1、 Recommendation ITU-R P.1815-1(10/2009)Differential rain attenuationP SeriesRadiowave propagationii Rec. ITU-R P.1815-1 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 serv
2、ices, 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
3、 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 by
4、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.int
5、/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 propagation
6、 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 emissions
7、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, 2009 ITU 2009 All rights reserved. No part of this publication may be reproduced, by any means whatsoever, without written perm
8、ission of ITU. Rec. ITU-R P.1815-1 1 RECOMMENDATION ITU-R P.1815-1 Differential rain attenuation (Question ITU-R 208/3) (2007-2009) Scope This Recommendation predicts the joint differential rain attenuation statistics between a satellite and two locations on the surface of the Earth. The ITU Radioco
9、mmunication Assembly, considering a) that it is necessary to have appropriate techniques to predict differential attenuation due to rain between satellite paths from a single satellite to multiple locations on the surface of the Earth for the purpose of sharing analyses; b) that estimates of the spa
10、tial correlation of rain rate are available; c) that methods have been developed to predict differential attenuation between space-Earth paths due to rain, recommends 1 that the methods described in Annex 1 should be used to predict differential rain attenuation on satellite paths between a single s
11、atellite and multiple locations on the surface of the Earth. Annex 1 Description of differential rain attenuation method 1 Introduction The method described in this Annex predicts the joint differential rain attenuation statistics between a satellite and two locations on the surface of the Earth and
12、 is applicable to frequencies up to 55 GHz, elevation angles above approximately 10, and site separations between 0 and at least 250 km. This method considers the statistical and temporal characteristics of rain cell size, rain intensity and movement of rain cells related to differential rain attenu
13、ation. 2 Rec. ITU-R P.1815-1 FIGURE 1 Differential attenuation geometry The geometry is shown in Fig. 1, where A1and A2, are the rain attenuations on path 1 and path 2, respectively. The desired statistic is the joint probability that the attenuation on the first path, A1, is between a and b, and th
14、e attenuation on the second path, A2, is less than or equal to A1 c; i.e. Pra A1 b, A2 A1 c. This joint probability is shown graphically in Fig. 2 as the integrated probability within the shaded region. FIGURE 2 Desired joint probability distribution Rec. ITU-R P.1815-1 3 The joint probability withi
15、n the shaded region of Fig. 2 can be well-approximated as the sum of the integrated probabilities within the narrow vertical rectangular regions as illustrated in Fig. 3. FIGURE 3 Approximation to desired joint probability distribution The joint probability within the shaded region in Fig. 3 can the
16、n be computed as the difference between the joint probability within the shaded region in Fig. 4 and the joint probability within the shaded region in Fig. 5. FIGURE 4 Pr(A1 a) Pr(A1 b) 4 Rec. ITU-R P.1815-1 FIGURE 5 =+niciaAiaAciaAiaA12121)1(,2)1( Pr)1(,2)1( PrFrom Figs. 4 and 5, the joint probabil
17、ity Pra A1 b, A2 A1 c can be well-approximated by: ()()=+=niciaAiaAciaAiaAbAaAcAAbAa1212111121)1(,2)1(Pr)1(,2)1(PrPrPr,Prwhere: nab = and the number of points, n, is selected so the approximation is sufficiently accurate. A step size, , of 0.01 dB generally provides sufficient accuracy. This method
18、can also be used to compute other desired joint probabilities. For example, the joint probability Pra A1 b, A2 d shown in the shaded region of Fig. 6 is: Pra A1 b, A2 d = PrA1 a PrA1 b Pr(A1 a, A2 d) Pr(A1 b, A2 d) Rec. ITU-R P.1815-1 5 FIGURE 6 dAbAa 21,Pr 2 Annual differential attenuation statisti
19、cs If annual differential attenuation statistics are required, the probability bAaA 21,Pr can be computed using the prediction method described in Annex 2, based on fitting the single-site rain attenuations vs. annual probabilities of occurrence, aA 1Pr and bA 2Pr , to log-normal probability distrib
20、utions. The rain attenuation vs. annual probability of occurrence can be predicted using the method described in 2.2.1.1 of Recommendation ITU-R P.618. Annual differential attenuation statistics can be obtained using the following procedure: Step 1: Obtain the annual rain attenuation vs. probability
