1、 Recommendation ITU-R P.526-13(11/2013)Propagation by diffractionP SeriesRadiowave propagationii Rec. ITU-R P.526-13 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 service
2、s, 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 Radiocommunication As
3、semblies 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 by pat
4、ent 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.int/pu
5、bl/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 propagation RA
6、 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 emissions V V
7、ocabulary and related subjects Note: This ITU-R Recommendation was approved in English under the procedure detailed in Resolution ITU-R 1. Electronic Publication Geneva, 2013 ITU 2013 All rights reserved. No part of this publication may be reproduced, by any means whatsoever, without written permiss
8、ion of ITU. Rec. ITU-R P.526-13 1 RECOMMENDATION ITU-R P.526-13 Propagation by diffraction (Question ITU-R 202/3) (1978-1982-1992-1994-1995-1997-1999-2001-2003-2005-2007-2009-2012-2013) Scope This Recommendation presents several models to enable the reader to evaluate the effect of diffraction on th
9、e 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, recommends that the
10、 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 ground or other
11、 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 traced with th
12、e 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 context, before
13、going further into the prediction methods for this propagation mechanism, a few basic concepts are given in this section. 2.1 Fresnel ellipsoids and Fresnel zones In studying radiowave propagation between two points A and B, the intervening space can be subdivided by a family of ellipsoids, known as
14、 Fresnel ellipsoids, all having their focal points at A and B such that any point M on one ellipsoid satisfies the relation: 2 Rec. ITU-R P.526-13 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 wavelengt
15、h. 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-consistent
16、 units by: 2/12121+=ddddnRn(2) or, in practical units: 2/12121)(550+=fddddnRn(3) where f is the frequency (MHz) and d1and d2are the distances (km) between transmitter and receiver at the point where the ellipsoid radius (m) is calculated. Some problems require consideration of Fresnel zones which ar
17、e 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 takes place a
18、long 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. ITU-R P.52
19、6-13 3 FIGURE 1 Definition of penumbra width P.0526-01Transmitterhorizonwh2.3 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 the transmitter horizon whe
20、re 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 considered smooth and the
21、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 obstacle alone without any
22、 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 radius; no specular re
23、flection 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 Earth can be considere
24、d 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). 4 Rec. ITU-R P.526-13 b) Isolated obstacles T
25、he 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 The profile consists of s
26、everal 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)()(d2exp)( jSCssjFc(6) where j is t
27、he complex operator equal to 1, and C() and S() are the Fresnel cosine and sine integrals defined by: =02d2cos)( ssC (7a) =02d2sin)( ssS (7b) The complex Fresnel integral Fc() can be evaluated by numerical integration, or with sufficient accuracy for most purposes for positive using: 40for4)(4)exp()
28、(1102 (18) )1.0log(20)(3BBYG + for B 2 (18a) If KYG log202)( + ),()(),()(22/1212/11(19) where: ()1280.1096.1 =limX (19a) ()0,(),(1779.1)0,(),( YYYKY += (19b) (Y,0) and (Y,) are given by: +=3.0255.0)log(5.0tanh15.0)0,(YY (19c) +=25.0255.0)log(5.0tanh15.0),(YY (19d) Consequently, the minimum distance
29、dminfor which equation (13) is valid is given by: ),()(),()(22/1212/11KYYKYYXXlimmin+= (19e) and dminis obtained from Xminusing equation (14a). 10 Rec. ITU-R P.526-13 3.1.2 Calculation by nomograms Under the same approximation condition (the first term of the residue series is dominant), the calcula
30、tion may also be made using the following formula: )(H)(H)(Flog20210hhdEE+= dB (20) where: E : received field strength; 0: field strength in free space at the same distance; d : distance between the extremities of the path; h1 and h2: heights of the antennas above the spherical earth. The function F
31、 (influence of the distance) and H (height-gain) are given by the nomograms in Figs 3, 4, 5 and 6. These nomograms (Figs 3 to 6) give directly the received level relative to free space, for k = 1 and k = 4/3, and for frequencies greater than approximately 30 MHz. k is the effective Earth radius fact
32、or, defined in Recommendation ITU-R P.310. However, the received level for other values of k may be calculated by using the frequency scale for k = 1, but replacing the frequency in question by a hypothetical frequency equal to f / k2for Figs 3 and 5 and ,/ kf for Figs 4 and 6. Very close to the gro
