Search Results(13733)

2023-07-27
PIER M
Vol. 118, 71-82
Improved Side-Lobe Suppression by Optimizing the Beam Synthetization in Uniform Circular Arrays for OAM Generation
Layth Abogneem , Ahmad Alamayreh and Nidal Qasem
Enhancing the capacity of wireless communications systems is necessary to manage growing networks. Thus, this work presents an analytical model for describing the deterioration in orbital angular momentum (OAM). The proposed model is based on a uniform circular array, which can be applied in OAM generation to obtain the desired beam properties. First, the side-lobe problem in OAM applications is examined and resolved by optimizing the beam synthetization. Then, comparisons between the two window techniques are used to evaluate their impacts. Finally, the effects of selecting the optimal window technique and width on the solutions are investigated. Numerical results and the comparisons between derived formulas and those obtained via full-wave numerical simulations are shown.
2023-07-26
PIER Letters
Vol. 111, 103-110
A Compact Tunable Microstrip Bandpass Filter with Tuning Range and Bandwidth Enhanacement
Shuang Li , Shengxian Li , Jun Liu and Neng Zhang
This letter presents a compact constant absolute bandwidth (ABW) frequency tunable bandpass filter (BPF) with bandwidth and tuning range enhancement. The fundamental structure consists of two varactor-loaded step-impedance resonators (SIRs) and input/output feeding lines. By adjusting the position of varactors, the slope of coupling coefficient between the two resonators can bechanged easily, which is crucial to realizing constant ABW. The tuning range is improved due to the application of varactor-loaded SIR. To expand the bandwidth, interdigital coupling structures between varactor-loaded SIRs are adopted. Besides, source-load coupling is introduced, and two transmission zeroes (TZs) are generated on both sides of the passband to enhance the rejection level of stopband. The measured results show that the proposed BPF achieves a center frequency tuning range from 0.79 to 1.2 GHz (41.2%), and the 3-dB ABW remains 108 ± 5 MHz. The insertion loss (IL) is 1.8-2.2 dB, and the return loss is greater than 10 dB during the whole tuning range.
2023-07-25
PIER C
Vol. 135, 69-81
A Folded Rectenna on a Flexible Substrate for 5G Energy Harvesting Applications
Mustapha Bajtaoui , Mohammed Ali Ennasar , Mariem Aznabet , Abdelmounaim Tachrifat and Otman El Mrabet
This paper presents the design, fabrication, and measurement results of a flexible folded dipole rectenna for 5G technology. The proposed rectenna is a single-sided structure fabricated on a flexible Kapton substrate with a maximum RF to DC conversion efficiency close to 53% for an input power of -9 dBm at 3.5 GHz with 3-KΩ. Moreover, the measured results show that the conversion efficiency is above 40% across a broad range of input power levels (from -14 to -8 dBm). The paper discusses the prototype's design and simulation results, fabrication steps, and measurement results. The proposed rectenna is compact, low-cost, and flexible, making it suitable for wearable applications.
2023-07-25
PIER M
Vol. 118, 59-69
Time Domain Modeling Method for the Coupling Analysis of Branched Lines Excited by Ambient Wave
Zhihong Ye , Xin Xia , Changchang Lu and Yu Zhang
An efficient time domain hybrid method, consisting of the finite-difference time-domain (FDTD) method, Norton's theorem, transmission line (TL) equations, and some interpolation techniques, is presented to realize the fast coupling simulation of branched lines (BLs) radiated by ambient wave. Firstly, the branched lines are decomposed into multiple independent multi-conductor transmission lines (MTLs) according to the branched nodes. Then the TL equations with interpolation techniques are employed to build the coupling model of each MTL. The transient responses on these MTLs are solved by the FDTD method, which are employed to extract the Norton circuits of these MTLs acting on the branched nodes according to the Norton's theorem. Finally, the correlation matrix of the voltages and currents at the ports of the branched nodes is derived and solved. Meanwhile, these voltages are fed back to the corresponding MTLs as boundaries to realize the interference signal transmission among the BLs. Numerical examples about the coupling of branched lines contributed by five wires in free space and complex environment are simulated and compared with that of traditional FDTD to verify the correctness and efficiency of this proposed method.