21、 of occurrence using the ITU-R rain attenuation prediction method described in 2.2.1.1 of Recommendation ITU-R P.618. Step 2: Apply the differential rain attenuation prediction method described in 1, where the appropriate probabilities ()2211,Pr aAaA are calculated using the method described in Anne
22、x 2. 3 Worst-month differential attenuation statistics If worst-month differential attenuation statistics are required, Recommendation ITU-R P.841 can be used to convert single-site annual rain attenuation statistics to single-site worst-month rain attenuation statistics. Worst-month differential at
23、tenuation statistics can be obtained using the following procedure: Step 1: Obtain the annual rain attenuation vs. probability of occurrence using the ITU-R rain attenuation prediction method described in 2.2.1.1 of Recommendation ITU-R P.618. Step 2: Convert the annual rain attenuation statistics t
24、o worst-month rain attenuation statistics using the ITU-R worst-month conversion method described in Recommendation ITU-R P.841. Step 3: Apply the differential rain attenuation prediction method described in 1, where the appropriate probabilities ()2211,Pr aAaA are calculated using the method descri
25、bed in Annex 2. 6 Rec. ITU-R P.1815-1 Annex 2 Description of differential rain attenuation prediction method 1 Analysis The differential rain attenuation prediction method assumes a log-normal distribution of rain intensity and rain attenuation. This method predicts ()2211,Pr aAaA , the joint probab
26、ility (%) that the attenuation on the path to the first site is greater than a1and the attenuation on the path to the second site is greater than 2a . ()2211,Pr aAaA is the product of two joint probabilities: rP : joint probability that it is raining at both sites, and aP : conditional joint probabi
27、lity that the attenuations exceed a1and a2, respectively, given that it is raining at both sites; i.e.: ()arPPaA,aA = 100Pr2211% (1) These probabilities are: ()2122221212dd122exp12112rrrrrrPRRrrrr+= (2) where: () () 2700exp3060exp70 /d./d.r+= (3) and ()21ln ln22221212dd122exp1211ln1ln12ln2ln2aaaaaaP
28、AAAAmama aaaa+= (4) where: () () 2500exp06030exp940 /d./d.a+= (5) and Pa and Pr are complementary bivariate normal distributions. Rec. ITU-R P.1815-1 7 The parameter d is the separation between the two sites (km). The thresholds R1and R2are the solutions of: ()=kRkrainkrrRQP d2exp211001002(6) i.e.:
29、=1001rainkkPQR (7) where: kR : threshold for the k-th site, respectively rainkP : probability of rain (%) Q: complementary cumulative normal distribution Q1: inverse complementary cumulative normal distribution rainkP : for a particular location can be obtained from Step 3 of Annex 1 of Recommendati
30、on ITU-R P.837 using either local data or the ITU-R rainfall rate maps. The values of the parameters 121lnlnln,AAAmm and 2ln A are determined by fitting each single-site rain attenuation, Ai, vs. probability of occurrence, Pi, to the log-normal distribution: =iiAAirainkimAQPPlnlnln(8) These paramete
31、rs can be obtained for each individual location, or a single location can be used. The rain attenuation vs. annual probability of occurrence can be predicted using the method described in 2.2.1.1 of Recommendation ITU-R P.618. For each site, the log-normal fit of rain attenuation vs. probability of
32、occurrence is performed as follows: Step 1: DeterminerainkP (% of time), the probability of rain on the k-th path. Step 2: Construct the set of pairs Pi, Ai where Pi(% of time) is the probability the attenuation Ai(dB) is exceeded where PirainkP . The specific values of Pishould consider the probabi
33、lity range of interest; however, a suggested set of time percentages is 0.01%, 0.02%, 0.03%, 0.05%, 0.1%, 0.2%, 0.3%, 0.5%, 1%, 2%, 3%, 5% and 10%, with the constraint that Pi rainkP . Step 3: Transform the set of pairs Pi, Ai toirainkiAPPQ ln,1, where: ()=xttxQ de21228 Rec. ITU-R P.1815-1 Step 4: D
34、etermine the variables iAmlnand iAln by performing a least-squares fit to iiArainkiAimPPQAln1lnln +=for all i. The least-squares fit can be determined using the “Step-by-step procedure to approximate a complementary cumulative distribution by a log-normal complementary cumulative distribution” described in Recommendation ITU-R P.1057. An implementation of this prediction method in MATLAB and a reference to an approximation of the complementary bivariate normal distribution are available from the ITU-R, Study Group 3 website.
