1、 Recommendation ITU-R P.1853-1(02/2012)Tropospheric attenuation timeseries synthesisP SeriesRadiowave propagationii Rec. ITU-R P.1853-1 Foreword The role of the Radiocommunication Sector is to ensure the rational, equitable, efficient and economical use of the radio-frequency spectrum by all radioco
2、mmunication services, 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 Ra
3、diocommunication 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
4、declarations by 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 h
5、ttp:/www.itu.int/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 Radio
6、wave propagation 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 stan
7、dards emissions 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, 2012 ITU 2012 All rights reserved. No part of this publication may be reproduced, by any means whatsoever, with
8、out written permission of ITU. Rec. ITU-R P.1853-1 1 RECOMMENDATION ITU-R P.1853-1 Tropospheric attenuation time series synthesis (2009-2011) Scope This Recommendation provides methods to synthesize rain attenuation and scintillation for terrestrial and Earth-space paths and total attenuation and tr
9、opospheric scintillation for Earth-space paths. The ITU Radiocommunication Assembly, considering a) that for the proper planning of terrestrial and Earth-space systems it is necessary to have appropriate methods to simulate the time dynamics of the propagation channel; b) that methods have been deve
10、loped to simulate the time dynamics of the propagation channel with sufficient accuracy, recommends 1 that the method given in Annex 1 should be used to synthesize the time series of rain attenuation for terrestrial or Earth-space paths; 2 that the method given in Annex 1 should be used to synthesiz
11、e the time series of scintillation for terrestrial or Earth-space paths; 3 that the method given in Annex 1 should be used to synthesize the time series of total tropospheric attenuation and tropospheric scintillation for Earth-space paths. Annex 1 1 Introduction The planning and design of terrestri
12、al and Earth-space radiocommunication systems requires the ability to synthesize the time dynamics of the propagation channel. For example, this information may be required to design various fade mitigation techniques such as, inter alia, adaptive coding and modulation, and transmit power control. T
13、he methodology presented in this Annex provides a technique to synthesize rain attenuation and scintillation time series for terrestrial and Earth-space paths and total attenuation and tropospheric scintillation for Earth-space paths that approximate the rain attenuation statistics at a particular l
14、ocation. 2 Rec. ITU-R P.1853-1 2 Rain attenuation time series synthesis method 2.1 Overview The time series synthesis method assumes that the long-term statistics of rain attenuation is a log-normal distribution. While the ITU-R rain attenuation prediction methods in Recommendation ITU-R P.530 for t
15、errestrial paths and Recommendation ITU-R P.618 for Earth-space paths are not exactly log-normal, these rain attenuation distributions are well-approximated by a log-normal distribution over the most significant range of exceedance probabilities. The terrestrial and Earth-space rain attenuation pred
16、iction methods predict non-zero rain attenuation for exceedance probabilities greater than the probability of rain; however, the time series synthesis method adjusts the attenuation time series so the rain attenuation corresponding to exceedance probabilities greater than the probability of rain is
17、0 dB. For terrestrial paths, the time series synthesis method is valid for frequencies between 4 GHz and 40 GHz and path lengths between 2 km and 60 km. For Earth-space paths, the time series synthesis method is valid for frequencies between 4 GHz and 55 GHz and elevation angles between 5 and 90. Th
18、e time series synthesis method generates a time series that reproduces the spectral characteristics, fade slope and fade duration statistics of rain attenuation events. Interfade duration statistics are also reproduced but only within individual attenuation events. As shown in Fig. 1, the rain atten
19、uation time series, A(t), is synthesized from the discrete white Gaussian noise process, n(t). The white Gaussian noise is low-pass filtered, transformed from a normal distribution to a log-normal distribution in a memoryless non-linearity, and calibrated to match the desired rain attenuation statis