2023-07-25
PIER M
Vol. 118, 47-57
Time Domain Coupling Analysis of the Transmission Line Excited by the Leakage EM Fields from the Integrated Circuit with Shielded Enclosure
Zhihong Ye , Sihao Wang , Changchang Lu and Yu Zhang
At present, numerical methods suitable for the electromagnetic interference (EMI) analysis of the transmission line (TL) excited by the leakage electromagnetic (EM) fields generated by the integrated circuit (IC) of the electronic device are still rare. An efficient time domain hybrid method, consisting of the dynamic differential evolution (DDE) algorithm, transmission line equations, finite difference time domain (FDTD) method and non-uniform grid technique, is presented to realize the fast simulation of the leakage EM fields to the TL. Firstly, a source reconstruction method based on the DDE algorithm is employed to extract the equivalent dipole array to represent the leakage EM radiation from the IC of the device. Then, the coupling model of the TL excited by the leakage EM fields is constructed by the TL equations and non-uniform grid technique, and solved by the FDTD method to realize the synchronous calculation of the leakage EM field radiation and the transient responses on the TL. Finally, the correctness of the source reconstruction method has been tested, and the accuracy and efficiency of the proposed method have been verified via two simulation cases of the transmission line excited by leakage EM fields arising from IC in free space and shielded enclosure by comparing with that of the MOM method.
2023-07-25
PIER B
Vol. 101, 155-173
Soil Water Content Estimation Over Plantation Area Using FMCW Radar
Fildha Ridhia , Aloysius Adya Pramudita and Fiky Yosef Suratman
In plantation areas, soil conditions affect the crop's quality. One of the crucial elements in the soil for plant survival is soil water content (SWC). Radar system has advantages that can be implemented for measuring SWC in plantation areas. A radar system operates by utilizing electromagnetic waves to obtain the dielectric characteristics of the soil. However, the presence of tea plants has become an obstacle to the radar wave propagation toward the soil layer. Reflected signal, which is influenced by the presence of vegetation, makes the estimation of SWC inaccurate. Consequently, the estimation of SWC needs to consider the vegetation's effect. This study uses an FMCW radar system, which operates at a frequency of 24 GHz. A layer medium propagation model is proposed in this study to prove the relationship between the reflected signal and the SWC. The reflection coefficient extracted from the radar signal is used to estimate the SWC. The vegetation propagation constant was obtained from the average field measurement results. The gravimetric method is used to validate the SWC estimation in vegetation's presence using the radar system. The results of the field experiments showed that the proposed method succeeded in estimating the SWC by considering the presence of vegetation with an average error of 3.57%. The proposed method has the potential to be applied to plantation areas.
2023-07-24
PIER C
Vol. 135, 55-67
Dual-Band 4×4 Hexagonal SRR MIMO Antenna with Port Excitation-Controlled Gain and Directivity for WLAN/WiMAX Applications
Puneet Sehgal and Kamlesh Patel
This paper presents the total gain and directivity control with port excitation in a 4×4 hexagonal split-ring resonator (H-SRR) MIMO antenna for dual-band operation in 2.4/5.2 GHz bands. The MIMO antenna is shown more than 15 dB isolation between antenna elements placed orthogonally, and a spacing was introduced between them to achieve higher isolation in the first proposed design, then, a Z-shaped structure of specific dimensions was inserted to further improve the isolation between antenna elements. The simulated and measured return losses and transmission coefficients confirmed the improved performances for impedance bandwidth and isolation. The gain, axial ratio, and radiation pattern performances of the 4×4 H-SRR MIMO antenna are studied by exciting different port combinations of the four ports of the proposed antenna. A wide range of gain and axial ratio variations are observed on exciting single, dual, triple, and quad-ports of the proposed MIMO antenna and discussed using the radiation patterns. Also, various MIMO parameters, ECC < 0.04, TARC < -10 dB, MEG < -6 dB, DG < 10 dB, and CCL < 0.4 bits per second per Hz, are found in the 2.4/5.2 GHz bands, which confirms the applicability of proposed H-SRR MIMO antenna with polarization diversity.
