks of a hypersonic vehicle.

Evaluation of BER for the EHF Communication System Serving Sharp-Coned Reentry Vehicles

“Communication blackout” could lead to severe risks to reentry vehicles. Previous studies have shown that EHF (extremely high frequency) communication is a potential solution to the “communications blackout” and was mostly used for blunt-coned vehicles. EHF communication with sharp-coned vehicles was rarely concerned before. In the present study, the propagation characteristics of the modulated EHF signals in a time-varying plasma sheath covering sharp-coned vehicles were studied numerically. The plasma sheath was obtained by solving a hypersonic fluid dynamics model. The signals propagation model is developed based on geometric optical theories. The carrier frequencies concerned in the present study are the “atmospheric window” frequencies, which are 94, 140, and 225 GHz, respectively. Based on the signal propagation characteristics, the EHF communication system was modeled. The modulation modes concerned in the present study are the 2ASK, 2PSK, and 2FSK, respectively. The results show that 1) the transmission coefficient of EHF signals in the side channel of the plasma sheath of the sharp-coned reentry vehicle increases with carrier frequency, 2) the gap between different channels at specific carrier frequency decreases with time, 3) the phase shift tends to be stable as the carrier frequency increases, and 4) the bit error rate (BER) varies with time and is affected by the location of the onboard antenna, carrier frequency, and modulation mode. The study shows that, in order to achieve good BER performance for the EHF communication system, 2PSK modulation of the signal at 140 GHz is recommended, and the onboard antenna is suggested to be installed on the wall and close to the bottom of the sharp-coned vehicle.

Numerical modeling on the bit error rate of EHF communication in time-varying hypersonic plasma sheath

Plasma sheaths enveloping hypersonic vehicles could yield a communication blackout. Many previous studies have shown that the electromagnetic wave in an extremely high frequency (EHF) band could penetrate a hypersonic plasma sheath effectively. In other words, the EHF communication could be a potential solution to the communication blackout problem. Nevertheless, most of those works used to concern only the EHF signal attenuation. In addition, those works normally treated plasma sheaths as a static plasma layer. However, plasma sheaths always keep evolving. In the present study, the modulated EHF signal propagation in a time-varying plasma sheath was investigated numerically. The plasma sheath was obtained with a hypersonic hydrodynamical model that has been utilized in previous studies. The EHF signal propagation was modeled based on theories of geometrical optics. The frequencies studied are 94, 140, and 225 GHz. The investigation revealed that not only signal attenuation but also the phase shifts for carrier waves vary with time. Their impact on the bit error rate (BER) of the EHF communication system was studied numerically. The modulation modes concerned in the present study are 2ASK, 2PSK, 4QAM, and Non-Coherent demodulation 2FSK (NC-2FSK). According to the study, the BER keeps varying with time. This study also showed that the BER is impacted by the carrier frequency, modulation mode, and the demodulation method. According to the comparison and the analysis, the suggested modulation modes are 2PSK and 4QAM at the carrier frequency of 140 GHz, which could lead to smaller and more stable BER for the EHF communication system utilized by hypersonic vehicles.

Analysis of inverse synthetic aperture radar imaging in the presence of time-varying plasma sheath

The plasma sheath can induce radar signal modulation, causing not only ineffective target detection, but also defocusing in inverse synthetic aperture radar (ISAR) imaging. In this paper, through establishing radar echo models of the reentry object enveloped with time-varying plasma sheath, we simulated the defocusing of ISAR images in typical environment. Simulation results suggested that the ISAR defocusing is caused by false scatterings, upon which the false scatterings’ formation mechanism and distribution property are analyzed and studied. The range of false scattering correlates with the electron density fluctuation frequency. The combined value of the electron density fluctuation and the pulse repetition frequency jointly determines the Doppler of false scattering. Two measurement metrics including peak signal-to-noise ratio and structural similarity are used to evaluate the influence of ISAR imaging.

