Diffraction, Part 3
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Path Loss, Delay Spread, and Outage Models As Functions of Antenna Height for Microcellular System Design
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 43, NO. 3, AUGUST 1994 487 Path Loss, Delay Spread, and Outage Models as Functions of Antenna Height for Microcellular System Design Martin J. Feuerstein, Kenneth L. Blackard, Member, IEEE, Theodore S. Rappaport, Senior Member, IEEE, Scott Y. Seidel, Member, IEEE, and Howard H. Xia Abstract-This paper presents results of wide-band path loss be encountered in a microcellular system using lamp-post- and delay spread measurements for five representative microcel- mounted base stations at street comers, Measurement locations Mar environments in the San Francisco Bay area at 1900 MHz. were chosen to coincide with places where microcellular Measurements were made with a wide-band channel sounder using a 100-ns probing pulse. Base station antenna heights of systems will likely be deployed in urban and suburban areas. 3.7 m, 8.5 m, and 13.3 m were tested with a mobile receiver The power delay profiles recorded at each receiver lo- antenna height of 1.7 m to emulate a typical microcellular cation were used to calculate path loss and delay spread. scenario. The results presented in this paper provide insight into Path loss and delay spread are two important methods of the satistical distributions of measured path loss by showing the characterizing channel behavior in a way that can be related validity of a double regression model with a break point at a distance that has first Fresnel zone clearance for line-of-sight to system performance measures such as bit error rate [4] topographies. The variation of delay spread as a function of and outage probability [7]. -
Fresnel Diffraction.Nb Optics 505 - James C
Fresnel Diffraction.nb Optics 505 - James C. Wyant 1 13 Fresnel Diffraction In this section we will look at the Fresnel diffraction for both circular apertures and rectangular apertures. To help our physical understanding we will begin our discussion by describing Fresnel zones. 13.1 Fresnel Zones In the study of Fresnel diffraction it is convenient to divide the aperture into regions called Fresnel zones. Figure 1 shows a point source, S, illuminating an aperture a distance z1away. The observation point, P, is a distance to the right of the aperture. Let the line SP be normal to the plane containing the aperture. Then we can write S r1 Q ρ z1 r2 z2 P Fig. 1. Spherical wave illuminating aperture. !!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!! 2 2 2 2 SQP = r1 + r2 = z1 +r + z2 +r 1 2 1 1 = z1 + z2 + þþþþ r J þþþþþþþ + þþþþþþþN + 2 z1 z2 The aperture can be divided into regions bounded by concentric circles r = constant defined such that r1 + r2 differ by l 2 in going from one boundary to the next. These regions are called Fresnel zones or half-period zones. If z1and z2 are sufficiently large compared to the size of the aperture the higher order terms of the expan- sion can be neglected to yield the following result. l 1 2 1 1 n þþþþ = þþþþ rn J þþþþþþþ + þþþþþþþN 2 2 z1 z2 Fresnel Diffraction.nb Optics 505 - James C. Wyant 2 Solving for rn, the radius of the nth Fresnel zone, yields !!!!!!!!!!! !!!!!!!! !!!!!!!!!!! rn = n l Lorr1 = l L, r2 = 2 l L, , where (1) 1 L = þþþþþþþþþþþþþþþþþþþþ þþþþþ1 + þþþþþ1 z1 z2 Figure 2 shows a drawing of Fresnel zones where every other zone is made dark. -
Fresnel Integral Computation Techniques
FRESNEL INTEGRAL COMPUTATION TECHNIQUES ALEXANDRU IONUT, , JAMES C. HATELEY Abstract. This work is an extension of previous work by Alazah et al. [M. Alazah, S. N. Chandler-Wilde, and S. La Porte, Numerische Mathematik, 128(4):635{661, 2014]. We split the computation of the Fresnel Integrals into 3 cases: a truncated Taylor series, modified trapezoid rule and an asymptotic expansion for small, medium and large arguments respectively. These special functions can be computed accurately and efficiently up to an arbitrary preci- sion. Error estimates are provided and we give a systematic method in choosing the various parameters for a desired precision. We illustrate this method and verify numerically using double precision. 