1、 Recommendation ITU-R P.526-14 (01/2018) Propagation by diffraction P Series Radiowave propagation ii Rec. ITU-R P.526-14 Foreword The role of the Radiocommunication Sector is to ensure the rational, equitable, efficient and economical use of the radio-frequency spectrum by all radiocommunication se
2、rvices, including satellite services, and carry out studies without limit of frequency range on the basis of which Recommendations are adopted. The regulatory and policy functions of the Radiocommunication Sector are performed by World and Regional Radiocommunication Conferences and Radiocommunicati
3、on Assemblies supported by Study Groups. Policy on Intellectual Property Right (IPR) ITU-R policy on IPR is described in the Common Patent Policy for ITU-T/ITU-R/ISO/IEC referenced in Annex 1 of Resolution ITU-R 1. Forms to be used for the submission of patent statements and licensing declarations b
4、y patent holders are available from http:/www.itu.int/ITU-R/go/patents/en where the Guidelines for Implementation of the Common Patent Policy for ITU-T/ITU-R/ISO/IEC and the ITU-R patent information database can also be found. Series of ITU-R Recommendations (Also available online at http:/www.itu.i
5、nt/publ/R-REC/en) Series Title BO Satellite delivery BR Recording for production, archival and play-out; film for television BS Broadcasting service (sound) BT Broadcasting service (television) F Fixed service M Mobile, radiodetermination, amateur and related satellite services P Radiowave propagati
6、on RA Radio astronomy RS Remote sensing systems S Fixed-satellite service SA Space applications and meteorology SF Frequency sharing and coordination between fixed-satellite and fixed service systems SM Spectrum management SNG Satellite news gathering TF Time signals and frequency standards emission
7、s V Vocabulary and related subjects Note: This ITU-R Recommendation was approved in English under the procedure detailed in Resolution ITU-R 1. Electronic Publication Geneva, 2018 ITU 2018 All rights reserved. No part of this publication may be reproduced, by any means whatsoever, without written pe
8、rmission of ITU. Rec. ITU-R P.526-14 1 RECOMMENDATION ITU-R P.526-14 Propagation by diffraction (Question ITU-R 202/3) (1978-1982-1992-1994-1995-1997-1999-2001-2003-2005-2007-2009-2012-2013-2018) Scope This Recommendation presents several models to enable the reader to evaluate the effect of diffrac
9、tion on the received field strength. The models are applicable to different obstacle types and to various path geometries. The ITU Radiocommunication Assembly, considering that there is a need to provide engineering information for the calculation of field strengths over diffraction paths, recommend
10、s that the methods described in Annex 1 be used for the calculation of field strengths over diffraction paths, which may include a spherical earth surface, or irregular terrain with different kinds of obstacles. Annex 1 1 Introduction Although diffraction is produced only by the surface of the groun
11、d or other obstacles, account must be taken of the mean atmospheric refraction on the transmission path to evaluate the geometrical parameters situated in the vertical plane of the path (angle of diffraction, radius of curvature, height of obstacle). For this purpose, the path profile has to be trac
12、ed with the appropriate equivalent Earth radius (Recommendation ITU-R P.834). If no other information is available, an equivalent Earth radius of 8 500 km may be taken as a basis. 2 Basic concepts Diffraction of radiowaves over the Earths surface is affected by terrain irregularities. In this contex
13、t, before going further into the prediction methods for this propagation mechanism, a few basic concepts are given in this section. 2 Rec. ITU-R P.526-14 2.1 Fresnel ellipsoids and Fresnel zones In studying radiowave propagation between two points A and B, the intervening space can be subdivided by
14、a family of ellipsoids, known as Fresnel ellipsoids, all having their focal points at A and B such that any point M on one ellipsoid satisfies the relation: 2AB MBAM n (1) where n is a whole number characterizing the ellipsoid and n = 1 corresponds to the first Fresnel ellipsoid, etc., and is the wa
15、velength. As a practical rule, propagation is assumed to occur in line-of-sight (LoS), i.e. with negligible diffraction phenomena if there is no obstacle within the first Fresnel ellipsoid. The radius of an ellipsoid at a point between the transmitter and the receiver can be approximated in self-con
16、sistent units by: 2/12121 dd ddnR n (2) or, in practical units: 2/12121 )(550 fdd ddnR n (3) where f is the frequency (MHz) and d1 and d2 are the distances (km) between transmitter and receiver at the point where the ellipsoid radius (m) is calculated. Some problems require consideration of Fresnel