2023-07-23
PIER
Vol. 178, 1-12
Reservoir Computing and Task Performing through Using High-β Lasers with Delayed Optical Feedback
Tao Wang , Can Jiang , Qing Fang , Xingxing Guo , Yahui Zhang , Chaoyuan Jin and Shuiying Xiang
Nonlinear photonic sources including semiconductor lasers have been recently utilized as ideal computation elements for information processing. They supply energy-efficient way and rich dynamics for classification and recognition tasks. In this work, we propose and numerically study the dynamics of complex photonic systems including high-β laser element with delayed feedback and functional current modulation, and employ nonlinear laser dynamics of near-threshold region for the application in reservoir computing. The results indicate a perfect (100%) recognition accuracy for the pattern recognition task and an accuracy about 98% for the Mackey-Glass chaotic sequences prediction. Therefore, the system shows an improvement of performance with low-power consumption. In particular, the error rate is an order of magnitude smaller than previous works. Furthermore, by changing the DC pump, we are able to modify the number of spontaneous emission photons of the system, which then allows us to explore how the laser noise impacts the performance of the reservoir computing system. Through manipulating these variables, we show a deeper understanding on the proposed system, which is helpful for the practical applications of reservoir computing.
2023-07-23
PIER B
Vol. 101, 137-154
A MIMO PIFA Loaded with CSRR-SRR Quadruplets for WLAN, ISM Band, and S-/C-Band Wireless Applications
Srujana Vahini Nandigama , Kunooru Bharath and Dasari Ramakrishna
The article presents a multiband symmetrically placed two elements, inverted-F multiple inputs multiple outputs (MIMO) antenna for wireless LAN (WLAN), Industrial, Society and Medical (ISM) band, S-/C-band applications. Decoupling (S12 < -15 dB) between the two antenna elements of MIMO antenna is improved by introducing metallic vias at the top ends of the patch. The MIMO antenna has been fabricated and measured on a piece of low-cost, low-profile, FR-4 substrate. A combination of parasitic loading of 4-units (quadruplet) of square-split ring resonators (SRRs) and complementary split ring resonator (CSRR) cells have been used to achieve quad-bands for lower than -10 dB total active reflection coefficients and additionally to improve isolation between antenna elements. The paper also presents the tabularized and graphical investigations of the analyzed and measured resultant MIMO parameters like; envelope correlation coefficient (ECC), diversity gain (DG), total active reflection coefficients (TARC), MIMO-VSWR (voltage standing wave ratio), channel capacity loss (CCL), etc. and are found approximately close to each other with small acceptable errors. The other important parameters (reflection coefficients, radiation pattern, E-plane and H-plane polar plots, electric field vector (E) distribution, and current density vector (J) distribution) of the proposed antenna were also demonstrated and measured using a vector network analyzer (Agilent N5247A VNA) and 18 GHz Anechoic chamber in the microwave research laboratory. The MIMO (1×2) antenna is best suitable for Bluetooth/WLAN/Wi-Fi (2.45-2.57 GHz) and ISM band, FIXED, MOBILE, RADIO Location, Amateur & Amateur-satellite service (2.45 GHz) within impedance bandwidth (S11 < -10 dB) from 2.45-2.57 GHz lower band, and n46 (5.40-5.49 GHz) upper band.
2023-07-22
PIER C
Vol. 135, 43-53
Design of Compact Wide-Beam Broadband Antenna for Wide-Angle Scanning Applications
Da Yu , Hongmei Liu , Shuo Li , Zhongbao Wang and Shao-Jun Fang
In this paper, a compact antenna with wideband and wide beam is proposed. It is composed of a rectangular patch etched on a substrate, a feeding probe, two metal columns, and a ground plane. By inserting air gap between the substrate and the ground, as well as using the coupled feeding, wide impedance bandwidth is obtained. By inserting two metal columns on the two sides of the patch for inducing longitudinal current, the HPBW of the antenna in the operation bandwidth can be widened. Design evolutions are provided for the proposed antenna, and main parameters are investigated for obtaining the adjusting rules. For validation, a prototype operating at 5.8 GHz is fabricated, where the dimension is only 0.31λ0 × 0.11λ0 × 0.11λ0. Measurement results show that a fractional bandwidth of 24% is achieved for |S11| < -10 dB. In this bandwidth, the measured gain is larger than 2.5 dBi with a maximum gain of 3.5 dBi. At E-plane, the measured HPBWs are in the range of 130°~190°, and the values are around 120° at H-plane.
