Geometrical Theory Of Diffraction Research Articles

Three-Dimensional Ray-Tracing-Based Propagation Prediction Model for Macrocellular Environment at Sub-6 GHz Frequencies

This paper presents a 3D ray-tracing model using geometrical optics and the uniform theory of diffraction in radio channel characterizations of macrocellular environments. On the basis of the environmental information obtained from a digitized map, the model is effectively applied. A technique considering multiple reflections and diffractions through the ray path classification is utilized in this model. Ray paths belonging to each ray category are determined using different methods. The proposed model is justified (the prediction accuracy of the model is better than 6.5 dB) with measurement data for the two scenarios and can provide reliable theory as a basis for radio wave propagation prediction and network planning in urban macrocellular environments.

Radiation resistance matrix for baffled simply curved plates for sound power applications

Sound power, a standard metric used to quantify product noise, is determined through the vibration-based sound power (VBSP) method. This method involves measuring surface velocities and utilizing an acoustic radiation resistance matrix, R, dependent on the structure's geometry. While R matrix expressions have been established for baffled flat plates, fully closed cylinders, and fully closed spheres, this work presents the first analytical expression tailored for baffled simply curved plates with uniform curvature. This development, based on eigenfunction expansion and the uniform theory of diffraction, extends the VBSP method's capabilities for accurate sound power assessment from these structures. Experimental validation involved testing three plates of varying curvature in a reverberation chamber, comparing the VBSP method with the ISO 3741 pressure-based standard. One of the curved plates underwent additional testing in an anechoic chamber following the ISO 3745 standard, confirming the VBSP method's accurate sound power measurements down to the 160 Hz one-third octave band. The same plate was tested in uncontrolled acoustic environments — a busy hallway and an outdoor location. The VBSP results showed strong agreement with ISO 3741, affirming the method's robustness for measuring sound power from baffled simply curved plates in acoustically challenging real-world conditions. This underscores the practicality of the VBSP method, enabling accurate sound power measurements of baffled curved plates in the presence of substantial background noise and environmental variability.

Investigation on a compact wideband omnidirectional circularly polarized antenna in an indoor propagation channel for 2.4 GHz application

SummaryIn this paper, for the first time, the capability of a compact low‐cost wideband omnidirectional circularly polarized (CP) antenna to suppress multipath fading characteristics in a typical indoor propagation channel for 2.4 GHz applications is investigated. A ray tracing method based on the geometrical optics and uniform theory of diffraction is applied to analyze an indoor propagation channel using the measured radiation patterns of the proposed antenna. The design uses a conventional monopole antenna with a circular ground plane to generate a vertically polarized electric field. Sequentially flag‐shaped stubs are then added to the ground plane to produce horizontally polarized electric field and to improve the impedance bandwidth of the proposed antenna. The antenna is designed for 2.4 GHz WLAN application with 10 dB impedance bandwidth of 25.5% and 3 dB axial ratio (AR) bandwidth of 24.5%. The polarization can be readily changed between the left‐hand circular polarization (LHCP) and right‐hand circular polarization (RHCP) by altering the direction of the coaxial probe (monopole) or varying the orientation of the printed bended stubs. Both the LHCP and RHCP prototypes of the proposed antenna are designed, fabricated, and tested, and the similar results are obtained.

Equivalence of knife‐edge diffraction model and uniform geometrical theory of diffraction applying Fresnel approximation for an absorbing screen

AbstractThe knife‐edge diffraction model (KED) and the uniform geometrical theory of diffraction (UTD) have been widely used to predict the shadowing effect at millimetre‐wave (mmWave) bands. This letter proposes a mathematical derivation to rigorously prove that, for an absorbing screen, UTD applying the narrow‐angle Fresnel approximation is equivalent to KED. The simulation scenarios are designed to validate the proposal by comparing KED with UTD in the narrow‐angle (less than 20°) and wide‐angle (over 20°) regions at mmWave bands (20100 GHz). Simulated results agree with the proposal that KED is identical to UTD with a low error of less than 0.1 dB in the narrow‐angle region, while they have a difference with an error of over 1 dB in the wide‐angle region. In addition, the average computational time is measured and results in both UTD and KED taking approximately 8.0 ms for one test. From the proposal, it can be theoretically explained the differences and similarities between KED and UTD for an absorbing screen.

