1、 Rec. ITU-R P.1623-1 1 RECOMMENDATION ITU-R P.1623-1 Prediction method of fade dynamics on Earth-space paths (Question ITU-R 201/3) (2003-2005) The ITU Radiocommunication Assembly, considering a) that for a variety of radiocommunication services, design objectives have to be met that require informa
2、tion on the dynamics of outage events; b) that for the evaluation of parameters associated with the risk of failure to provide a certain quality and reliability of service, the probability of occurrence of fades of a certain duration must be known; c) that for the evaluation of internal parameters i
3、nside a fade mitigation technique (FMT) control loop (used to improve the quality and reliability of service), the probability of occurrence of fade slope corresponding to a given attenuation threshold must be known; d) that there is a need to provide engineering information for the calculation of f
4、ade duration, interfade duration and fade slope statistics, recommends 1 that the methods described in Annex 1 2.2 be used for the calculation of the statistics of fade duration due to the combined effects of attenuation (gases, clouds and rain) and scintillation on Earth-space paths; 2 that the met
5、hods described in Annex 1 3.2 be used for the calculation of the statistics of fade slope due to attenuation on Earth-space paths. Annex 1 1 Introduction In the design of a variety of telecommunication systems, the dynamic characteristics of fading due to atmospheric propagation are of concern to op
6、timize system capacity and meet quality and reliability criteria. Examples are fixed networks that include a space segment and systems that apply fade mitigation or resource sharing techniques. Several temporal scales can be defined, and it is useful to have information on fade slope, fade duration
7、and interfade duration statistics for a given attenuation level (Fig. 1). Fade duration is defined as the time interval between two crossings above the same attenuation threshold whereas interfade duration is defined as the time interval between two crossings below the same attenuation threshold. Fa
8、de slope is defined as the rate of change of attenuation with time. 2 Rec. ITU-R P.1623-1 1623-01FIGURE 1Features characterizing the dynamics of fade eventsFadedurationFadeepisodesInterfadeintervalPrecipitation event Inter-event intervalPrecipitationeventFadeslopeFade thresholdTimeFade depthOf parti
9、cular interest in the context of availability criteria is the distinction between fades of shorter and longer duration than 10 s. Knowledge of the distribution of fade duration as a function of fade depth is also a prerequisite for the application of risk concepts in the provision of telecommunicati
10、on services. In addition, information about the expected fade slope is essential to assess the required minimum tracking rate of a fade mitigation system. 2 Fade and interfade duration 2.1 Requirements for fade duration information Fade duration is an important parameter to be taken into account in
11、system design for several reasons: system outage and unavailability: fade duration statistics provide information on number and duration of outages and system unavailability due to propagation on a given link and service; sharing of the system resource: it is important from the operators point-of-vi
12、ew to have an insight into the statistical duration of an event in order to assign the resource for other users; FMT: fade duration is of concern to define statistical duration for the system to stay in a compensation configuration before coming back to its nominal mode; system coding and modulation
13、: fade duration is a key element in the process of choosing forward error correction codes and best modulation schemes; for satellite communication systems, the propagation channel does not produce independent errors but blocks of errors. Fade duration impacts directly on the choice of the coding sc
14、heme (size of the coding word in block codes, interleaving in concatenated codes, etc.). 2.2 Fade duration prediction method Fade duration can be described by two different cumulative distribution functions: 1 P(d D|a A), the probability of occurrence of fades of duration d longer than D (s), given
15、that the attenuation a is greater than A (dB). This probability can be estimated from the ratio of the number of fades of duration longer than D to the total number of fades observed, given that the threshold A is exceeded. Rec. ITU-R P.1623-1 3 2 F(d D|a A), the cumulative exceedance probability, o
16、r, equivalently, the total fraction (between 0 and 1) of fade time due to fades of duration d longer than D (s), given that the attenuation a is greater than A (dB). This probability can be estimated from the ratio of the total fading time due to fades of duration longer than D given that the thresh