20、tics. FIGURE 1 Block diagram of the rain attenuation time series synthesizer Low-pass filter Memoryless non-linear device CalibrationWhitegaussian noiseXt()exp( + ( )mX t AoffsetAt()Rain attenuation (dB)kp + nt()The time series synthesizer is defined by five parameters: m: mean of the log-normal rai
21、n attenuation distribution : standard deviation of the log-normal rain attenuation distribution p: probability of rain : parameter that describes the time dynamics (s1) Aoffset:offset that adjusts the time series to match the probability of rain (dB) 2.2 Step-by-step method The following step-by-ste
22、p method is used to synthesize the attenuation time series Arain(kTs), k = 1, 2, 3, , where sT is the time interval between samples, and k is the index of each sample. Rec. ITU-R P.1853-1 3 A Estimation of m and The parameters m and are determined from the cumulative distribution of rain attenuation
23、 vs. probability of occurrence. Rain attenuation statistics can be determined from local measured data, or, in the absence of measured data, the rain attenuation prediction methods in Recommendation ITU-R P.530 for terrestrial paths and Recommendation ITU-R P.618 for Earth-space paths can be used. F
24、or the path and frequency of interest, perform a log-normal fit of rain attenuation vs. probability of occurrence as follows: Step A1: Determine Prain(% of time), the probability of rain on the path. Praincan be well approximated as P0(Lat,Lon) derived in Recommendation ITU-R P.837. Step A2: Constru
25、ct the set of pairs Pi, Ai where Pi(% of time) is the probability the attenuation Ai(dB) is exceeded where Pi Prain. The specific values of Pishould consider the probability 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
26、 10%, with the constraint that Pi Prain. Step A3: Transform the set of pairs Pi, Ai to () iiAPQ ln,1, where: ()=xttxQ de2122(1) Step A4: Determine the variables iAmlnand iAln by performing a least-squares fit to ()iiAiAimPQAln1lnln +=for all i. The least-squares fit can be determined using the “Step
27、-by-step procedure to approximate a complementary cumulative distribution by a log-normal complementary cumulative distribution” described in Recommendation ITU-R P.1057. B Low-pass filter parameter Step B1: The parameter = 2 104(s1). C Attenuation offset Step C1: The attenuation offset, Aoffset(dB)
28、, is computed as: +=1001erainPQmoffsetA (2) D Time series synthesis The time series, Arain(kTs), k = 1, 2, 3, . is synthesized as follows: Step D1: Synthesize a white Gaussian noise time series, n(kTs), where k = 1, 2, 3, . with zero mean and unit variance at a sampling period, Ts, of 1 s. Step D2:
29、Set X(0) = 0 Step D3: Filter the noise time series, n(kTs), with a recursive low-pass filter defined by: () ( )() ()ssskTnTkXkTX +=211 for k = 1, 2, 3, (3) where: sT= e (4) 4 Rec. ITU-R P.1853-1 Step D4: Compute Yrain(kTs), for k = 1, 2, 3, . as follows: ()()skTXmsrainkTY+= e (5) Step D5: Compute Ar
30、ain(kTs) (dB), for k = 1, 2, 3, . as follows: () () 0,MaximumoffsetssrainAkTYkTA = (6) Step D6: Discard the first 200 000 samples from the synthesized time series (corresponding to the filter transient). Rain attenuation events are represented by sequences whose values are above 0 dB for a consecuti
31、ve number of samples. 3 Scintillation time series synthesis method As shown in Fig. 2, a scintillation time series, ()tsci , can be generated by filtering white Gaussian noise, n(t), such that the asymptotic power spectrum of the filtered time series has an f8/3roll-off and a cut-off frequency, fc,
32、of 0.1 Hz. Note that the standard deviation of the scintillation increases as the rain attenuation increases. FIGURE 2 Block diagram of the scintillation time series synthesizer Whitegaussian noisent()Low-pass filterMagnitude (dB)Frequencyc80/3 dB/decadesci( )Scintillation (dB)t4 Integrated cloud li
33、quid water content time series synthesis method 4.1 Overview As it is suggested in Recommendation ITU-R P.840, the time series synthesis method approximates the statistics of the long-term integrated liquid water content (ILWC) by a log-normal distribution. The time series synthesis method generates
34、 a time series that reproduces the spectral characteristics, rate of change and duration statistics of cloud liquid content events. As shown in Fig. 3, the liquid content time series, L(t), is synthesized from the discrete white Gaussian noise process, n(t). The white Gaussian noise is low-pass filt