Space Target Tracking with the HRRP Characteristic-Aided Filter via Space-Based Radar

Approaching space target tracking is a typical and challenging mission in the space situational awareness (SSA) field. As the space-based radar is able to monitor the space targets of interest full-weather all-time, the space-based radar system is utilized in this paper. However, most multi-target tracking (MTT) filters in target tracking studies merely utilize the location or narrow measurements, and many potentially valuable electromagnetic scattering characteristics are missed, which leads to space target false tracking problems. The space-based radar transmits a wide-band signal, and the measured high-resolution range profile (HRRP) information is an effective characteristic for different target discrimination. Therefore, the HRRP characteristics of space targets are implemented into the update recursion of the MTT filter, which can be utilized to improve the tracking performance. Then, to predict the target HRRP sequence, the geometrical theory of diffraction (GTD) model is utilized. Additionally, a modified spatial spectrum method with a novel covariance matrix is designed to improve the scattering parameter estimation accuracy. Finally, an adapting threshold is devised for merging the Gaussian mixture (GM) components weights. The proposed threshold is on the basis of the proposed HRRP characteristic-aided probability hypothesis density (PHD) filter, and it can tackle the problem of space target discrimination. Simulation results validate the effectiveness and robustness of the proposed probability hypothesis density (HGI-PHD) filter aided by HRRP information and improved with GM weights.

TEFISTA-Net: A learnable method for high-resolution range profile reconstruction with low-frequency ultra-wideband radar

In low-frequency ultra-wideband (LFW) radar, the reconstruction of high-resolution range profile (HRRP) is an important task. The state-of-the-art compressive sensing (CS) method for HRRP reconstruction based on geometrical theory of diffraction (GTD) requires manual algorithm parameter tuning and is computationally expensive. In this paper, we propose a deep learning-based CS method for LFW radar HRRP reconstruction. We design a neural network architecture, i.e., target enhancement-based FISTA-Net (TEFISTA-Net), by unrolling the fast iterative shrinkage thresholding algorithm (FISTA). A new loss function based on the target-to-background ratio (TBR) is introduced for network training with the target enhancement capability in low signal-to-noise ratio (SNR) scenarios. The algorithm parameters in the traditional CS methods are substituted by network parameters learned from training data, getting rid of manual parameter tuning. In addition, simple convolution operations in our new method lead to lower computational complexity compared with existing methods. Experimental results based on diverse data show that the proposed method leads to higher computational efficiency with similar or better performance in comparison with existing state-of-the-art methods.

Dynamic Electromagnetic Scattering Simulation of Tilt-Rotor Aircraft in Multiple Modes.

To study the electromagnetic scattering of tilt-rotor aircraft during multi-mode continuous flight, a dynamic simulation approach is presented. A time-varying mesh method is established to characterize the dynamic rotation and tilting of tilt-rotor aircraft. Shooting and bouncing rays and the uniform theory of diffraction are used to calculate the multi-mode radar cross-section (RCS). And the scattering mechanisms of tilt-rotor aircraft are investigated by extracting the micro-Doppler and inverse synthetic aperture radar images. The results show that the dynamic RCS of tilt-rotor aircraft in helicopter and airplane mode exhibits obvious periodicity, and the transition mode leads to a strong specular reflection on the rotor's upper surface, which increases the RCS with a maximum increase of about 36 dB. The maximum micro-Doppler shift has functional relationships with flight time, tilt speed, and wave incident direction. By analyzing the change patterns of maximum shift, the real-time flight state and mode can be identified. There are some significant scattering sources on the body of tilt-rotor aircraft that are distributed in a planar or point-like manner, and the importance of different scattering sources varies in different flight modes. The pre-studies on the key scattering areas can provide effective help for the stealth design of the target.

Research on Propagation Characteristics Based on Channel Measurements and Simulations in a Typical Open Indoor Environment

At present, it is difficult to obtain the indoor propagation loss quickly and accurately by directly using measurements in the millimeter wave band. To solve this problem, in this paper, a ray tracing method suitable for indoor scenes based on geometric optics theory, the uniform theory of diffraction and image theory is presented; the space-alternation generalized expectation-maximization (SAGE) algorithm is used to analyze the measured data and the multipath information of the wireless channel is analyzed; three deep learning models are used to predict the path loss at different receiving distances based on 1600 sets of path loss data. The results show that the comparison between the ray tracing and experimental results shows a good agreement. Moreover, the root-mean-square error (RMSE) and mean absolute error (MAE) of the long short-term memory (LSTM) network are the smallest, and the LSTM has a better fitting effect on the propagation loss sequences predicted at more distant locations when compared with the recurrent neural network (RNN) and gate recurrent unit (GRU) methods, which can better reflect the propagation trend. This provides theoretical support for the layout of base stations and network optimization in typical open indoor environments.