33、und the field strength is practically independent of the height. This phenomenon is particularly important for vertical polarization over the sea. For this reason Fig. 6 includes a heavy black vertical line AB. If the straight line should intersect this heavy line AB, the real height should be repla
34、ced by a larger value, so that the straight line just touches the top of the limit line at A. NOTE 1 Attenuation relative to free space is given by the negative of the values given by equation (20). If equation (20) gives a value above the free-space field, the method is invalid. NOTE 2 The effect o
35、f line AB is included in the numerical method given in 3.1.1. Rec. ITU-R P.526-13 11 FIGURE 3 Diffraction by a spherical Earth effect of distance P.0526-03Frequencyfor=1kFrequency for= 4/3kDistance (km)Level(dB)inrelationtofree spaceHorizontal polarization over land and seaVertical polarization over
36、 land(The scales joined by arrows should be used together)1.51.51.51009080706050403020101510090807060504030201015891502003004005006007008009001 00012345678920151050 5 10 15 20 10 15 20 25 30 35 40 50 60 70 80 90 100 150 200 250 300 35030405060708090100 MHz1502003004005006007008009001 GHz2345678910 G
37、Hz15GHz 1098765432900800700600500400300200150MHz 10090807060504030GHz 12012 Rec. ITU-R P.526-13 FIGURE 4 Diffraction by a spherical Earth height-gain P.0526-041.51.5Height of antennaabove ground (m)Height-gain (dB)H( )hHorizontal polarization land and seaVertical polarization land Frequency fork = 1
38、 k = 4/32 0001 5001 0009008007006005004003002001501009080706050403020151098765431801601401201009080706050403020100 10 20 3015GHz 1098765432900800700600500400300200150MHz 1009080706050403030405060708090100 MHz1502003004005006007008009001 GHz2345678910 GHz15GHz 1Rec. ITU-R P.526-13 13 FIGURE 5 Diffrac
39、tion by a spherical Earth effect of distance P.0526-05Frequencyfor=1kFrequencyfor=4/3kDistance (km)Level(dB)relativetofree spaceVertical polarization over sea(The scales joined by arrows should be used together)1.51.51.51009080706050403020101510090807060504030201015891502003004005006007008009001 000
40、12345678920151050 5 10 15 20 10 15 20 25 30 35 40 50 60 70 80 90 100 150 200 250 300 350GHz 1098765432900800700600500400300200150MHz 1009080706050403030405060708090100 MHz1502003004005006007008009001 GHz2345678910 GHz15GHz 114 Rec. ITU-R P.526-13 FIGURE 6 Diffraction by a spherical Earth height-gain
41、 P.0526-06Rec. ITU-R P.526-13 15 3.2 Diffraction loss for any distance at 10 MHz and above The following step-by-step procedure should be used for a spherical-earth path of any length at frequencies of 10 MHz and above, for effective Earth radius ae 0. The method uses the calculation in 3.1.1 for ov
42、er-the-horizon cases, and otherwise an interpolation procedure based on a notional effective-earth radius. The procedure uses self-consistent units and proceeds as follows: Calculate the marginal LoS distance given by: ( )212 hhadelos+= (21) If d dloscalculate diffraction loss using the method in 3.
43、1.1. No further calculation is necessary. Otherwise continue: Calculate the smallest clearance height between the curved-earth path and the ray between the antennas, h (see Fig. 7), given by: ddadhdadhhee1222221122+= (22) )1(21bdd += (22a) 12ddd = (22b) +=3)1(323arccos313cos312mmcmmb (22c) 2121hhhhc
44、+= (22d) )(4212hhadme+= (22e) Calculate the required clearance for zero diffraction loss, hreq, given by: dddhreq552.021= (23) If h hreqthe diffraction loss for the path is zero. No further calculation is required. Otherwise continue: Calculate the modified effective earth radius, aem, which gives m
45、arginal LoS at distance d given by: 16 Rec. ITU-R P.526-13 2215.0+=hhdaem(24) Use the method in 3.1.1 to calculate the diffraction loss for the path using the modified effective earth radius aem in place of the effective earth radius ae, and designate this loss Ah. If Ahis negative, the diffraction
46、loss for the path is zero, and no further calculation is necessary. Otherwise calculate the interpolated diffraction loss, A (dB), given by: hreqAhhA /1 = (25) 4 Diffraction over isolated obstacles or a general terrestrial path Many propagation paths encounter one obstacle or several separate obstac
47、les and it is useful to estimate the losses caused by such obstacles. To make such calculations, it is necessary to idealize the form of the obstacles, either assuming a knife-edge of negligible thickness or a thick smooth obstacle with a well-defined radius of curvature at the top. Real obstacles h
48、ave, of course, more complex forms, so that the indications provided in this Recommendation should be regarded only as an approximation. In those cases where the direct path between the terminals is much shorter than the diffraction path, it is necessary to calculate the additional transmission loss due to the longer path. The data given below apply when the wavelength is fairly small in relation to the size of the obstacles, i.e. mainly to VHF and shorter waves ( f 30 MHz). FIGURE 7 Path clearance P.0526-07P: Reflection pointh1hh2d1d2P4.1 Single knife-edge obstacle In th
