Radar Experiment Research Articles

Broadband multi‐carrier linear frequency modulation signal reception with subcarrier frequency offset deramp processing

AbstractIn this paper, a broadband multi‐carrier linear frequency modulation (LFM) signal reception method with subcarrier frequency offset deramp processing is proposed and investigated. The proposed frequency offset deramp processing is implemented by mixing the multi‐carrier LFM radar echo with a multi‐carrier LFM reference that has a different subcarrier frequency interval. With this design, the sampling rate of the radar receiver is remarkably reduced and crosstalk‐free separation of different subcarrier signals is easily conducted in the frequency domain. To fuse the multiple subcarriers and fill the frequency gaps, a sparse reconstruction method is employed to obtain the broadband response, which is essential for achieving high range resolution detection. The effectiveness of the proposed method is validated through an experiment in which the reception of an 8‐carrier LFM signal is conducted and a total bandwidth of 6 GHz after multi‐carrier fusion is demonstrated. An inverse synthetic aperture radar imaging experiment is also conducted with the results verifying the good potential of the proposed method in practical applications.

Weather Radar Calibration Method Based on UAV-Suspended Metal Sphere.

Weather radar is an active remote sensing device used to monitor the full lifecycle changes in severe convective weather with high spatial and temporal resolution. Effective radar calibration is a crucial foundation for ensuring the high-quality application of observational data. This paper utilizes a UAV platform equipped with a high-precision RTK system and standard metal spheres to study the principles and methods of metal sphere calibration, constructing a complete calibration process and calibration accuracy evaluation metrics. Additionally, a collocated radar comparison observation experiment was conducted for cross-validation, and metal sphere calibration tests were performed on problematic radars. The experimental results indicate the following: (1) The combined application of a high-precision RTK system and a laser range camera can provide real-time position information on the metal sphere, improving the efficiency of radar target acquisition. (2) The calibration method based on UAV-suspended metal spheres can periodically conduct the quantitative calibration of Z and ZDR, achieving calibration accuracies within 0.5 dB and 0.2 dB, respectively, and supports the qualitative inspection of key parameters such as beamwidth and pulse width. (3) During field tests, a high success rate "coarse adjustment + fine adjustment + staring" sphere-finding technique was established, based on automatic switching between RHI, PPI, and FIX scanning modes. This method directs the UAV to adjust the metal sphere to the center of the radar distance bin, reducing the impact of uneven beam filling and bin crossing, ensuring the accuracy of scattering characteristic measurements.

Surface properties of the seas of Titan as revealed by Cassini mission bistatic radar experiments

Saturn’s moon Titan was explored by the Cassini spacecraft from 2004 to 2017. While Cassini revealed a lot about this Earth-like world, its radar observations could only provide limited information about Titan’s liquid hydrocarbons seas Kraken, Ligeia and Punga Mare. Here, we show the results of the analysis of the Cassini mission bistatic radar experiments data of Titan’s polar seas. The dual-polarized nature of bistatic radar observations allow independent estimates of effective relative dielectric constant and small-scale roughness of sea surface, which were not possible via monostatic radar data. We find statistically significant variations in effective dielectric constant (i.e., liquid composition), consistent with a latitudinal dependence in the methane-ethane mixing-ratio. The results on estuaries suggest lower values than the open seas, compatible with methane-rich rivers entering seas with higher ethane content. We estimate small-scale roughness of a few millimeters from the almost purely coherent scattering from the sea surface, hinting at the presence of capillary waves. This roughness is concentrated near estuaries and inter-basin straits, perhaps indicating active tidal currents.

Snow water equivalent retrieved from X- and dual Ku-band scatterometer measurements at Sodankylä using the Markov Chain Monte Carlo method