Analysis of Echo Characteristics of Spatially Inhomogeneous and Time-Varying Plasma Sheath

The “black barrier” phenomenon caused by plasma sheath during the reentry of a high-speed target will seriously affect the detection of radar echo by a ground monitoring station, which is not conducive to making corresponding adjustments to different situations in real-time. The echo reflects the information of the target’s position and speed, which is significant for real-time monitoring and effective strike. In this work, the effect of a high-speed target plasma sheath on electromagnetic wave echo characteristics was investigated by using the proposed spatially inhomogeneous and time-varying plasma sheath model. The Z-transform finite-difference time domain (Z-FDTD) method was adopted to calculate the time domain and frequency domain results of the echo in plasma sheaths with spatially inhomogeneous, uniform and spatially inhomogeneous and time-varying electron density distributions. The effects of different time-varying parameters and plasma parameters on the echo characteristics of the plasma sheath were analyzed. The results show that the reflected echo in spatially inhomogeneous and time-varying plasma is less than that of the other two. The magnitude of the reflected echo is proportional to the time-varying parameter peak coefficient and Gaussian width, and inversely proportional to the collision frequency and plasma thickness. The theoretical results provide important guidance for ground monitoring and anti-stealth.

Effect of Time-Varying Plasma Sheath on Hypersonic Vehicle-Borne Radar Target Detection

Hypersonic vehicle-borne radar target detection will suffer from time-varying plasma sheath which is formed during hypersonic flight. In this study, effect of time-varying plasma sheath on hypersonic vehicle-borne radar target detection is investigated. First, the radar echo model coupling time-varying plasma sheath effect is proposed using an analytical computation method. The regulation of electron density variation is based on flow parameters. Coherent integration result with the present of time-varying plasma sheath effect is derived. The degradations of hypersonic vehicle-borne radar target detection under time-varying plasma sheath are studied through real hypersonic vehicle flight cases. Simulation results shows that high electron density of time-varying plasma sheath will cause significant attenuation, which will lead to decrease of detection probability. In some cases, the signal-noise ratio (SNR) threshold that target can be detected increases more than 40 dB compared with situation without time-varying plasma sheath. Moreover, time-varying plasma sheath will cause time-varying amplitude and phase in pulse and between different pulses, causing intra-pulse and inter-pulse modulation phenomena. These phenomena lead to the disappearance of peak value in range-Doppler plane which will degrade the coherent accumulation as well as target detection performance. By using plasma sheath electron density diagnosis method on vehicle, compensation factor according to the electron density can be established to compensate plasma sheath effect in radar echoes. Simulations results based on real hypersonic vehicle flight flow parameters confirm the conclusions above. The work in this paper will benefit the design and application of hypersonic vehicle-borne radar in the future.

Short-Frame Fountain Code for Plasma Sheath With “Communication Windows”

The surface of a hypersonic vehicle traveling at a speed exceeding Mach 10 is covered by a plasma sheath. The plasma sheath is a complex dynamic random medium that seriously attenuates electromagnetic (EM) waves and generates the so-called blackout phenomenon. However, owing to changes in vehicle flight parameters, such as the angle of attack, speed, and altitude, or the effects of plasma weakening control measures, the attenuation effect of the plasma sheath on EM waves weakens for a short time. At times, the amplitude of the EM waves is higher than the communication threshold, and the EM waves penetrate the plasma sheath in a so-called “communication window”. However, the random temporal variance of the plasma sheath parameters causes the required parameters of the “communication windows” to appear randomly, resulting in the traditional communication methods that needs to keep the communication link open for a long time being no longer applicable. To maximize the use of these “communication windows”, this paper proposes a short-frame fountain code (SFFC), constructs a time-varying plasma sheath channel model, and studies the relationship between the SFFC parameters and the transmission performance of this particular channel. Simulation and experimental results show that the use of SFFC improves the reliability of communication through the plasma sheath. The uninterrupted and correct transmission of information can be achieved even when the plasma equivalent frequency is close to the carrier frequency.