35、ered, truncated to match the desired cloud probability of occurrence, and transformed from a truncated normal distribution to a conditioned log-normal distribution in a memoryless non-linearity. Rec. ITU-R P.1853-1 5 FIGURE 3 Block diagram of the cloud ILWC time series synthesizer Low-pass filter Ca
36、libration Memoryless non-linear deviceWhitegaussian noisent()k1p + 1k2p + 21+ 2Correlatedgaussian processGtc()()PCLWCloud liquidwater content (mm)exp Q-1 Lt()1QG t()C + mPCLWThe time series synthesizer is defined by eight parameters: m: mean of the log-normal rain attenuation distribution : standard
37、 deviation of the log-normal rain attenuation distribution PCLW: probability of clouds : truncation threshold of the correlated Gaussian noise 1: parameter that describes the time dynamics of the process fast component (s1) 2: parameter that describes the time dynamics of the process slow component
38、(s1) 1: parameter that describes the weight of the process fast component 2: parameter that describes the weight of the process slow component 4.2 Step-by-step method The following step-by-step method is used to synthesize the cloud liquid water content time series L(kTs), k = 1, 2, 3, , where sT is
39、 the time interval between samples, and k is the index of each sample. A Estimation of m, and PCLWThe mean, m, standard deviation, , and probability of liquid water, PCLW, parameters of the log-normal distribution are available in the form of maps from Recommendation ITU-R P.840. For the location of
40、 interest, determine the conditional log-normal parameters as follows: Step A1: Determine the parameters, m1, m2, m3, m4, 1, 2, 3,4, PCLW1, PCLW2, PCLW3and PCLW4 at the four closest grid points of the digital maps provided in Recommendation ITU-R P.840. Step A2: determine the m, and PCLWparameters v
41、alue at the desired location by performing a bi-linear interpolation of the four values of each parameter at the four grid points as described in Recommendation ITU-R P.1144. B Low-pass filter parameters Step B1: The parameter 1= 7.17 104(s1). Step B2: The parameter 2= 2.01 105(s1). Step B3: The par
42、ameter 1= 0.349. Step B4: The parameter 2= 0.830. 6 Rec. ITU-R P.1853-1 C Truncation threshold Step C1: The truncation threshold is computed as: ()CLWPQ1= (7) where the Q function is defined in 2.2.A and documented in Recommendation ITU-R P.1057. D Time series synthesis The time series, L(kTs), k =
43、1, 2, 3, . is synthesized as follows: Step D1: Synthesize a white Gaussian noise time series, n(kTs), where k = 1, 2, 3, . with zero mean and unit variance at a sampling period, Ts, of 1 s. Step D2: Set X1(0) = 0; X2(0) = 0 Step D3: Filter the noise time series, n(kTs), with two recursive low-pass f
44、ilters defined by: () ( )() ()() ( )() ()+=+=sssssskTnTkXkTXkTnTkXkTX22222211111111for k = 1, 2, 3, (8) where: =ssTT21ee21(9) Step D4: Compute Gc(kTs), for k = 1, 2, 3, . as follows: () () ()sssCkTXkTXkTG2211+= (10) Step D5: Compute L(kTs) (dB), for k = 1, 2, 3, . as follows: ()()+=)(for0)(for)(1exp
45、1sCsCsCCLWskTGkTGmkTGQPQkTL(11) Step D6: Discard the first 500 000 samples from the synthesized time series (corresponding to the filter transient). Cloud events are represented by sequences whose values are above 0 mm for a consecutive number of samples. 5 Integrated water vapour content time serie
46、s synthesis method 5.1 Overview The time series synthesis method assumes that the long-term statistics of integrated water vapour content (IWVC) is a Weibull distribution. While the ITU-R IWVC distributions predicted in Recommendation ITU-R P.836 are not exactly Weibull, these IWVC distributions are
47、 well-approximated by a Weibull distribution over the most significant range of exceedance probabilities. Rec. ITU-R P.1853-1 7 The time series synthesis method generates a time series that reproduces the spectral characteristics and the distribution of water vapour content. As shown in Fig. 4, the
48、water vapour content time series, V(t), is synthesized from the discrete white Gaussian noise process, n(t). The white Gaussian noise is low-pass filtered and transformed from a normal distribution to a Weibull distribution in a memoryless non-linearity. FIGURE 4 Block diagram of the integrated wate
49、r vapour content time series synthesizer kp + vLow-pass filter Memoryless non-linear deviceGtv()Correlatedgaussian processWhitegaussian noisent() Vt()Water vapourcontent (mm)(log ( ( )QG tv1/The time series synthesizer is defined by three parameters: : parameter of the Weibull IWVC distribution : parameter of the Weibull IWVC distribution V: parameter that describes the time dynamics (s1) 5.2 Step-by-step m