Abstract. Radar at high frequency is a promising technique for fine-resolution snow water equivalent (SWE) mapping. In this paper, we extend the Bayesian-based Algorithm for SWE Estimation (BASE) from passive to active microwave (AM) application and test it using ground-based backscattering measurements at three frequencies (X and dual Ku bands; 10.2, 13.3, and 16.7 GHz), with VV polarization obtained at a 50° incidence angle from the Nordic Snow Radar Experiment (NoSREx) in Sodankylä, Finland. We assumed only an uninformative prior for snow microstructure, in contrast with an accurate prior required in previous studies. Starting from a biased monthly SWE prior from land surface model simulation, two-layer snow state variables and single-layer soil variables were iterated until their posterior distribution could stably reproduce the observed microwave signals. The observation model is the Microwave Emission Model of Layered Snowpacks 3 and Active (MEMLS3&a) based on the improved Born approximation. Results show that BASE-AM achieved an RMSE of ∼ 10 cm for snow depth and less than 30 mm for SWE, compared with the RMSE of ∼ 20 cm snow depth and ∼ 50 mm SWE from priors. Retrieval errors are significantly larger when BASE-AM is run using a single snow layer. The results support the potential of X- and Ku-band radar for SWE retrieval and show that the role of a precise snow microstructure prior in SWE retrieval may be substituted by an SWE prior from exterior sources.

A novel detector for range-spread target detection based on HRRP-pursuing

Range-spread target (RST) detection is a concerned issue in high-resolution radar. Exploitation of target scattering characteristic can improve the detection performance of a RST, but is usually unavailable because of the non-cooperative nature of the target. In this work, a two-stage implemented detector based on an optimized radar workflow is proposed to address this problem. In the first stage, named high-resolution range profile-pursuing (HRRP-pursuing), a fast Fourier transform-initialized Akaike information criterion (AIC) algorithm is proposed to estimate target HRRP using historical echoes. In the second stage, the proposed detector uses the estimated HRRP as a reference signal and performs matched filtering to realize RST detection. Theoretical analysis of the false alarm property of the detector is derived. The effectiveness of the proposed detector is verified using simulated and real radar data experiments and the influences of the number of used historical echoes and target sparseness on detection performance are discussed.

Impact of Direct Radar Reflectivity Data Assimilation on the Simulation of Mesoscale Descending Inflow and Secondary Eyewall Formation in Hurricane Matthew (2016)

AbstractThe impact of assimilating ground‐based radar reflectivity on the rainband structure and secondary eyewall formation (SEF) of Hurricane Matthew (2016) is investigated within the framework of the Hurricane Weather Research and Forecasting model and its hybrid three‐dimensional ensemble‐variational data assimilation (DA) system. Compared to the control experiment (no radar reflectivity DA), the radar reflectivity DA experiment shows a clear signal of concentric eyewall and eyewall replacement cycle. Results demonstrate that radar reflectivity DA improves the stratiform rainband analysis, resulting in the mid‐level cooling associated with mesoscale descending inflow (MDI). The MDI further contributes to the low‐level acceleration maximum with boundary layer dynamics and triggers new convective updrafts in the SEF region. Momentum budget analysis also suggests that the mean vertical advection of absolute angular momentum plays an important role in the local momentum tendency in the SEF region in Hurricane Matthew (2016).

Performance of the Thies Clima 3D Stereo Disdrometer: Evaluation during Rain and Snow Events.

Imaging disdrometers are widely used in field campaigns to provide information on the shape of hydrometeors, together with the diameter and the fall velocity, which can be used to derive information on the shape-size relations of hydrometeors. However, due to their higher price compared to laser disdrometers, their use is limited to scientific research purposes. The 3D stereo (3DS) is a commercial imaging disdrometer recently made available by Thies Clima and on which there are currently no scientific studies in the literature. The most innovative feature of the 3DS is its ability in capturing images of the particles passing through the measurement volume, crucial to provide an accurate classification of hydrometeors based on information about their shape, especially in the case of solid precipitation. In this paper. the performance of the new device is analyzed by comparing 3DS with the Laser Precipitation Monitor (LPM) from the same manufacturer, which is a known laser disdrometer used in many research works. The data used in this paper were obtained from measurements of the two instruments carried out at the Casale Calore site in L'Aquila during the CORE-LAQ (Combined Observations of Radar Experiments in L'Aquila) campaign. The objective of the comparison analysis is to analyze the differences between the two disdrometers in terms of hydrometeor classification, number and falling speed of particles, precipitation intensity, and total cumulative precipitation on an event basis. As regards the classification of precipitation, the two instruments are in excellent agreement in identifying rain and snow; greater differences are observed in the case of particles in mixed phase (rain and snow) or frozen phase (hail). Due to the different measurement area of the two disdrometers, the 3DS generally detects more particles than the LPM. The performance differences also depend on the size of the hydrometeors and are more significant in the case of small particles, i.e., D < 1 mm. In the case of rain events, the two instruments are in agreement with respect to the terminal velocity in still air predicted by the Gunn and Kinzer model for drops with a diameter of less than 3 mm, while, for larger particles, terminal velocity is underestimated by both the disdrometers. The agreement between the two instruments in terms of total cumulative precipitation per event is very good. Regarding the 3DS ability to capture images of hydrometeors, the raw data provide, each minute, from one to four images of single particles and information on their size and type. Their number and coarse resolution make them suitable to support only qualitative analysis of the shape of precipitating particles.