A Novel Demodulation Method Based on Spectral Clustering for Phase-Modulated Signals Interrupted by the Plasma Sheath Channel

The phenomenon of radio blackout due to a plasma sheath during reentry has attracted much attention over the last several decades. However, radio blackout has long puzzled aerospace researchers and has not yet been completely resolved. Owing to the effects of the time-varying plasma sheath channel environment, the constellation of received signals exhibits multiple manifolds, making the traditional algorithms based on Euclidean distance unable to perform demodulation. In the current study, we proposed a novel demodulation method based on spectral clustering for phase-modulated signals interrupted by the plasma sheath channel. Experimental results revealed that as long as the receiving radio waves were above the floor of receiver’s dynamic range, the proposed algorithm effectively classified received signals after time-varying plasma. The parasitic modulation interference caused by time-varying plasma was restrained effectively through the novel algorithm. In contrast to the traditional communication method, the proposed method can be applied to telemetry, track and command, as well as communication between reentry vehicles and near-space hypersonic vehicles in future.

A Joint Demodulation and Estimation Algorithm for Plasma Sheath Channel: Extract Principal Curves With Deep Learning

For reentry communication, owing to the influence of the time-varying plasma sheath, the received IQ baseband signals are severely rotated on constellation. Researches have shown that the frequency of electron density varies from 20kHz to 100 kHz which is on the same order as the symbol rate of most TT&C communication systems and traditional estimation algorithms cannot track the variation of channel. In this letter, motivated by principal curve analysis, we propose a deep learning (DL) algorithm which is called symmetric manifold network (SMN) to extract the curves on the constellation and classify the signals based on the curves. The key advantage is that SMN can achieve joint optimization of demodulation and estimation. From our simulation results, the new algorithm significantly reduces the symbol error rate (SER) compared to existing algorithms and enables accurate estimation of fading with extremely high bandwidth utilization rate.

Effects of Plasma Sheath on Parameter Estimations of Linear Frequency Modulation Pulse Signal

A space vehicle traveling in the atmosphere at hypersonic speed is enveloped by a time-varying plasma sheath, and the performance of onboard radar reconnaissance system will be significantly interrupted. Plasma sheath would generate parasitic modulations of the amplitude and phase of radar signals. Therefore, based on the transmission coefficient of radar wave in time-varying plasma sheath, the Wigner–Hough transform and autocorrelation time-domain signal detection method are used to estimate the frequency- and time-domain parameters of the linear frequency modulation (LFM) pulse signal statistically. A variation rule of the estimation errors of signal parameters is established under various plasma characteristics parameter and frequency and bandwidth of LFM waves. The critical signal-to-noise ratio that is the threshold value for failure of signal parameter estimation has been accurately obtained for different electron densities and radar frequencies. The calculation results could provide useful information for onboard electronic reconnaissance system in further applications.

Bit Error Rate and Channel Capacity Performance of Telemetry Modulation Methods Under Typical Reentry Plasma Sheath Channel

Due to the severe impact of plasma turbulence on electromagnetic waves, the dynamic plasma sheath can degrade communication quality, even resulting in communication blackouts. This article studies the effect of different frequency bands and two typical telemetry modulation methods on communication signals under a time-varying plasma sheath channel. First, considering plasma dynamics on different scales, a typical reentry plasma sheath channel response is simulated and analyzed. Then, the average bit error rate (BER) and channel capacity of $M$ -ary phase-shift keying (MPSK) and $M$ -ary frequency-shift keying (MFSK) evaluating the telemetry communication performance are derived theoretically and simulated numerically based on the typical reentry plasma sheath channel response. The simulation results show that BPSK and noncoherent-MFSK (NC-MFSK) in the Ka -band and above bands have a preferable communication performance; when bit-to-noise ratio > 10 dB, BER $ and channel capacity loss $ for both BPSK and NC-MFSK ( $M\ge 8$ ) modulations in the especial reentry plasma condition (ERPC). Comparing BPSK and NC-MFSK in the Ka -band and above bands, the performances of BER and channel capacity follow the order: NC-MFSK ( $M \ge 8$ ) > BPSK > NC-4FSK > NC-2FSK. In particular, results indicate that under the dynamic plasma channel, terahertz communication can effectively improve communication performance and alleviate communication blackout.