17、zones which are the zones obtained by taking the intersection of a family of ellipsoids by a plane. The zone of order n is the part between the curves obtained from ellipsoids n and n 1, respectively. 2.2 Penumbra width The transition from light to shadow defines the penumbra region. This transition
18、 takes place along a narrow strip (penumbra width) in the boundary of geometric shadow. Figure 1 shows the penumbra width (W) in the case of a transmitter located a height, h, above a smooth spherical earth, which is given by: 3/12 eaw m (4) where: : wavelength (m) ae: effective Earth radius (m) Rec
19、. ITU-R P.526-14 3 FIGURE 1 Definition of penumbra width P .052 6-01T r a ns m i t t e rhor i z onwh2.3 Diffraction zone The diffraction zone of a transmitter extends from the LoS distance where the path clearance is equal to 60% of the first Fresnel zone radius, (R1), up to a distance well beyond t
20、he transmitter horizon where the mechanism of troposcatter becomes predominant. 2.4 Obstacle surface smoothness criterion If the surface of the obstacle has irregularities not exceeding h, where: 3/1204.0 Rh m (5) where: R: obstacle curvature radius (m) : wavelength (m); then the obstacle may be con
21、sidered smooth and the methods described in 3 and 4.2 may be used to calculate the attenuation. 2.5 Isolated obstacle An obstacle can be considered isolated if there is no interaction between the obstacle itself and the surrounding terrain. In other words, the path attenuation is only due to the obs
22、tacle alone without any contribution from the remaining terrain. The following conditions must be satisfied: no overlapping between penumbra widths associated with each terminal and the obstacle top; the path clearance on both sides of the obstacles should be, at least, 0.6 of the first Fresnel zone
23、 radius; no specular reflection on both sides of the obstacle. 2.6 Types of terrain Depending on the numerical value of the parameter h (see Recommendation ITU-R P.310) used to define the degree of terrain irregularities, three types of terrain can be classified: a) Smooth terrain The surface of the
24、 Earth can be considered smooth if terrain irregularities are of the order or less than 0.1R, where R is the maximum value of the first Fresnel zone radius in the propagation path. In this case, the prediction model is based on the diffraction over the spherical Earth (see 3). b) Isolated obstacles
25、4 Rec. ITU-R P.526-14 The terrain profile of the propagation path consists of one or more isolated obstacles. In this case, depending on the idealization used to characterize the obstacles encountered in the propagation path, the prediction models described in 4 should be used. c) Rolling terrain Th
26、e profile consists of several small hills, none of which form a dominant obstruction. Within its frequency range Recommendation ITU-R P.1546 is suitable for predicting field strength but it is not a diffraction method. 2.7 Fresnel integrals The complex Fresnel integral is given by: 02 )()(d2e x p)(
27、jSCssjF c(6) where j is the complex operator equal to 1, and C() and S() are the Fresnel cosine and sine integrals defined by: 02 d2c o s)( ssC(7a) 02 d2s in)( ssS(7b) The complex Fresnel integral Fc() can be evaluated by numerical integration, or with sufficient accuracy for most purposes for posit
28、ive using: 40f o r4)(4)e x p ()(110 xxjbaxjxF nnnnc(8a) 4f o r4)(4)e x p (21)(110 xxjdcxjxjF nnnnc(8b) where: x = 0.5 2 (9) and an, bn, cn and dn are the Boersma coefficients given below: a0 = +1.595769140 b0 = -0.000000033 c0 = +0.000000000 d0 = +0.199471140 a1 = -0.000001702 b1 = +4.255387524 c1 =
29、 -0.024933975 d1 = +0.000000023 a2 = -6.808568854 b2 = -0.000092810 c2 = +0.000003936 d2 = -0.009351341 a3 = -0.000576361 b3 = -7.780020400 c3 = +0.005770956 d3 = +0.000023006 a4 = +6.920691902 b4 = -0.009520895 c4 = +0.000689892 d4 = +0.004851466 a5 = -0.016898657 b5 = +5.075161298 c5 = -0.00949713
30、6 d5 = +0.001903218 a6 = -3.050485660 b6 = -0.138341947 c6 = +0.011948809 d6 = -0.017122914 a7 = -0.075752419 b7 = -1.363729124 c7 = -0.006748873 d7 = +0.029064067 a8 = +0.850663781 b8 = -0.403349276 c8 = +0.000246420 d8 = -0.027928955 a9 = -0.025639041 b9 = +0.702222016 c9 = +0.002102967 d9 = +0.01
31、6497308 a10 = -0.150230960 b10 = -0.216195929 c10 = -0.001217930 d10 = -0.005598515 a11 = +0.034404779 b11 = +0.019547031 c11 = +0.000233939 d11 = +0.000838386 Rec. ITU-R P.526-14 5 C() and S() may be evaluated for negative values of by noting that: C() = C() (10a) S() = S() (10b) 3 Diffraction over
32、 a spherical Earth The additional transmission loss due to diffraction over a spherical Earth can be computed by the classical residue series formula. A computer program GRWAVE, available from the ITU, provides the complete method. A subset of the outputs from this program (for antennas close to the