Yolk-shell construction of Co0.7Fe0.3 modified with dual carbon for broadband microwave absorption

The rational and effective combination of multicomponent materials and the design of subtle microstructure for efficient microwave absorption are still challenging. In this study, carbon-coated CoFe with heterogeneous interfaces was space-restricted in the void space of hollow mesoporous carbon spheres through a facile approach involving electrostatic adsorption and annealing, and a high-performance microwave absorber (MAs) (denoted as Co0.7Fe0.3@C@void@C) was successfully prepared. The heterostructure, three-dimensional lightweight porous morphology, and electromagnetic synergy strategy enabled the Co0.7Fe0.3@C@void@C material with yolk-shell structure to exhibit surprising microwave absorption properties. When the annealing temperature and filler loading were 550° C and 15 wt%, respectively, the composites exhibited an effective absorption bandwidth (EAB) of 7.16 GHz at 2.48 mm and a minimum reflection loss of −24.1 dB at 2.11 mm. A maximum EAB of 7.21 GHz at 2.37 mm could be achieved for the composite prepared with an annealing temperature of 650° C. In addition, radar cross-section experiments demonstrated, the potential practical applicability of Co0.7Fe0.3@C@void@C. This work expands a new avenue to develop high-performance and lightweight MAs with ingenious microstructure.

New Approach to Designing Functional Materials for Stealth Technology: Radar Experiment with Bilayer Absorbers and Optimization of the Reflection Loss

AbstractMicrowave power absorption by a two‐layer system deposited on a metallic surface is studied in the experimental setup emulating the response to a radar signal. Layers containing hexaferrite and iron powder in a dried paint of thickness under 1 mm are used. The data is analyzed within a theoretical model derived for a bilayer system from the transmission line theory. A good agreement between experimental and theoretical results is found. The advantage of using a bilayer system over a single‐layer system is demonstrated. How the maximum microwave absorption (minimum reflection) can be achieved through the optimization of the filling factors and thicknesses of the two layers is shown.

Ground-based noontime D-region electron density climatology over northern Norway

Abstract. The bottom part of the Earth's ionosphere is the so-called D region, which is typically less dense than the upper regions. Despite the comparably lower electron density, the ionization state of the D region has a significant influence on signal absorption for propagating lower to medium radio frequencies. We present local noon climatologies of electron densities in the upper middle atmosphere (50–90 km) at high latitudes as observed by an active radar experiment. The radar measurements cover 9 years (2014–2022) from the solar maximum of cycle 24 to the beginning of cycle 25. Reliable electron densities are derived by employing signal processing, applying interferometry methods, and applying the Faraday-International Reference Ionosphere (FIRI) model. For all years a consistent spring–fall asymmetry of the electron density pattern with a gradual increase during summer as well as a sharp decrease at the beginning of October was found. These findings are consistent with very low frequency (VLF) studies showing equivalent signatures for nearby propagation paths. It is suggested that the meridional circulation associated with downwelling in winter could cause enhanced electron densities through NO transport. However, this mechanism can not explain the reduction in electron density in early October.

Integrated Geophysical and Geochemical Analyses for Assessment of Potential Coal Prospects in Tirah Area, Khyber Pakhtunkhwa, Pakistan