17、old A is exceeded, to the total exceedance time of the threshold. For a given reference period, the number of fades of duration longer than D is estimated by multiplying the probability of occurrence P(d D|a A) by the total number of fades exceeding the threshold, Ntot(A). Likewise, an estimate of t
18、he total exceedance time due to fade events of duration longer than D is obtained by multiplying the fraction of time F(d D|a A) by the total time that the threshold is exceeded, Ttot(A). The two-segment model presented here consists of a log-normal distribution function for long fades and a power-l
19、aw function for short fades. The boundary between short and long fades is given by the threshold duration Dtcalculated in the model. The power-law model is valid for fade durations longer than 1 s. Fades of shorter duration do not contribute significantly to total outage time. The following provides
20、 estimates of the parameters required for the model and finally defines the two-segment model for both distribution functions, i.e. the occurrence probability P and the exceedance probability (or fraction of time) F. The model is expected to be valid for durations longer than 1 s. The following para
21、meters are required as input to the model: f : frequency (GHz): 10-50 GHz : elevation angle (degrees): 5-60 A : attenuation threshold (dB). The step-by-step calculation of the fade duration distribution is as follows: Step 1: Calculate the mean duration D0of the log-normal distribution of the fracti
22、on of fading time due to fades of long duration, given that the attenuation is greater than A, as: s8039.04.14.00AfD = (1) Step 2: Calculate the standard deviation of the lognormal distribution of the fraction of fading time due to fades of long duration as: 027.005.085.1 Af= (2) Step 3: Calculate t
23、he exponent of the power-law distribution of the fraction of fading time due to fades of short duration as: 003.065.0055.0 Af= (3) Step 4: Calculate the boundary between short and long fade durations, Dt, as: se39.00221+=pptDD (4) where: 814.0885.01=p (5) 61.123.205.122+=p (6) 4 Rec. ITU-R P.1623-1
24、Step 5: Calculate the mean duration D2of the log-normal distribution of the probability of occurrence of fading events of long duration as: se202= DD (7) Step 6: Calculate the fraction of time k due to fades of duration less than Dtas: 12020)ln()ln()ln()ln()1(1+=DDQDDDQDDkttt(8) where: Q: standard c
25、umulative distribution function for a normally distributed variable: xzQxzde21)(221= (9) Step 7: Calculate the probability of occurrence of fade events of duration d longer than D given that attenuation a is greater than A as: =)|(1For DAaDdPDDt(10) =)ln()ln()ln()ln()|(For22DDQDDQDAaDdPDDttt(11) Ste
26、p 8: Calculate the cumulative probability of exceedance, i.e. the total fraction of fade time due to fades of duration d longer than D: =11)|(1ForttDDkAaDdFDD (12) =)ln()ln()ln()ln()1()|(For00DDQDDQkAaDdFDDtt(13) Step 9: If required, the total number of fades of duration d longer than D for a given
27、threshold A can be calculated from: )()|(),( ANAaDdPADNtot= (14) Rec. ITU-R P.1623-1 5 Similarly, the total fading time due to fades of duration d longer than D for the threshold A is: s)()|()|( ATAaDdFAaDdTtot= (15) for the reference period of interest, where Ttot(A) is the total time the threshold
28、 A is exceeded and Ntot(A) is the total number of fades exceeding the minimum duration of 1 s. These parameters can be obtained in the following way: Ttot(A) should be obtained from local data. If this long-term statistic is not available, an estimate can be calculated from Recommendation ITU-R P.61
29、8. In this case the procedure consists in calculating the CDF of total attenuation, deriving the percentage of time the considered attenuation threshold A is exceeded and then the associated total exceedance time Ttot(A) for the reference period considered. Once Ttot(A) has been obtained, Ntot(A) ca
30、n be calculated as: =11)()(ttottotDkATAN (16) The above method was tested against the Radiocommunication Study Group 3 fade duration data bank for frequencies between 11 and 50 GHz and for elevation angles between 6 and 60. The arithmetic mean of the logarithmic error (ratio of the predicted to the
31、measured fade duration at the same probability level) was found to be 30% for fade durations shorter than 10 s and between 25% and 80% for fade durations longer than 10 s. As far as the standard deviation is concerned, it was found to range between 80% and 150%, demonstrating the high natural variab