On UV Photon Distribution of Discharge in GIS Busbar Based on Ray Tracing

In order to clarify the distribution law of the ultraviolet photon field in gas insulated switchgear busbar, meanwhile to correct the detection range of the ultraviolet sensor, the optical model of the gas insulated switchgear busbar based on the uniform theory of diffraction is proposed based on ray tracing. the distributions of the radiation ultraviolet fields are calculated when partial discharge occurs at the key positions such as basin insulator and conductor. Based on the average irradiance, maximum irradiance, and attenuation characteristics, the distribution law in the busbar is further analyzed, which provides a new method to confirm the location of ultraviolet sensors.

Near-to-Far Field RCS Calculation Using Correction Optimization Technique

Radar cross section (RCS) is a scattering measure of an object that scatters to the radar. However, existing methods for near-field (NF) measurement and data processing rarely extract amplitude characteristics, and there is a lack of effective verification of far-field (FF) data in the process of NF to FF transformation, which leads to inaccuracies in FF prediction accuracy. In this paper, we propose a method to establish the relationship between the NF and FF RCS using the state space method (SSM), which is based on accurate estimation of the NF amplitude in NF measurement, and then deriving the FF RCS from the NF scattering signal convolved with a near-to-far kernel. The proposed solution to address the uncertainty issue in reference FF data involves using the geometric theory of diffraction (GTD) scattering center model as the reference FF data and establishing a linear equation with the derived FF model. The negative gradient search (NGS) system identification concept is used to optimize the FF model in order to reduce the discrepancy between the reference and derived values. Finally, the corrected RCS error is provided as additional proof of the effectiveness of these techniques in enhancing near-to-far transformation accuracy by examining the outcomes of three experiments.

UTD-Based Ray-Tracing MIMO Channel Modeling for the Next-Generation Communications Within Underground Tunnels

Limited work has previously been conducted into deterministic modeling of the 5 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> Generation (5G) millimeter (mm)-wave wireless communications within geometrically non-uniform tunnels. This study predicts and analyzes broadband Multiple–Input Multiple–Output (MIMO) propagation in underground mine tunnels for 5G communications and beyond. At extremely short wavelength, each rugged and uneven surface of the tunnel is modelled as a group of diffracting rectangular prism wedges. A deterministic Ray-Tracing (RT) MIMO model is developed based on the Uniform Theory of Diffraction (UTD). All predicted MIMO sub-channels have been successfully fitted with the experimental measurements. MIMO multipath fading of underground tunnels are found to be lognormally distributed and strongly depends on the tunnel’s size and shape.

A Convolutional Neural Network for Parameter Estimation of the Bi-GTD Model

In this paper, a novel parameter estimation method based on a convolutional neural network (CNN) is proposed to extract geometrical features of radar objects. The CNN’s design is inspired by the inversion process of a physically relevant model, called the geometrical theory of diffraction (GTD) model, whose bistatic form can be used to describe the bistatic scattering response from the target in the netted radar system. This model-inspired inversion method can automatically compensate for phase errors between multiple signal channels and obtain better parameter estimation performance than traditional methods, such as the orthogonal matching pursuit (OMP), the estimation of signal parameters via rotational invariance techniques (ESPRIT) and the multiple signal classification (MUSIC). The experimental results not only verify the validity of the proposed intelligent inversion method but also demonstrate the interpretability and generalization ability of the CNN, whose architecture is designed based on mathematical derivation.