This study presents a comprehensive investigation of the Paleocene coal in the Tirah area, District Khyber, Khyber Pakhtunkhwa, Pakistan, utilizing onsite Electrical Resistivity Tomography (ERT) and Ground Penetrating Radar (GPR) experiments combined with geochemical analyses of obtained coal-rock samples. ERT and GPR profiles, along with geochemical data, were collected and meticulously analyzed to assess the potential and quality of coal seams based on coal ranking, aiming to delineate their spatial distribution and future exploitation prospects. The study reveals a wide range of resistivity values, spanning from 8.93 Ωm to 2472 Ωm. The uppermost layer, comprising silt and clay with water saturation, exhibits resistivity values ranging from 8.93 Ωm to 50 Ωm. The subsequent stratum, characterized by wet sandstone with minor shale and clay, has resistivity values between 50 Ωm and 95.3 Ωm. Significantly, the zone with resistivity values between 95.3 Ωm and 800 Ωm is identified as the probable host of the coal seams. Based on the results, the coal seams are estimated to exist at depths ranging from 14 to 23 m, with resistivity values between 95.3 Ωm and 800 Ωm. GPR results further corroborate these findings, revealing coal-bearing strata at various depths, thus confirming the ERT results. Additionally, proximate and ultimate analysis provided insights into the quality of the coal, with average concentration values of moisture content (6.95%), ash content (22.12%), volatile matter (28.55%), fixed carbon (42.40%), carbon content (55.35%), hydrogen (4.7%), nitrogen (0.95%), sulfur (4.82%), and oxygen (10.06%). Comparative analyses of the obtained results with local coals from the Salt Range in Punjab, Pakistan, and coal from Ogboyaga, Nigeria, confirm that the studied coal ranks as sub-bituminous. This comprehensive assessment offers valuable insights into the potential and quality of Paleocene coal in the studied region and is applicable to other areas with similar geological settings.

Space-Based THz Radar Fly-Around Imaging Simulation for Space Targets Based on Improved Path Tracing

Aiming at the space target detection application of a space-based terahertz (THz) radar, according to the imaging mechanism of broadband THz radars, a THz radar imaging simulation method based on improved path tracing is proposed. Firstly, the characterization method of THz scattering characteristics based on Kirchhoff’s approximation method is introduced. The multi-parameter THz bidirectional reflectance distribution function (THz-BRDF) models of aluminum (Al), white-painted Al, and polyimide film at 0.215 THz are fitted according to the theoretical data, with fitting errors below 4%. Then, the THz radar imaging simulation method based on improved path tracing is presented in detail. The simulation method utilizes path tracing to simulate parallelized THz radar echo signal data, considering multi-path energy scattering based on the THz-BRDF model. Finally, we conducted THz radar imaging simulation experiments. The influences in the imaging process of different fly-around motions are analyzed, and a comparison experiment is conducted with the fast-physical optics (FPO) method. The comparative results indicate that the proposed method exhibits richer and more realistic features compared with the FPO method. The simulation experiments results demonstrate that the proposed method can provide a data source for ground algorithm testing of THz radars, particularly in evaluating the target detection and recognition algorithm based on deep learning, providing strong support for the application of space-based THz radars in the future.

Measurement and evaluation method of radar anti-jamming effectiveness based on principal component analysis and machine learning

With the development of modern electronic countermeasure technology, the fight between radar jamming and anti-jamming has become increasingly fierce. Experts have done a lot of highly effective work on radar anti-jamming performance. However, the emergence of various new complex interferences has rendered existing methods unable to meet the needs. In this manuscript, we consider the measurement and evaluation method of radar anti-jamming effectiveness based on principal component analysis and machine learning. Firstly, taking into account the diversity of variables in radar countermeasure experiments and the complexity of constraints between variables, we propose a bipartite covering array for the experimental scheme, which requires that each level combination of any radar parameter and jammer parameter occurs at least once, to ensure the rationality of the experiments. Secondly, according to the characteristics of multiple jammers and the analysis of impacts on radar performances, we combine the existing indicators and use the principal component analysis method to obtain two comprehensive indicators, which better reflect radar performances. Finally, we select the best model as a prediction for radar comprehensive indicators by comparing several machine learning algorithm models, including classification and regression tree, random forest, xgboost, and SVM. Additional experiments verify the effectiveness of the resulted model.