1. Introduction The Fresnel integrals and their simultaneous parametric plot, the clothoid, have numerous applications including; but not limited to, optics and electromagnetic theory [8, 15, 16, 17, 21], robotics [2,7, 12, 13, 14], civil engineering [4,9, 20] and biology [18]. There have been numerous works over the past 70 years computing and numerically approximating Fresnel integrals. Boersma established approximations using the Lanczos tau-method [3] and Cody computed rational Chebyshev approx- imations using the Remes algorithm [5]. Another approach includes a spreadsheet computation by Mielenz [10]; which is based on successive improvements of known relational approximations. Mielenz also gives an improvement of his work [11], where the accuracy is less then 1:e-9. More recently, Alazah, Chandler-Wilde and LaPorte propose a method to compute these integrals via a modified trapezoid rule [1]. Alazah et al. remark after some experimentation that a truncation of the Taylor series is more efficient and accurate than their new method for a small argument [1]. -
Line-Of-Sight-Obstruction.Pdf
App. Note Code: 3RF-E APPLICATION NOT Line of Sight Obstruction 6/16 E Copyright © 2016 Campbell Scientific, Inc. Table of Contents PDF viewers: These page numbers refer to the printed version of this document. Use the PDF reader bookmarks tab for links to specific sections. 1. Introduction ................................................................ 1 2. Fresnel Zones ............................................................. 4 3. Fresnel Zone Clearance ............................................. 6 4. Effective Earth Radius ............................................... 7 5. Signal Loss Due to Diffraction .................................. 9 6. Conclusion ............................................................... 10 Figures 1-1. Wavefronts with 180° Phase Shift ....................................................... 2 1-2. Multipath Reception ............................................................................. 2 1-3. Totally Obstructed LOS ....................................................................... 3 1-4. Knife-Edge Type Obstruction .............................................................. 4 2-1. Fresnel Zones ....................................................................................... 5 3-1. Effective Ellipsoid Shape ..................................................................... 6 3-2. Path Profile Traversing Uneven Terrain with Knife-Edge Obstruction ....................................................................................... 7 5-1. Diffraction Parameter .......................................................................... -
Analytical Evaluation and Asymptotic Evaluation of Dawson's Integral And
Analytical evaluation and asymptotic evaluation of Dawson’s integral and related functions in mathematical physics V. Nijimbere School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada Abstract Dawson’s integral and related functions in mathematical physics that in- clude the complex error function (Faddeeva’s integral), Fried-Conte (plasma dispersion) function, (Jackson) function, Fresnel function and Gordeyev’s in- tegral are analytically evaluated in terms of the confluent hypergeometric function. And hence, the asymptotic expansions of these functions on the complex plane C are derived using the asymptotic expansion of the confluent hypergeometric function. Keywords: Dawson’s integral, Complex error function, Plasma dispersion function, Fresnel functions, Gordeyev’s integral, Confluent hypergeometric function, asymptotic expansion 1. Introduction Let us consider the first-order initial value problem, D′ +2zD =1,D(0) = 0. (1) arXiv:1703.06757v1 [math.CA] 14 Mar 2017 Its solution given by the definite integral z z2 η2 daw z = D(z)= e− e dη (2) Z0 Email address: [email protected] (V. Nijimbere) Preprint submitted to Elsevier March 21, 2017 is known as Dawson’s integral [1, 17, 24, 27]. Dawson’s integral is related to several important functions (in integral form) in mathematical physics that include Faddeeva’s integral (also know as the complex error function or Kramp function) [9, 10, 22, 18, 27] z z2 2i z2 z2 2i η2 w(z)= e− 1+ e daw z = e− 1+ e dη , (3) √π √π Z0 Fried-Conte function (or plasma dispersion function) [4, 11] z z2 2i z2 z2 2i η2 Z(z)= i√πw(z)= i√πe− 1+ e daw z = i√πe− 1+ e dη , √π √π Z0 (4) (Jackson) function [14] G(z)=1+ zZ(z)=1+ i√πzw(z) z2 2i z2 =1+ i√πze− 1+ e daw z √π z z2 2i η2 =1+ i√πze− 1+ e dη , (5) √π Z0 and Fresnel functions C(x) and S(x) [1] defined by the relation z iπz2 e 2 daw √iπz = eiπη dη = C(x)+ iS(x), (6) √iπ Z0 where z z C(x)= cos(πη2)dη and S(x)= sin (πη2)dη. -
