DOCSLIB.ORG

Characterization Tools for Estimate Radar Signals with Partial Obstructions

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Characterization Tools for Estimate Radar Signals with Partial Obstructions ERAD 2012 - THE SEVENTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY Characterization tools for estimate radar signals with partial obstructions Juan Antonio Romo Argota 1, Mercedes Maruri Machado 2, Ivan Iglesias 1, Sabina Ustamujic 1 1Department of Electronics and Telecomunications, E.T.S.I Bilbao, University of Basque Country. Alameda Urquijo s/n, Bilbao, Spain [email protected] 2Department of Applied Mathematics, E.T.S.I Bilbao, University of Basque Country. Alameda Urquijo, Bilbao, Spain [email protected] 1. Introduction When radar signals travel along paths close to the Earth’s surface, there is a possibility that the wave front is partially obstructed by terrain irregularities such as hills or mountains, or even by artificial structures (buildings). This phenomenon is called diffraction and it is a key factor as error source in weather radar estimations in complex orographic areas, specially for lowest radar antenna elevation angles. Under these conditions, when any diffraction is caused by terrain irregularities or obstacles the propagation of the signal energy will block partially (or even completely). Diffraction is studied through the analysis of the degree of obstruction suffered by the so called First Fresnel Ellipsoid or First Fresnel Zone. The energy contribution of the different ellipsoids to the total received power is a decreasing function of the order of ellipsoids. In consequence, the difraction losses are evaluated considering the first ellipsoid only and neglecting any effect due to the rest of ellipsoids. The received energy at any location is the contribution of the infinite paths that are contained by the plane which is perpendicular to the Pointing vector of a flat wave front. This concept is based on Huygens’ principle that states that any of the points of a flat wave front originates a spherical wave, that in turn, with all the spherical waves associated to other points of the flat wave front, will create an envelope that forms again a flat wave front at a distance r. The contribution of each path to the total received power will depend on the phase of each component associated to the flat wave front. Diffraction of direct ray of a microwave signal in the proximity to a partially blocking obstruction, creates a shadow zone in which diffracted signal energy is lost. When severe subrefraction conditions occur, the path followed by the wave front can be bent down and intersect with terrain obstacles. The first Fresnel ellipsoid will be free of obstacles (at least a 60% of its radius should be above any relevant terrain obstacle of the path profile). In exceptional cases where this condition cannot be fulfilled and for calculation purposes of diffraction associated to the subrefractive condition, there are different methods to estimate the diffraction loss value. 2. The abstract In this paper we develop a calculation algorithm to estimate diffraction losses. The method to be applied in each case will depend on the number and shape of the obstacles and the position of those obstacles in the propagation path. The main objective for this algorithm is the assessment of radar signals in scenarios within partial obstructions. Depending on the idealization used to characterize the obstacles encountered in the propagation path, different prediction models can estimate the path loss in vertical plane of a given point from ground level up to line of sight height. In this way power loss is calculated for different radar antenna elevation angles during rain events using a digital elevation model and different attenuation methods as function of the types of obstacles in the path. This power loss is compared with radar reflectivity at these points. Additional applications for this developed model are planning and interferences evaluation tools in the design and implementation of microwaves line of sight or satellite links. 3. Digital Elevation Model In general, most propagation prediction algorithms are based on detailed topographical information provided by Digital Terrain Elevation (DTE) models which are composed by digital terrain topographical databases and represented in the form of digital terrain maps. These models are used to evaluate the potential loss associated to diffraction. There is a variety of digital terrain models, with elevation data of different resolutions on a global scale that cover practically the whole surface of the Earth. Digital Elevation Models (DEM), in addition to digital terrain elevation data, require more details and features of the terrain including different soil types, vegetation layers, layers describing the existence of buildings and associated heights, etc. The first step of the suggested methodology involves the conversion of Digital Terrain Elevation files to X,Y,Z coordinates. This Digital Terrain Elevation is later combined with building height layers, available locally, to obtain the Digital Elevation Model (DEM), which are composed by digital topographical databases implemented in MySQL. ERAD 2012 - THE SEVENTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY 4. Profile extraction and obstacles identification and classification The path profile extraction is carried out directly from the topographical database and traced with the appropriate equivalent Earth radius. [1] The proposed tool detects automatically the obstacles in the path and the shape of them. An obstacle is identified if the clearance from the ray tracing is at least 57.7 % of the first Fresnel zone radius R 1 on both sides of the obstacle, at a given equivalent Earth radius. It is considered isolated if there is no interaction between the obstacle itself and the surrounding terrain. In turn, to determine if two obstacles must be considered as one isolated obstacle the distance between adjacent obstacles is verified and compared with the radius of the first Fresnel elipsoide. To make diffraction fading calculations it is necessary to idealize the complex forms of real obstacles, either assuming a knife-edge of negligible thickness or a thick smooth obstacle with a well-defined radius of curvature at the top. 5. Diffraction loss methods The used algorithmia to calculate the diffraction loss caused by different types, number and obstacles configurations along the path are basically derived from de the ITU-R models. [2] Different methods are used for the cases where there is a single isolated obstacle and for those where several irregularities are relevant in the path profile. 