Random symmetric phase feeding compensation method for phased array radar based on equivalent monopulse model

AbstractIn a phased array radar, the phase quantisation error of phase shifters can lead to the beam steering error (BSE) between the predetermined and the actual directions. Existing researches on phase feeding optimisation suffer from high computational complexity and large storage space. In this study, an equivalent monopulse method is first proposed to yield the BSE with O(N) complexity by formulating the equation between the phase quantisation error and BSE. Further, a symmetric phase feeding compensation (SPFC) method is developed on the basis of the proposed scheme to cancel the phase quantisation error employing a symmetric planar array. Subsequently, a random phase compensation method is formulated to further reduce the residual quantisation errors of SPFC, and a random symmetric phase feeding compensation (RSPFC) method is proposed. The proposed SPFC and RSPFC methods possess O(N) complexities and allow for parallel calculation of element phase feedings, thus making the proposed methods more applicable on the embedded beam controller of a phased array radar. Based on computer simulations and phased array radar experiments, the proposed SPFC and RSPFC methods are validated to yield superior beam pointing accuracies and can improve the fluctuations in angle tracking.

Long-time coherent integration algorithm for high-speed maneuvering target detection

Detection of high-speed maneuvering targets along with motion parameters estimation (MPE) are some of the challenging problems for modern radar systems. Such targets usually induce linear range migration (LRM), quadratic range migration (QRM), and Doppler frequency migration (DFM) problems in signal processing, resulting in severe performance degradation, especially when long time integration is needed for weak target detection. We propose an algorithm for coherent integration and MPE by combining the techniques of generalized dechirp (GD) and new axis rotation moving target detection (NAR-MTD), i.e., the GD-NAR-MTD algorithm, to solve the above problems. Specifically, the GD and NAR approaches can not only correct LRM, QRM, and DFM simultaneously with reduced rotation error in coordinate system transformation but also can abate the computational burden via frequency-domain implementation with rounding and complex addressing operations avoided, so the target’s echo energies can be well accumulated by MTD finally. Both simulation and practical radar experiments are conducted to validate the proposed algorithm. At the same time, the results by the other six typical algorithms are compared for demonstrating the superior performance of the proposed algorithm on detection and MPE. In addition, the equivalence between the practical radar experiment and the simulation experiment is analyzed by comparing the induced RMs and DFMs, which shows that the scaled equivalent experiment is persuasive in algorithm validation.

A Novel Coherent Integration Algorithm for Maneuvering Target Detection Based on Symmetric Instantaneous Autocorrelation Function

Detection and parameter estimation of maneuvering targets having a jerking motion are some of the challenging problems for modern radar systems. Such targets usually introduce range migration (RM) and Doppler frequency migration (DFM) problems leading to serious performance degradation in detection. To address these problems, a novel coherent integration (CI) algorithm is proposed based on a new symmetric instantaneous autocorrelation function (NSIAF), which can be utilized to reduce the order on the slow time and to eliminate the linear range migration (LRM) first. Then, the jerk and acceleration of the target are estimated after applying the keystone transform (KT) and the scaled Fourier transform (SFT); both of these are then used to construct the reference function for matched filtering. Finally, CI and target detection can be accomplished by the scaled inverse Fourier transform (SCIFT) after matched filtering. Both simulation data (this work) and practical radar experiment data (data set of others) were processed to validate the proposed algorithm. Compared with other representative algorithms, our algorithm can achieve a good balance between computational complexity and detection performance.

Simultaneous Multiscale Data Assimilation Using Scale‐ and Variable‐Dependent Localization in EnVar for Convection Allowing Analyses and Forecasts: Methodology and Experiments for a Tornadic Supercell

AbstractThis study introduces a simultaneous multiscale data assimilation method by implementing model space spatial scale‐dependent localization (SDL) and variable‐dependent localization (VDL) within an ensemble variational system. This method updates all resolved scales by assimilating all observations at once. The impact of such an approach is examined by a series of radar data assimilation experiments. Single‐observation experiments show that SDL concurrently and more properly updates the storm and its ambient environments compared to a traditional single scale localization (SSL) for radar data assimilation. Including VDL on top of SDL (SDLVDL) realistically decreases the spatial coverage and intensity of moisture increments compared to SDL. Comparisons are then performed on the analyses and forecasts of the 8 May 2003 Oklahoma City supercell storm. Results show that SDL improves the analyses and forecasts during the data assimilation cycling by producing more realistic enhanced low‐level convergences than SSL. SDLVDL obtains more accurate analyses and subsequent forecasts for moisture than SDL. SDLVDL yields the best performance in reflectivity forecasts and storm maintenance. Compared to SSL, SDL has higher forecast skills before 2230 UTC and produces degraded forecasts in the later lead time.