Oscillatority of Fresnel Integrals and Chirp-Like Functions
D ifferential E quations & A pplications Volume 5, Number 4 (2013), 527–547 doi:10.7153/dea-05-31 OSCILLATORITY OF FRESNEL INTEGRALS AND CHIRP–LIKE FUNCTIONS MAJA RESMAN,DOMAGOJ VLAH AND VESNA Zˇ UPANOVIC´ Dedicated to Luka Korkut, upon his retirement (Communicated by Yuki Naito) Abstract. In this review article, we present results concerning fractal analysis of Fresnel and gen- eralized Fresnel integrals. The study is related to computation of box dimension and Minkowski content of spirals defined parametrically by Fresnel integrals, as well as computation of box di- mension of the graph of reflected component function which are chirp-like function. Also, we present some results about relationship between oscillatority of the graph of solution of differ- ential equation, and oscillatority of a trajectory of the corresponding system in the phase space. We are concentrated on a class of differential equations with chirp-like solutions, and also spiral behavior in the phase space. 1. Introduction As coauthors of Luka Korkut, we present here an overview of his scientific con- tribution in fractal analysis of Fresnel integrals and chirp-like functions. We cite the main results from joint articles of Korkut, Resman, Vlah, Zubrini´ˇ candZupanovi´ˇ c, [18, 19, 20, 21, 22, 23]. The articles are mostly based on qualitative theory of differen- tial equations. A standard technique of this theory is phase plane analysis. We study trajectories of the corresponding system of differential equations in the phase plane, instead of studying the graph of the solution of the equation directly. Our main interest is fractal analysis of behavior of the graph of oscillatory solution, and of a trajectory of the associated system. -
Image Grating Metrology Using a Fresnel Zone Plate Chulmin
Image Grating Metrology Using a Fresnel Zone Plate by Chulmin Joo B.S. Aerospace Engineering, Korea Advanced Institute of Science and Technology (1998) Submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 2003 @ Massachusetts Institute of Technology 2003. All rights resH S T OF TECHNOLOGY OCT 0 6 2003 LIBRARIES A uthor ......... .. ........... Department of Mechanical Engineering August 20, 2003 Certified by .. ...... ................ Mark L. Schattenburg Principal Research Scientist Thesis Supervisor C ertified by .... ....................... George Barbastathis Assistant Professor, Mechanical Engineering Thesis Supervisor Accepted by ....... ............. Ain A. Sonin Chairman, Department Committee on Graduate Students BARKER Image Grating Metrology Using a Fresnel Zone Plate by Chulmin Joo Submitted to the Department of Mechanical Engineering on August 20, 2003, in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Abstract Scanning-beam interference lithography (SBIL) is a novel concept for nanometer- accurate grating fabrication. It can produce gratings with nanometer phase accuracy over large area by scanning a photoresist-coated substrate under phase-locked image grating. For the successful implementation of the SBIL, it is crucial to measure the spatial period, phase, and distortion of the image grating accurately, since it enables the precise stitching of subsequent scans. This thesis describes the efforts to develop an image grating metrology that is capable of measuring a wide range of image periods, regardless of changes in grat- ing orientation. In order to satisfy the conditions, the use of a Fresnel zone plate is proposed. -
Improving Comms with 5Ghz