1) Single knife-edge obstacle: Attenuation due to diffraction J(ν) (dB) is calculated by the equation derived from the Fresnel-Kirchhoff diffraction theory: J (ν ) = 9.6 + 20 log ( (ν – )1.0 2 + 1 + ν – 1.0 ) dB Where ν is a dimensionless parameter 2 1 1 ν = h + λ d1 d2 according to the geometrical parameters selected: λ wavelength (m) h clearance (m) d1 distance from de radar to the obstacle (km) d2 distance from the obstacle to the target (km) 2) Single rounded obstacle: Diffraction loss associated with this geometry, A, can be calculated from equation: A = J(ν ) + T J(ν) is the Fresnel-Kirchoff loss due to the equivalent knife-edge obstacle with a maximum height that equals the vertex of the parabola. T is the additional attenuation due to the curvature of the obstacle and can be calculated from geometric parameters of the obstacle. 3) Double obstacles: When there are two perfectly identified isolated obstacles in the route, either knife-edge or rounded, methods derived from the theory of diffraction on isolated obstacles are applied successively to the two obstacles, with the top of the first obstacle acting as a source for diffraction over the second obstacle. The total diffraction loss is then given by: L = L1 + L2 + Lc. The first diffraction path gives a loss L1 (dB) and the second diffraction path gives a loss L2 (dB). L1 and L2 are calculated considering an isolated obstacle in the path. A correction term Lc (dB) is added to take into account the separation between the edges. 4) Multiple obstacles: When there are multiple obstacles in the route we use a method derived from the cascade cylinder method. Figure 1 illustrates the geometry for an obstruction consisting of more than one string point. The following points are indicated by: w: closest string point or terminal on the transmitter side of the obstruction which is not part of the obstruction; x: string point forming part of the obstruction which is closest to the transmitter; y: string point forming part of the obstruction which is closest to the receiver; z: closest string point or terminal on the receiver side of the obstruction which is not part of the obstruction; v: vertex point made by the intersection of incident rays above the obstruction. ERAD 2012 - THE SEVENTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY Fig. 1 Geometry of a multipoint obstacle The letters w, x, y and z will also be indices to the arrays of profile distance and height samples. For an obstruction consisting of an isolated string point, x and y will have the same value, and will refer to a profile point which coincides with the vertex. Note that for cascaded cylinders, points y and z for one cylinder are points w and x for the next, etc. The total diffraction loss, in dB relative to free-space loss, may be written:: N N = ′ + ′′ + ′′ Ld ∑ Li L (w x)1 ∑ L (y z)i – 20 log C N dB i = 1 i = 1 L'i : diffraction loss over the i-th cylinder L"(w x)1 : sub-path diffraction loss for the section of the path between points w and x for the first cylinder L"(y z)i : sub-path diffraction loss for the section of the path between points y and z for all cylinders CN : correction factor to account for spreading loss due to diffraction over successive cylinders.
Load more

Recommended publications
  • 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].
    [Show full text]
  • 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.
    [Show full text]
  • 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 ..........................................................................
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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: .
    [Show full text]
  • 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.
    [Show full text]
  • 4. Fresnel and Fraunhofer Diffraction
    13. Fresnel diffraction Remind! Diffraction regimes Fresnel-Kirchhoff diffraction formula E exp(ikr) E PF= 0 ()θ dA ()0 ∫∫ irλ ∑ z r Obliquity factor : F ()θθ= cos = r zE exp (ikr ) E x,y = 0 ddξ η () ∫∫ 2 irλ ∑ Aperture (ξ,η) Screen (x,y) 22 rzx=+−+−2 ()()ξ yη 22 22 ⎡⎤11⎛⎞⎛⎞xy−−ξη()xy−−ξ ()η ≈+zz⎢⎥1 ⎜⎟⎜⎟ + =+ + ⎣⎦⎢⎥22⎝⎠⎝⎠zz 22 zz ⎛⎞⎛⎞xy22ξη 22⎛⎞ xy ξη =++++−+z ⎜⎟⎜⎟⎜⎟ ⎝⎠⎝⎠22zz 22 zz⎝⎠ zz E ⎡⎤k Exy(),expexp=+0 ()ikz i() x22 y izλ ⎣⎦⎢⎥2 z ⎡⎤⎡⎤kk22 ×+−+∫∫ exp⎢⎥⎢⎥ii()ξ ηξ exp()xyη ddξη ∑ ⎣⎦⎣⎦2 zz E ⎡⎤k Exy(),expexp=+0 ()ikz i() x22 y r izλ ⎣⎦⎢⎥2 z ⎡⎤⎡⎤kk ×+−+exp iiξ 22ηξexp xyη dξdη ∫∫ ⎢⎥⎢⎥() () Aperture (ξ,η) Screen (x,y) ∑ ⎣⎦⎣⎦2 zz ⎡⎤⎡⎤kk22 =+−+Ci∫∫ exp ⎢⎥⎢⎥()ξ ηξexp ixydd()η ξη ∑ ⎣⎦⎣⎦2 zz Fresnel diffraction ⎡⎤⎡⎤kk E ()xy,(,)=+ C Uξ ηξηξηξηexp i ()22 exp−i() x+ y d d ∫∫ ⎣⎦⎣⎦⎢⎥⎢⎥2 zz k 22 ⎧ j ()ξη+ ⎫ Exy(, )∝F ⎨ U()ξη , e2z ⎬ ⎩⎭ Fraunhofer diffraction ⎡⎤k Exy(),(,)=−+ C Uξη expi() xξ y η dd ξ η ∫∫ ⎣⎦⎢⎥z =−+CU(,)expξ ηξθηθξη⎡⎤ ik sin sin dd ∫∫ ⎣⎦()ξη Exy(, )∝F { U(ξ ,η )} Fresnel (near-field) diffraction This is most general form of diffraction – No restrictions on optical layout • near-field diffraction k 22 ⎧ j ()ξη+ ⎫ • curved wavefront Uxy(, )≈ F ⎨ U()ξη , e2z ⎬ – Analysis somewhat difficult ⎩⎭ Curved wavefront (parabolic wavelets) Screen z Fresnel Diffraction Accuracy of the Fresnel Approximation 3 π 2 2 2 z〉〉[()() x −ξ + y η −] 4λ max • Accuracy can be expected for much shorter distances for U(,)ξ ηξ smooth & slow varing function; 2x−=≤ D 4λ z D2 z ≥ Fresnel approximation 16λ In summary, Fresnel diffraction is … 13-7.