32、ility of this parameter. 2.3 Interfade duration Apart from fade duration statistics, it is also useful to characterize the time interval between two fades, called interfade duration. Once the level of the received signal has just crossed back over the margin threshold after an outage event, it is es
33、sential from the operators point-of-view to know statistically the duration before another outage event. Experimental results indicate that interfade duration statistics may be log-normally distributed; however, short duration interfade intervals resulting from tropospheric scintillation are expecte
34、d to follow a power-law form as found with short-term fade duration statistics. 3 Fade slope 3.1 Requirements for fade slope information It is important to be able to quantify fade slope for satellite communication systems for which Fade Mitigation Techniques may be implemented. The knowledge of the
35、 fade slope of the received signal is useful either to design a control loop that can follow signal variations, or to allow a better short term prediction of the propagation conditions. In both cases, the relevant information is the slope of the slowly varying component of the signal which involves
36、filtering out scintillation and rapid variations of rain attenuation. 3.2 Fade slope prediction method The fade slope probability distribution depends on climatic parameters, drop size distribution and therefore on the type of rain. The horizontal wind velocity perpendicular to the path is another c
37、limatic parameter of influence, determining the speed at which the horizontal rain profile passes 6 Rec. ITU-R P.1623-1 across the propagation path. Also, the expected fade slope at a given attenuation level is likely to decrease as path length increases due to the smoothing effect of summing differ
38、ent rain contributions, and, therefore, will increase as elevation angle increases on Earth-space paths. Furthermore, the measured fade slope is influenced by dynamic parameters, or time constants, of the receiving system. A receiver with a longer integrating time reduces the instantaneous fade chan
39、ge and spreads it over a longer period of time. The predicted distribution of fade slope is dependent on attenuation level A(t) and on the time interval length t. Also, the distribution depends on the 3 dB cut-off frequency of the low-pass filter which is used to remove tropospheric scintillation an
40、d rapid variations of rain attenuation from the signal. Experimental results show that a 3 dB cut-off frequency of 0.02 Hz allows scintillation and rapid variations of rain attenuation to be filtered out adequately. If scintillation and rapid variations of rain attenuation are not filtered out, the
41、signal will exhibit stronger fluctuations and the model will only predict those due to rain attenuation. In that case, the cut-off frequency required as an input is the sampling frequency. In the model, the fade slope at a certain point in time is defined from the filtered data as: dB/s2121)(tttAttA
42、t+= (17) The model is valid for the following ranges of parameters: frequencies from 10 to 30 GHz elevation angles from 10 to 50. The following parameters are required as input to the model: A : attenuation level (dB): 0-20 dB fB: 3 dB cut-off frequency of the low pass filter (Hz): 0.001-1 Hz t : ti
43、me interval length over which fade slope is calculated (s): 2-200 s. The step-by-step calculation of the fade slope distribution is as follows: Step 1: Calculate the function F which gives the dependence on the time interval length t and the 3 dB cut-off frequency of the low pass filter fB: ()bbbBBt
44、ftfF/12)2(/12),(+= (18) with b = 2.3. Step 2: Calculate the standard deviation of the conditional fade slope at a given attenuation level as: dB/s),( AtfFsB=(19) where s is a parameter which depends on climate and elevation angle; an overall average value in Europe and the United States of America,
45、at elevations between 10 and 50, is s = 0.01. Step 3a: Calculate p( | A) the conditional probability (probability density function) that the fade slope is equal to for a given attenuation value, A: 22)/(2)|(= Ap (20) Rec. ITU-R P.1623-1 7 Step 3b: If required, calculate p( | A), the conditional prob
46、ability (complementary cumulative distribution function) that the fade slope is exceeded for a given attenuation value, A: +=)/(arctan)/(1()/(21)|(2AP (21) or calculate p( | A), the conditional probability that the absolute value of the fade slope is exceeded for a given attenuation value, A: +=+=)(
47、arctan2)(1()(21d)|(d)|()|(2xAxpxAxpAP (22) The model given in equation (22) was tested against data between 12.5 GHz and 50 GHz. These results showed a good match to the shape of the fade slope cumulative distribution function as well as its variation with attenuation threshold A, interval length t and 3 dB cut-off frequency of the low pass filter fB.