Improving Comms With 5GHz Essential EG Guide ESSENTIAL GUIDES Introduction As broadcasters strive for more and RF technologies such as OFDM more unique content, live events are (Orthogonal Frequency Division growing in popularity. Consequently, Multiplexing) further improve the productions are increasing in complexity robustness of transmission. Rather than resulting in an ever-expanding number transmitting on one frequency, lower of production staff all needing access to symbol rate audio data is spread across high quality communications. Wireless multiple carriers to help protect against intercom systems are essential and multi-path interference and reflections, provide the flexibility needed to host essential for moving wireless handsets or today’s highly coordinated events. But highly dynamic environments. this ever-increasing demand is placing unprecedented pressure on the existing As 5GHz appears in the SHF range, it lower frequency solutions. displays some interesting beneficial characteristics associated with this The 5GHz spectrum offers new band, specifically directionality. This opportunities as the higher carrier allows engineers to direct narrow beams frequencies involved deliver more and steer them to make better use bandwidth for increased data of the available power. Furthermore, Tony Orme. transmission. In excess of twenty- interference with nearby transmissions five non-overlapping channels, each on the same frequency is reduced with a bandwidth of typically 20MHz, allowing frequency reuse. demonstrates the opportunity this technology has to outperform legacy The concept of constructive interference Broadcasters rely on clear and reliable systems based on lower frequencies provides signal amplification for communications now more than ever, such as DECT in the highly congested certain relative signal phases through especially when we consider how many 2.4GHz frequency spectrum. -
Reconfigurable Intelligent Surfaces: Bridging the Gap Between
1 Reconfigurable Intelligent Surfaces: Bridging the gap between scattering and reflection Juan Carlos Bucheli Garcia, Student Member, IEEE, Alain Sibille, Senior Member, IEEE, and Mohamed Kamoun, Member, IEEE. Abstract—In this work we address the distance dependence of is concentrated on algorithmic and signal processing aspects. reconfigurable intelligent surfaces (RIS). As differentiating factor In fact, the comprehension of the involved electromagnetic to other works in the literature, we focus on the array near- specificities has not been fully addressed. field, what allows us to comprehend and expose the promising potential of RIS. The latter mostly implies an interplay between More specifically, reconfigurable intelligent surfaces (RIS) the physical size of the RIS and the size of the Fresnel zones at correspond to the arrangement of a massive amount of in- the RIS location, highlighting the major role of the phase. expensive antenna elements with the objective of capturing To be specific, the point-like (or zero-dimensional) conventional and scattering energy in a controllable manner. Such a control scattering characterization results in the well-known dependence method varies widely in the literature [1]; among which PIN- with the fourth power of the distance. On the contrary, the characterization of its near-field region exposes a reflective diode and varactor based are popular. behavior following a dependence with the second and third In this context, the authors investigate an impedance con- power of distance, respectively, for a two-dimensional (planar) trolled RIS, although the addressed fundamentals are of a and one-dimensional (linear) RIS. Furthermore, a smart RIS much wider applicability. As a matter of fact, by characterizing implementing an optimized phase control can result in a power RIS in terms of the elements’ observed impedance, it is exponent of four that, paradoxically, outperforms free-space propagation when operated in its near-field vicinity. -
Fresnel Zone in VTI and Orthorhombic Media
Geophysical Journal International Geophys. J. Int. (2018) 213, 181–193 doi: 10.1093/gji/ggx544 Advance Access publication 2017 December 18 GJI Seismology Fresnel zone in VTI and orthorhombic media Downloaded from https://academic.oup.com/gji/article-abstract/213/1/181/4757074 by Norges Teknisk-Naturvitenskapelige Universitet user on 04 January 2019 Shibo Xu and Alexey Stovas Department of Geoscience and Petroleum, Norwegian University of Science and Technology, S.P.Andersens veg 15a, 7031 Trondheim, Norway. E-mail: [email protected] Accepted 2017 December 17. Received 2017 November 15; in original form 2017 September 16 SUMMARY The reflecting zone in the subsurface insonified by the first quarter of a wavelength and the portion of the reflecting surface involved in these reflections is called the Fresnel zone or first Fresnel zone. The horizontal resolution is controlled