SkyWatch: A Passive Multistatic Radar Network for the Measurement of Object Position and Velocity

Quantitative three-dimensional (3D) position and velocity estimates obtained by passive radar will assist the Galileo Project in the detection and classification of aerial objects by providing critical measurements of range, location, and kinematics. These parameters will be combined with those derived from the Project’s suite of electromagnetic sensors and used to separate known aerial objects from those exhibiting anomalous kinematics. SkyWatch, a passive multistatic radar system based on commercial broadcast FM radio transmitters of opportunity, is a network of receivers spaced at geographical scales that enables estimation of the 3D position and velocity time series of objects at altitudes up to 80[Formula: see text]km, horizontal distances up to 150[Formula: see text]km, and at velocities to [Formula: see text][Formula: see text]km/s ([Formula: see text][Formula: see text]Mach). The receivers are designed to collect useful data in a variety of environments varying by terrain, transmitter power, relative transmitter distance, adjacent channel strength, etc. In some cases, the direct signal from the transmitter may be large enough to be used as the reference with which the echoes are correlated. In other cases, the direct signal may be weak or absent, in which case a reference is communicated to the receiver from another network node via the internet for echo correlation. Various techniques are discussed specific to the two modes of operation and a hybrid mode. Delay and Doppler data are sent via internet to a central server where triangulation is used to deduce time series of 3D positions and velocities. A multiple receiver (multistatic) radar experiment is undergoing Phase 1 testing, with several receivers placed at various distances around the Harvard–Smithsonian Center for Astrophysics (CfA), to validate full 3D position and velocity recovery. The experimental multistatic system intermittently records raw data for later processing to aid development. The results of the multistatic experiment will inform the design of a compact, economical receiver intended for deployment in a large-scale, mass-deployed mesh network. Such a network would greatly increase the probability of detecting and recording the movements of aerial objects with anomalous kinematics suggestive of Unidentified Aerial Phenomena (UAP).

Interacting Effects of Precipitation and Potential Evapotranspiration Biases on Hydrological Modeling

AbstractThe quality of precipitation (P) and potential evapotranspiration (PET) data greatly affects the hydrological modeling performance. Considerable attention has been paid to identifying the influence of biased P or PET inputs independently. However, few studies have explored the joint interaction of biases in P and PET inputs on hydrological simulations. Here, we investigate the mutual compensation of P and PET biases on the performance of two widely used conceptual hydrological models, the Xinanjiang model and the Probability Distributed Model. P and PET from HYREX (HYdrological Radar EXperiment) and CAMELS‐GB (Catchment Attributes and Meteorology for Large‐sample Studies in Great Britain) data sets are collected over five catchments with varying characteristics in Great Britain. Different biases are added to these original time series to generate 6560 biased input scenarios. The results suggest that there is a certain compensational relationship between the biases in P and PET inputs to reproduce desirable streamflow simulations. A new hydrological proxy named Compensational Interaction Angle (CIA) is identified and found to be stationary with various modeling periods, as well as stable with different hydrological models despite model equifinality. Further, the CIA highly relates to the long‐term climate aridity ratio. The catchments with greater aridity have larger CIAs. This study offers a fresh perspective to analyze the input errors in hydrological modeling. The results can help to better understand P and PET interactions in hydrological modeling, and guide the selection/evaluation/bias‐correction of P and PET data sets for hydrological applications.

A study of radar reflection signal characteristics in multi-domain using a closed plasma generator

This paper theoretically and experimentally studies the radar reflection signal characteristics in a multi-domain using a closed plasma generator, especially for a correlation domain. A multi-domain computation method is proposed for a radar signal reflected by a metal covered with plasma. The reflected signal characteristics are studied in the time, frequency, and correlation domain. A closed plasma generator device is designed to verify the computation method for the radar signal reflected from metal plate covered with plasma experimentally. The plasma in the device is terminated by a transmission window at one end and a metal plate at another end, which is able to provide the environment for a radar signal reflection experiment. Based on the theoretical and the experimental results, the time and frequency domain of radar reflection signal not only show the amplitude attenuation characteristics but also frequency dispersion phenomenon. For the correlation domain characteristics of the radar reflection signal, the peak value in correlation domain significantly decreases, which demonstrates the stealth effect of the plasma. The effect of plasma and radar parameters on the peak value decrease phenomenon, as well as the stealth effect in the correlation domain, is further analyzed.