33、 ground and at lower frequencies) is presented in Recommendation ITU-R P.368. The following subsections describe numerical and nomogram methods which may be used for frequencies 10 MHz and above. For frequencies below 10 MHz, GRWAVE should always be used. Section 3.1 gives methods for over-the-horiz
34、on paths. Section 3.1.1 is a numerical method. Section 3.1.2 is a nomogram method. Section 3.2 is a method applicable for the smooth earth case for any distance and for frequencies 10 MHz and above. This utilizes the numerical method in 3.1.1. 3.1 Diffraction loss for over-the-horizon paths At long
35、distances over the horizon, only the first term of the residue series is important. Even near or at the horizon this approximation can be used with a maximum error around 2 dB in most cases. This first term can be written as the product of a distance term, F, and two height gain terms, GT and GR. Se
36、ctions 3.1.1 and 3.1.2 describe how these terms can be obtained from simple formula or from nomograms. 3.1.1 Numerical calculation 3.1.1.1 Influence of the electrical characteristics of the surface of the Earth The extent to which the electrical characteristics of the surface of the Earth influence
37、the diffraction loss can be determined by calculating a normalized factor for surface admittance, K, given by the formulae: in self-consistent units: 4/1223/1 )60()1(2 eH aKfor horizontal polarization (11) and 2/122 )60( HV KK for vertical polarization (12) or, in practical units: 4/1223/1 )/00018()
38、1()(36.0 ffaK eH (11a) 2/122 )/00018( fKK HV (12a) where: ae : effective radius of the Earth (km) 6 Rec. ITU-R P.526-14 : effective relative permittivity : effective conductivity (S/m) f : frequency (MHz). Typical values of K are shown in Fig. 2. FIGURE 2 Calculation of K P .0526-02805Normalizedfact
39、orforsurfaceadmittance,KF r e que nc yV e r t i c a lH or i z ont a l5 5 5 5 5 510 kH z 100 kH z 1 M H z 10 M H z 100 M H z 1 G H z 10 G H z522525251012103101103010231041510330102310415103If K is less than 0.001, the electrical characteristics of the Earth are not important. For values of K greater
40、than 0.001 and less than 1, the appropriate formulae given in 3.1.1.2 can be used. When K has a value greater than about 1, the diffraction field strength calculated using the method of 3.1.1.2 Rec. ITU-R P.526-14 7 differs from the results given by the computer program GRWAVE, and the difference in
41、creases rapidly as K increases. GRWAVE should be used for K greater than 1. This only occurs for vertical polarization, at frequencies below 10 MHz over sea, or below 200 kHz over land. In all other cases the method of 3.1.1.2 is valid. 3.1.1.2 Diffraction field strength formulae The diffraction fie
42、ld strength, E, relative to the free-space field strength, E0, is given by the formula: dB)()()(l o g20210 YGYGXFEE (13) where X is the normalized length of the path between the antennas at normalized heights Y1 and Y2 (and where 0log20 EE is generally negative). In self-consistent units: daX e3/12
43、(14) haY e3/1222 (15) or, in practical units: dafX e 3/23/1188.2 (14a) hafY e 3/13/23 10575.9 (15a) where: d : path length (km) ae : equivalent Earths radius (km) h : antenna height (m) f : frequency (MHz). is a parameter allowing for the type of ground and for polarization. It is related to K by th
44、e following semi-empirical formula: 424253.15.41 67.06.11 KK KK (16) For horizontal polarization at all frequencies, and for vertical polarization above 20 MHz over land or 300 MHz over sea, may be taken as equal to 1. For vertical polarization below 20 MHz over land or 300 MHz over sea, must be cal
45、culated as a function of K. However, it is then possible to disregard and write: 8 Rec. ITU-R P.526-14 3/53/22 89.6 fkK (16a) where is expressed in S/m, f (MHz) and k is the multiplying factor of the Earths radius. The distance term is given by the formula: F(X) = 11 + 10 log (X) 17.6 X for X 1.6 (1
46、7a) F(X) = 20 log (X) 5.6488X1.425 for X 2 (18) )1.0lo g(20)( 3BBYG for B 2 (18a) If KYG log202)( , set )(YG to the value Klog202 In the above: YB (18b) The accuracy of the diffracted field strength given by equation (13) is limited by the approximation inherent in only using the first term of the r
47、esidue series. Equation (13) is accurate to better than 2 dB for values of X, Y1 and Y2 that are constrained by the formula: limXKYYKYYX ),()(),()( 22/1212/11 (19) where: 1280.1096.1 limX (19a) )0,(),(1779.1)0,(),( YYYKY (19b) (Y,0) and (Y,) are given by: 3.0 255.0)l o g (5.0t a n h15.0)0,( YY(19c)
48、25.0 255.0)l o g (5.0t a n h15.0),( YY(19d) Consequently, the minimum distance dmin for which equation (13) is valid is given by: ),()(),()( 22/1212/11 KYYKYYXX limm i n (19e) Rec. ITU-R P.526-14 9 and dmin is obtained from Xmin using equation (14a). 3.1.2 Calculation by nomograms Under the same approximation condition (the first term of the residue series is dominant), the calculation may also be made using the followin