by acquisition factors and the size of the Fresnel zone. We derive an analytic expression for the radius of the Fresnel zone in time domain in transversely isotropic medium with a vertical symmetry axis (VTI) using the perturbation method from the parametric offset-traveltime equation. The acoustic assumption is used for simplification. The Shanks transform is applied to stabilize the convergence of approximation and to improve the accuracy. The similar strategy is applied for the azimuth-dependent radius of the Fresnel zone in orthorhombic (ORT) model for a horizontal layer. Different with the VTI case, the Fresnel zone in ORT model has a quasi-elliptic shape. We show that the size of the Fresnel zone is proportional to the corresponding traveltime, depth and the frequency. -
Radio Wave Propagation Fundamentals
Chapter 2: Radio Wave Propagation Fundamentals M.Sc. Sevda Abadpour Dr.-Ing. Marwan Younis INSTITUTE OF RADIO FREQUENCY ENGINEERING AND ELECTRONICS KIT – The Research University in the Helmholtz Association www.ihe.kit.edu Scope of the (Today‘s) Lecture D Effects during wireless transmission of signals: A . physical phenomena that influence the propagation analog source & of electromagnetic waves channel decoding . no statistical description of those effects in terms digital of modulated signals demodulation filtering, filtering, amplification amplification Noise Antennas Propagation Time and Frequency Phenomena Selective Radio Channel 2 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Propagation Phenomena refraction reflection zR zT path N diffraction transmitter receiver QTi path i QRi yT xR y Ti yRi xT path 1 yR scattering reflection: scattering: free space - plane wave reflection - rough surface scattering propagation: - Fresnel coefficients - volume scattering - line of sight - no multipath diffraction: refraction in the troposphere: - knife edge diffraction - not considered In general multipath propagation leads to fading at the receiver site 3 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics The Received Signal Signal fading Fading is a deviation of the attenuation that a signal experiences over certain propagation media. It may vary with time, position Frequency and/or frequency Time Classification of fading: . large-scale fading (gradual change in local average of signal level) . small-scale fading (rapid variations large-scale fading due to random multipath signals) small-scale fading 4 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Propagation Models Propagation models (PM) are being used to predict: . -
Recommendation Itu-R P.530-9
Rec. ITU-R P.530-9 1 RECOMMENDATION ITU-R P.530-9 Propagation data and prediction methods required for the design of terrestrial line-of-sight systems (Question ITU-R 204/3) (1978-1982-1986-1990-1992-1994-1995-1997-1999-2001) The ITU Radiocommunication Assembly, considering a) that for the proper planning of terrestrial line-of-sight systems it is necessary to have appropriate propagation prediction methods and data; b) that methods have been developed that allow the prediction of some of the most important propagation parameters affecting the planning of terrestrial line-of-sight systems; c) that as far as possible these methods have been tested against available measured data and have been shown to yield an accuracy that is both compatible with the natural variability of propagation phenomena and adequate for most present applications in system planning, recommends 1 that the prediction methods and other techniques set out in Annexes 1 and 2 be adopted for planning terrestrial line-of-sight systems in the respective ranges of parameters indicated. ANNEX 1 1 Introduction Several propagation effects must be considered in the design of line-of-sight radio-relay systems. These include: – diffraction fading due to obstruction of the path by terrain obstacles under adverse propagation conditions; – attenuation due to atmospheric gases; – fading due to atmospheric multipath or beam spreading (commonly referred to as defocusing) associated with abnormal refractive layers; – fading due to multipath arising from surface reflection; – attenuation due to precipitation or solid particles in the atmosphere; – variation of the angle-of-arrival at the receiver terminal and angle-of-launch at the transmitter terminal due to refraction; 2 Rec.