Investigation on reason of range profile distortion of plasma sheath target

The range profile of the plasma sheath target is always found to be distorted when using the linear frequency modulation signal as the radar detection signal. As a result, the detection and tracking of the target became hard, or even failure. Here, three possible reasons of the range profile distortion is investigated in detail: (i) The broadening of the particles in the radial direction of the radar detection when the plasma sheath is produced; (ii) The scatterers in one range gate have different radial velocities that the range profile is dispersion due to the range-Doppler coupling effect; (iii) The amplitude and frequency of the echo signal are modulated by the time-varying plasma sheath. Here, the influence of the above three mechanisms on the range profile is simulated. In addition, for the accurate detection and tracking of these targets, the reason of the distortion should be distinguished. Therefore, several methods are proposed to distinguish the different mechanisms for the range profile distortion.

FDTD Simulation of Three-Wave Scattering Process in Time-Varying Cold Plasma Sheath

In this paper, a three-dimensional finite-difference time-domain (FDTD) method is developed to simulate the three-wave scattering process as a numerical experiment of the nonlinear interaction between two monochromatic plane waves in a plasma slab. This electromagnetic (EM)-plasma coupled system is governed by Maxwell's equations and the momentum equations of electron-only cold plasma. To model the system using the FDTD method, a simple and efficient periodic boundary condition is proposed and analyzed using the Floquet mode theory. The simulation result for the plasma slab with a linearly increasing electron density profile demonstrates that it is feasible to use the proposed formulations for the three-wave scattering process. Then, additional simulations are performed for the plasma slab with different electron density profiles and different incident angles of a signal wave as case studies to show the capability of the developed method for various environments.

Analysis of the electromagnetic scattering characteristics in two-dimensional time-varying and spatially non-uniform plasma sheath

Hypersonic vehicles are affected by plasma sheath, which influences information transmission and target recognition. This study analyzes the scattering characteristics of different parameters of electromagnetic (EM) waves in a time-varying plasma sheath. The finite-difference time-domain algorithm is applied. An empirical formula of plasma collision frequency is used, and the electron density is assumed to vary with time, causing the plasma frequency to also vary with time and rise exponentially. Different time-varying laws on EM scattering are compared. Radar cross section of different parameters, including the flight altitude, flight Mach number, attack angle, cyclotron frequency of the electron, incident EM wave frequency, and incident EM wave angle, is calculated and analyzed in time-varying plasma.

Instantaneous polarization statistic property of EM waves incident on time-varying reentry plasma

An analytical method is proposed in this paper to study the effect of time-varying reentry plasma sheath on the instantaneous polarization statistic property of electromagnetic (EM) waves. Based on the disturbance property of the hypersonic fluid, the spatial-temporal model of the time-varying reentry plasma sheath is established. An analytical technique referred to as transmission line analogy is developed to calculate the instantaneous transmission coefficient of EM wave propagation in time-varying plasma. Then, the instantaneous polarization statistic theory of EM wave propagation in the time-varying plasma sheath is developed. Taking the S-band telemetry right hand circularly polarized wave as an example, effects of incident angle and plasma parameters, including the electron density and the collision frequency on the EM wave's polarization statistic property are studied systematically. Statistical results indicate that the lower the collision frequency and the larger the electron density and incident angle is, the worse the deterioration of the polarization property is. Meanwhile, in conditions of critical parameters of certain electron density, collision frequency, and incident angle, the transmitted waves have both the right and left hand polarization mode, and the polarization mode will reverse. The calculation results could provide useful information for adaptive polarization receiving of the spacecraft's reentry communication.