Exploring the Validity of Plane and Spherical Millimeter-Wave Incidences for Multiple-Diffraction Calculations in Wireless Communication Systems

The focus of this work is to determine at which threshold can the results for both plane and spherical wave incidence assumptions either converge or deviate when performing multiple diffraction attenuation calculations. The analysis has been carried out—for various millimeter-wave frequencies, inter-obstacle spacings, and angles of incidence—by employing a pair of two-dimensional (2D) hybrid formulations based on both the uniform theory of diffraction and physical optics (UTD-PO). This way, we seek to demonstrate under which circumstances each wave incidence assumption can be valid in environments that entail millimeter-wave bands. Based on this, we may ensure the minimum necessary distance from the transmitter to the first diffracting obstacle for the convergence of the spherical wave incidence solution onto that of the plane wave with a relative error below 0.1%. Our results demonstrate that for less than four diffracting elements, the minimum necessary distance engages in quasi-linear behavior under variations in both the angle of incidence and obstacle spacing. Notably, the considered frequencies (60–100 GHz) have almost no bearing on the results. Our findings will facilitate the simplified, more accurate and realistic planning of millimeter-wave radio communication systems, with multiple diffractions across various obstacles.

Numerical geometric acoustics: An eikonal-based approach for modeling sound propagation in 3D environments

We present algorithms for solving high-frequency acoustic scattering problems in complex domains. The eikonal and transport partial differential equations from the WKB/geometric optic approximation of the Helmholtz equation are solved recursively to generate boundary conditions for a tree of eikonal/transport equation pairs, describing the phase and amplitude of a geometric optic wave propagating in a complicated domain, including reflection and diffraction. Edge diffraction is modeled using the uniform theory of diffraction. For simplicity, we limit our attention to domains with piecewise linear boundaries and a constant speed of sound. The domain is discretized into a conforming tetrahedron mesh. For the eikonal equation, we extend the jet marching method to tetrahedron meshes. Hermite interpolation enables second order accuracy for the eikonal and its gradient and first order accuracy for its Hessian, computed using cell averaging. To march the eikonal on an unstructured mesh, we introduce a new method of rejecting unphysical updates by considering Lagrange multipliers and local visibility. To handle accuracy degradation near caustics, we introduce several fast Lagrangian initialization algorithms. We store the dynamic programming plan uncovered by the marcher in order to propagate auxiliary quantities along characteristics. We introduce an approximate origin function which is computed using the dynamic programming plan, and whose 1/2-level set approximates the geometric optic shadow and reflection boundaries. We also use it to propagate geometric spreading factors and unit tangent vector fields needed to compute the amplitude and evaluate the high-frequency edge diffraction coefficient. We conduct numerical tests on a semi-infinite planar wedge to evaluate the accuracy of our method. We also show an example with a more realistic building model with challenging architectural features. Finally, we demonstrate a simple approach to extending the method to handle nonconstant speeds of sound by modifying the semi-Lagrangian updates to account for a varying speed.

Analyzing multiple acoustic diffraction over a wide barrier using equivalent knife-edge geometries and Babinet's principle (L)

We present a new method for the calculation of the multiple acoustic diffraction caused by the presence of a wide barrier. Our solution decomposes the initial scenario into an equivalent sum of geometries that only consider knife-edges. Then, by applying Babinet's principle, the total acoustic field that reaches the receiving point, which can be located at an arbitrary position, can be calculated via the uniform theory of diffraction. This method is mathematically less complex and computationally more efficient than most existing techniques. The results are validated (with and without ground reflection) by the solid agreement obtained with other solutions that solve the problem by considering the wide barrier as such, with our proposed method yielding a lower computational time (except against semi-empirical formulations) and better accuracy when compared with measurements. The presented solution can be applied in urban environments where the impact of traffic noise on residential buildings located along roads or highways needs to be evaluated, as well as in scenarios in which the insertion loss caused by a rectangular obstacle, such as a noise barrier, is to be calculated.

Stealth performance evaluation of helicopter against airborne early warning radar considering trimming control

Airborne pulse Doppler radar is a key threat to the military helicopter, and assessing the stealth performance of helicopter against airborne early warning radar is helpful to the helicopter’s stealth design and operational planning. In this paper, the Shooting and Bouncing Ray (SBR) and Uniform Theory of Diffraction (UTD) based high-frequency algorithms are used to calculate the Radar Cross Section (RCS) of helicopter, and the radar range equations are used to evaluate the stealth performance. In order to account for the effects of rotor flapping motions during actual flight, the aerodynamics model of whole helicopter is established and the attitudes and controls of helicopter at different flight states are trimmed and input into the RCS calculation module. The effects of helicopter flight speed, flying direction and operational environment on radar stealth performance are studied in focus. It is demonstrated by the results that the trimming control does have a great influence of more than 5 dB on the RCS of helicopter, and the introduction of the trim calculation brings the helicopter’s returns calculation closer to the reality. Variations in flight speed lead to the changes in the stealth performance of helicopter against Early Warning Aircraft (EWA), and the helicopter flight speed can be planned according to the operational requirements to minimize exposure distance or exposure time. Variations in flying direction mainly affect the detection properties of helicopter returns, and flying in the same direction with EWA usually gives the helicopter better low-observability than flying head-on. Variations in operational environment mainly affect the radar detection performance and the sensitivity of the detection performance to external factors; the same amount of change in some external factor causes a different amount of change in the helicopter’s detectability in different environments.