2023-07-21
PIER C
Vol. 135, 35-42
Quasi-Elliptic Triple Passband Filter Using Stub Loaded Step Impedance Resonator and Non-Resonating T Structure
Anirban Neogi and Jyoti Ranjan Panda
This article presents a simple method to introduce multiple Transmission Zeros in the stopbands of a triple passband Chebyshev filter and also suppress the spurious bands below a satisfactory level, so that it can be treated as a Quasi-Elliptic filter. A pair of Stub Loaded Step Impedance Resonators (SLSIRs) is used to produce the Chebyshev filter with central passbands at 2.5, 5.5, and 9 GHz. An asymmetric Non-Resonating T (NRT) structure is implemented on each of the SLSIR to achieve the improved skirt selectivity. Each non-resonating structure produces three Transmission Zeros (in total six). In addition to the satisfactory stopband performances, the Quasi-Elliptic triple band filter produces insertion losses of |0.4|, |0.6|, and |0.7| dB at three centre frequencies respectively. Simulation of the proposed filter is done using HFSS13 software, and to validate the simulation, a prototype is fabricated on an Arlon AD250 (Dielectric Constant 2.5, height 0.76 mm) substrate.
2023-07-20
PIER M
Vol. 118, 37-46
Optically Transparent Dual-Polarized Cross Dipole Antenna with Metal Mesh Film for 5G Applications
Haowei Xi , Xiao-Liang Ge , Kuiwen Xu , Jianhua Shen , Xianglong Liu and Su Xu
Optically transparent antennas have attracted increasing interest in recent years. However, the inherent ohmic loss of transparent conductor used in antennas will always introduce degradation of radiation efficiency. It is of most importance to find the optimization between the material loss and radiation efficiency. In this paper, we design and experimentally demonstrate a high-performance optically transparent dual-polarized cross dipole antenna over 3.4-3.8 GHz for 5G wireless communication based on the characteristic analysis of surface current distribution. By making current distribution uniform on the radiators and reducing the current on the ground, the mutual coupling between the elements is alleviated, and the radiation efficiency can be optimized. The proposed antenna is fabricated with 0.118-Ohm/sq meshed metal, and the optical transparency of antenna is 81%. The proposed antenna achieves a voltage standing wave ratio (VSWR) of less than 1.3, radiation efficiency of 72% (84% of pure copper) and a peak gain of 4.5 dBi (5.1 dBi of pure copper). Compared to current state-of-arts, the proposed antenna exhibits better performance of the figure of merit (FOM) in terms of the bandwidth, optical transparency and radiation efficiency. Our work paves the way to diverse application of beyond-5G wireless communication.
2023-07-19
PIER
Vol. 177, 107-126
Remote Material Characterization with Complex Baseband FMCW Radar Sensors
Ahmed M. Hegazy , Mostafa Alizadeh , Amr Samir , Mohamed Basha and Safieddin Safavi-Naeini
This paper presents the theoretical basis and experimental validation for a technique to remotely characterize materials using FMCW radar sensors with complex baseband architecture. Our theoretical work proves that the magnitude and phase of the input reflection coefficient of a material can be accurately extracted from the baseband data of a complex-baseband FMCW radar. This complex reflection coefficient can be used to calculate the dielectric constant, loss tangent, thickness, and layer setup of a material with high accuracy due to the extra information obtained from the phase of the reflection coefficient. The analysis starts with a theoretical model for the complex reflection coefficient of a flat material slab suspended in air. We then introduce a formulation for the complex reflection coefficient existing in the complex baseband of an FMCW radar signal. We finally present the experimental testing preformed using TI mmWave radar on two different material samples and introduce the test results for extracting the material dielectric properties and thickness using three different extraction methods compared against nominal values from literature. The test results prove the high accuracy of our technique resulting from the utilization of both magnitude and phase information of the input refection coefficient, despite the relatively long free-space measurement distance and the multi-path reflections test environment.