Study of the influence of time-varying plasma sheath on radar echo signal

The time-varying plasma sheath surrounding a reentry spacecraft (or object) can influence the radar detection of the spacecraft seriously, causing detection error or even track loss. To study the influence of plasma sheath on radar detection, a time-varying plasma sheath model based on scattering matrix method is constructed. In the model, the surface media of reentry object is considered, together with some algorithm adjustments to avoid computational singularity, and the time-varying characteristics of plasma sheath are taken into account based on available measured data. By the model, the reflection coefficient of plasma sheath and the radar echo reflected by plasma-covered object are both calculated. And then a processing method of time-varying echo signal based on ambiguity function are put forward, by which the time delay and Doppler frequency of echo signal are analyzed. In the simulation, the rules of a series of time-varying parameters of plasma affecting the reflection coefficient are analyzed. Then, by ambiguity function analysis, the influence rules of plasma sheath on radar echo are revealed, accompanied by some qualitative and quantitative results. The proposed model, method, and simulation results are thought to be helpful for the radar detection of plasma-covered reentry objects.

Improved Type3-PLL to Mitigate Parasitic Amplitude Modulation Effects Caused by Time-Varying Plasma Sheath

Time-varying plasma sheath likely causes parasitic amplitude and phase modulation effects on communication signals. It can increase the carrier tracking error of tracking telemetry and command systems for hypersonic vehicles flying in near space, and it may lead to loss of lock under serious conditions. This paper comprehensively analyzes the influence mechanism of the amplitude modulation effects on the loss threshold of Type3-phase-locked loop (PLL) in phase-locked receivers. Analysis result shows that amplitude fading in time-varying plasma sheaths is similar to the Gaussian distribution unrelated to the fluctuant densities. The standard deviation of amplitude fading increases with the fluctuant intensity. The 8% fluctuant intensity of electron density begins to have a significant impact on the lock probability of Type3-PLL. On the basis of the analysis results and the amplitude modulation effects, Type3-PLL with a prefiltering (PF-Type3-PLL) method is proposed to mitigate the amplitude modulation effects. PF is placed before the discriminators of Type3-PLL to restrict the amplitude variation within a reasonable range. The tracking loop PF-Type3-PLL is tested with spatial–temporal fluctuant plasma sheath model and compared with the traditional Type3-PLL. Tracking results show that PF-Type3-PLL is more robust than the traditional Type3-PLL. The phase error jitter is significantly reduced when the fluctuant intensity is 8%, and the loss threshold is reduced by 4 dB. The robustness is also enhanced under different loop noise bandwidths (5–15 Hz).

Influence of Time-Varying Plasma Sheath on the Lock Condition of Phase-Locked Loop for TT&C Carrier Tracking System

Time-varying plasma sheath likely causes a parasitic phase modulation effect on communication signals. It is essential to understand the effect of plasma sheath on the tracking telemetry and command (TT&C) systems for blackout mitigation. This paper comprehensively investigates the impact of parasitic phase modulation effect on the TT&C tracking system of Ka band signals, especially single-frequency and phase-modulated signals. A fluctuant electron density model in the space-time domain is initially established. The phase noise caused by the time-varying plasma sheath is then obtained through wave impedance numerical calculation method. The effect of the time-varying plasma sheath with different fluctuant intensities on the carrier tracking performance is investigated and quantitatively analyzed by imposing phase noise on a phase-locked loop model. Simulation results show that a large fluctuant intensity corresponds to a great impact on the lockout threshold. A critical fluctuant intensity is observed in the three typical TT&C signals. The effect of the time-varying plasma sheath on phase-modulated signals is more severe than that on single-frequency signals. The maximum tolerable fluctuant intensities are 12%, 10%, and 6% for single-frequency signals, binary phase shift keying signals, and quadrature phase shift keying signals, respectively. With the critical fluctuant intensity, their lockout thresholds are increased to 0, 6, and 4 dB, respectively.

Research on the FDTD method of scattering effects of obliquely incident electromagnetic waves in time-varying plasma sheath on collision and plasma frequencies

This study analyzes the scattering characteristics of obliquely incident electromagnetic (EM) waves in a time-varying plasma sheath. The finite-difference time–domain algorithm is applied. According to the empirical formula of the collision frequency in a plasma sheath, the plasma frequency, temperature, and pressure are assumed to vary with time in the form of exponential rise. Some scattering problems of EM waves are discussed by calculating the radar cross section (RCS) of the time-varying plasma. The laws of the RCS varying with time are summarized at the L and S wave bands.