An Accurate Echo-Acquisition Method for PEC/Coated Targets by GTD-Based Gridless Compressed Sensing

A novel geometrical theory of diffraction (GTD)-based echo-generation approach for perfectly electromagnetic conducting (PEC) and coated targets is proposed, which applies gridless compressed sensing (CS). First, the GTD model for both the PEC and coated targets is established. These GTD models can thus be used to obtain the scattering-echo. The gridless CS method is then used to estimate the GTD model’s phase information, offering a continuous parametric estimation. Next, the genetic algorithm (GA) is used to determine the amplitude and frequency dependency. Finally, the scattering echo at various observed angles can be quickly recorded, yielding high-resolution range profile imaging results. The numerical results show that the proposed method predicts echo more accurately than traditional optimization methods.

Ray-Tracing Model for Generalized Geodesic-Lens Multiple-Beam Antennas

geodesic-lenses are a compelling alternative to traditional planar dielectric lens antennas, as they are low loss and can be manufactured with a simple mechanical design. However, a general approach for the design and analysis of more advanced geodesic-lens antennas has been elusive, limiting the available tools to rotationally symmetric surfaces. In this article, we present a fast and efficient implementation built on geometrical optics and scalar diffraction theory. A numerical calculation of the shortest ray path (geodesic) using an open-source library helps quantify the phase of the electric field in the lens aperture, while the amplitude is evaluated by applying ray-tube power conservation theory. The Kirchhoff-Fresnel diffraction formula is then employed to compute the far field of the lens antenna. This approach is validated by comparing the radiation patterns of a transversely compressed geodesic Luneburg lens (elliptical base instead of circular) with the ones computed using commercial full-wave simulators, demonstrating a substantial reduction in computational resources. The proposed method is then used in combination with an optimization procedure to study possible compact alternatives of the geodesic Luneburg lens with size reduction in both the transverse and vertical directions.

Simulation of Multiple Acoustic Diffraction Based on An Iterative Ray Tracing Method

The classical geometrical theory of diffraction is not available for simulating multiple diffractions in wave propagation. To improve the simulating accuracy for multiple diffractions, a multiple acoustic diffraction simulating method based on ray iteration tracing is proposed in this paper. In this method, the ray occurring at the edge of the wall is split into multiple sub-rays. Then, these sub-rays are continually traced based on the classical ray-tracing theory. The numerical verification demonstrates that this method is valid for simulating multiple diffractions.

Research on the computational method of creeping waves diffraction of arbitrary complex target based on the planar mesh model.

For a long time, due to the difficulty of obtaining accurate propagation trajectories, the research on creeping waves is limited to canonical geometries or simple targets, which leads to the situation that it is relatively mature in theoretical research on creeping waves, while the practical application scope of creeping waves for complex targets is narrow. In this paper, a thorough electromagnetic computation method for creeping waves on complex planar mesh model is systematically proposed. This approach broadens the field of creeping waves applications due to the generality of planar mesh models in electromagnetic engineering. The contents consist of the tracing of creeping waves, the calculation of the diffraction field, and the coupling effect with other scattering mechanisms. Aiming at the trajectory of creeping waves, we propose a set of tracing algorithms that enable rapid, real-time tracing based on analytical geometry and related computer graphics algorithms. Utilizing information such as vertices, triangles, and topological relations in the mesh model, one can recover the mathematical properties of the surfaces of the model and then, the corresponding parameters can be obtained. Therefore, the uniform geometrical theory of diffraction (UTD) can be used to accurately calculate the diffraction field. Moreover, for complex targets, the multiple coupling effect caused by creeping waves is the main source of radar echoes in many cases, which is not unimportant. Hence based on the electromagnetic accurate modeling, the coupling mechanism of creeping waves and various scattering mechanisms are studied. The research content is expected to have high application values in target recognition and characteristics.