2023-07-19
PIER C
Vol. 135, 23-34
A 3 dB Compact UWB Hybrid Coupler for 5G Millimeter-Wave Applications
Mohamed Atef Abbas , Abdemegeed Mahmoud M. A. Allam , Abdelhamid Gaafar , Hadia El-Hennawy and Mohamed Fathy Abo Sree
This paper presents a 3 dB compact Ultra-Wide-Band (UWB) Substrate Integrated Gap Waveguide (SIGW) based hybrid coupler suitable for 5G mm-wave applications. It is a key component in signal processing for wireless communication. It provides a way to control the power distribution of the signal along different ports. It could be used to achieve beamforming and adaptive antenna system. The design steps started with implementing a unit cell of the gap waveguide structure satisfying the required bandwidth of the coupler. A supercell is then implemented. A network of complete ridges is constructed. A further step is to design a coupling section which achieves the required power distribution along the coupling and isolated ports. This coupling section is implemented using a novel approach of inserting an elliptical slot with variable major and minor axes with a certain orientation that achieves the standard performance of a 3 dB directional coupler with 90° ± 5% phase shift. For precise adjustment of this amplitude and phase, vias are further added perpendicular to the major axis of the slot. Its dimension and location have to be optimized. The Finite-Integral-Time-Domain (FDTD) analysis method is adopted (CST Microwave Studio). In addition, another novel approach is developed on this coupler such that the transition and gap layer is implemented on the same PCB layer, which saves the number of layers to only two layers compared to the usual three layers used in literature. Also, using SIGW technology saves the collapse of the top ground layer on the ridge structure, and only plastic pins are used to fix the two layers. The proposed coupler is fabricated and tested, and the results show that it serves the majority of frequency bands employed in 5G systems in the USA and Canada.
2023-07-19
PIER M
Vol. 118, 25-35
Moving Metallic Slab Illuminated by a Plane Wave: Theory and Numerical Analysis Using the Finite Difference Time Domain Method
Mohammad Marvasti and Halim Boutayeb
The response of a uniformly moving metallic slab to an electromagnetic plane wave, at normal incidence, is studied. The analysis is based on the application of boundary conditions to Maxwell's equations as a function of time. The Doppler effect and amplitude of the obtained reflected wave agree with the literature. Moreover, a transferred wave which has not been analyzed in the literature is demonstrated. The frequency shift and the amplitude of this wave are studied analytically with the same technique used for the reflected wave. The transfer of electromagnetic wave through the metallic slab is made possible by the presence of a static magnetic field inside the moving metallic slab, if the motion of the slab is opposite to the direction of propagation of the incident wave. The amplitude of the transferred wave is approximately 2v/c times the amplitude of the incidence wave, with v being the speed of motion and c the speed of light in vacuum. This amplitude is thus very small for non-relativistic speeds. The analytical results are validated by full-wave simulations based on the Finite Difference Time Domain method, where both reflected and transferred waves are demonstrated. Furthermore, numerical electric field and magnetic field distributions are presented at different time instants.
2023-07-18
PIER Letters
Vol. 111, 93-102
High Sensitivity Passive Wireless Humidity Sensor Based on Polyvinyl Alcohol
Bo Wang , Fei Gao , Youwei Li , Ke Wang and Shengli Cao
A low cost and compact chipless Radio Frequency Identification (RFID) humidity sensor with the size of 18 * 18 * 0.5 mm3 is designed for environmental humidity monitor. The sensor consists of a circular resonator and a rectangular substrate, which utilizes the polyvinyl alcohol (PVA) humidity sensitive material for relative humidity (RH) sensing. The PVA humidity sensitive material covers the sensor surface. The working principle of the sensor is that the change of environmental humidity results in the changing of dielectric constant of PVA and thus shifting of the resonant frequency of the sensor. The real-time humidity can be observed by monitoring the resonant frequency. The simulation results show that the humidity sensing range of the designed humidity sensor is 21.9% RH~52.5% RH, corresponding to the resonant frequency range of the sensor from 2.76 GHz to 2.51 GHz with the total offset 250 MHz. The maximum humidity sensitivity was 23.08 MHz/% RH within the monitoring range. The designed humidity sensor has the advantages of low cost, compact and simple structure, which is suitable for humidity monitoring in various complex environments.
2023-07-17
PIER C
Vol. 135, 13-22
A Novel EBG Dual-Band Antenna Structure for X-Band and WLAN Applications
Loubna Rmili , Bousselham Samoudi , Adel Asselman and Sanae Dellaoui
This paper presents a novel dual-band dielectric electromagnetic band gap (EBG) antenna that operates in both wireless local area network (WLAN) and X-band satellite applications. The proposed structure comprises new double EBG layers placed on the top face and fed by a coaxial probe. The design and parametric analysis of the band gap structure have been performed using Ansys HFSS simulation software. The measurement results are found in good agreement with the simulation results, indicating that the proposed antenna design is a promising solution for dual-band applications. As a result, we have found significant enhancement in gain up to 8.1 dB and 9.3 dB at both frequencies of 5 GHz and 9.8 GHz.