    [Show full text]
  • Microwave Path Engineering April 2005
    Microwave Path Engineering USTTI Course 19-311 September 24, 2019 Course Outline 1. Microwave Components 2. RF Propagation 3. Link Budget 4. Reliability 5. Interference Analysis © 2014 CommScope, Inc. 2 Microwave Diagram Antenna Antenna Waveguide Waveguide Radio Radio © 2014 CommScope, Inc. 3 Radio Equipment © 2014 CommScope, Inc. 4 Radio Equipment Theoretical Error Performance of Digital Modulation Schemes -2 Excludes FEC Improvement • “Waterfall” -3 Curves -4 -5 -6 -7 -8 Log BER Probability (e.g. = -6 BER) 10-6 -9 BPSK -10 -11 4 PSK QPSK 8 PSK 4 QAM 16 QAM 64 QAM 256 QAM -12 5 10 15 20 25 30 35 40 C/N (RF Carrier-to-Noise Ratio) dB © 2014 CommScope, Inc. 5 Radio Equipment • Threshold – Minimum receiver input level below which BER becomes excessive due to thermal noise • The 10-6 BER threshold is called the Static Threshold • The 10-3 BER threshold is called the Dynamic or Outage Threshold • Oversaturation Level – Maximum receiver input level above which BER becomes excessive due to overdriving electronics into saturation (distortion) • Receiver can operate with low error rate between threshold and oversaturation dynamic range © 2014 CommScope, Inc. 6 Radio Equipment - Data Rates of Common Interfaces North American Digital Hierarchy Designation Data Rate DS0's (# of VC) DS1 (T1) 1.544 Mb/s 24 DS2 (T2) 6.312 Mb/s 96 DS3 (T3) 45 Mb/s 672 3xDS3 135 Mb/s 2016 DS5 (T5) 400 Mb/s 5760 European Digital Hierarchy Designation Data Rate DS0's (# of VC) E1 2.048 Mb/s 32 E2 8.448 Mb/s 128 E3 34.4 Mb/s 512 E4 139.3 Mb/s 2048 E5 565 Mb/s 8192 Optical Signal Hierarchy SONET Designation SDH Designation Data Rate STS-3 STM-1 155.52 Mb/s STS-12 STM-4 622.08 Mb/s STS-48 STM-16 2488.32 Mb/s STS-192 STM-64 9953.28 Mb/s © 2014 CommScope, Inc.
    [Show full text]
  • Optimizing the RF Link
    Application Note Optimizing the RF Link One of the most frequent questions we get is “how far can your radios go?” This is not an easy question to answer, as there are many factors that go into this. This application note gives an overview of the major considerations and discusses methods to optimize the link performance. Our intention is to provide some useful insights which can help during the design of a RF link. Our overall recommendation is to design a link with about 10-15 dB fade margin to account for changes in the environmental and operational conditions. Mobile nodes change the orientation that can affect the link margin. Use the highest gain antenna and keep maximum distance between the antennas possible within the physical constraints of the system. The objective is to operate the link with the highest SNR (RSSI) possible (Sweet spot for Smart Radio is around -60 dB to -70 dB RSSI). Higher RSSI level will allow the link to operate at the highest modulation, provide the best throughput, interference resistance and reliability. Factors affecting the RF link By laws of physics, the RF link range, can be expressed in simple terms as a function of - RF Link Range = f(Tx power, Rx sensitivity, Antenna Gain, Path loss). Unpacking this shows us that many factors affect the RF link range. Here we list the major factors affecting the RF link and we will briefly discuss each of them and provide some insights that can help achieve the long range links. 1. Operating frequency 2. RF power 3.
    [Show full text]