2023-07-17
PIER B
Vol. 101, 119-135
Element Thinning Using Discrete Cat Swarm Optimization for 5G/6G Applications
Sahiti Vankayalapati , Lakshman Pappula and Debalina Ghosh
An efficient method for designing narrow beams having minimum peak side lobe level (PSLL) and maintaining power efficiency (reducing active elements) for 5G/6G base stations with large antenna arrays is proposed. To ensure high efficiency in a multi-dimensional complex nonlinear optimization problem with several constraints thinning of antenna of antenna arrays is considered. For performing exhaustive search on the large number of feasible solutions a novel algorithm named discrete cat swarm optimization (DCSO) is usedand is a binary adaptation of real-valued cat swarm optimization (CSO). To testify the efficiency of DCSO a set of standard benchmarked multimodal functions are used. The proposed algorithmsexhibit heuristic nature, so the stability of the proposed method has been authenticated by using statistical test. Later the algorithm is applied to the optimization of a large planar antenna array (PAA) of size 10×20 (200 elements) to suppress the PSLL. Furthermore, the results of the synthesis are compared with literature marking low PSLL and convergence speed as pointers. The comparative results delineate the superiority of the DCSO over the existing discrete versioned traditional algorithms with respect to solution accuracy and speed of convergence. DCSO introducesa higher degree of flexibility to the field of binary-valued thinned antenna array synthesis problems.
2023-07-16
PIER C
Vol. 134, 249-261
Design of Three-Band Two-Port MIMO Antenna for 5G and Future 6G Applications Based on Fence-Shaped Decoupling Structure
Zhonggen Wang , Wanying Ren , Wenyan Nie , Weidong Mu and Chenlu Li
In this paper, a new design of a highly isolated tri-band antenna for 5G and future 6G applications is proposed. The overall dimensions of the proposed antenna are just 56.4 × 36.6 mm2; moreover, it contains two monopole antenna units and a defective ground. The tri-band characteristics of the antenna are achieved by improving the single antenna patch structure. The structure is improved based on the original T-shaped decoupling structure to create a fence-shaped decoupling structure consisting of an improved T-shaped and an improved rectangular structure. This will greatly improve isolation by efficiently absorbing the coupling current. Therefore, the proposed antenna system is designed and tested to reach the 5G dual bands of 3.38 GHz-3.61 GHz, 4.51 GHz-4.96 GHz, and the future 6G band of 6.06 GHz-7.51 GHz. The results show that, relative to other antennas, this antenna has an isolation degree in the operating band greater than 13.1 dB. In addition, the antenna has good radiation characteristics and an acceptable envelope correlation coefficient.
2023-07-15
PIER B
Vol. 101, 101-117
A Uniform Additional Term Using Fock-Type Integral to Unify Edge Diffraction, Creeping Diffraction, and Reflection in Lit and Shadowed Regions
Xin Du and Jun-Ichi Takada
The uniform geometrical theory of diffraction (UTD) calculating edge diffraction, creeping diffraction, and reflection, has been widely used to predict the shadowing problems for the beyond 5th generation. The limitation of the previous work, which only discussed the relationship between edge diffraction and reflection in the lit region, has motivated the analysis of the difference between creeping diffraction and edge diffraction in the shadowed region. In this paper, as the difference between creeping diffraction and edge diffraction from a dielectric circular cylinder and an absorber screen, respectively, a novel additional term is derived based on the UTD in the shadowed region. In addition, a uniform additional term using the Fock-type integral is proposed to unify the formulations in the lit and shadowed regions. The proposed uniform additional term is validated by the UTD and exact solutions of a dielectric circular cylinder at millimeter-wave or sub-terahertz bands. From the discussion of the results, the proposal can not only unify the formulations in the lit and shadowed regions but also eliminate the fictitious interference. Through the proposal, we can separate the contribution of the shadowed Fresnel zone number (FZ) and boundary conditions (i.e., the surface impedance and polarization). The frequency characteristics of the shadowed FZ and boundary conditions are analyzed and simulated near a shadow boundary at a high frequency (10 GHz-100 GHz). The results imply that there is almost no dependency (less than 1 dB) on boundary conditions in the lit region while there are few dependencies (more than 1 dB) on boundary conditions in the shadowed region. This work attempts to unify three different propagation mechanisms, i.e., reflection, edge diffraction, and creeping diffraction, by using one formula.