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342 ITU-R Multipath Probability Model
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A method for predicting the single-frequency (or narrowband) fading distribution suitable for large fade depths A in the average worst month
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in any part of the world (based on ITU-R p530-12) 5 and for detailed link design is given as follows: P0 = Kd32 (1+| p| 097 100032 f 000085 hL A /10 [%] ) where f = frequency (GHz) hL = altitude of the lower antenna (ie, the smaller of he and hr) (m) A = fade depth (dB) and the geoclimatic factor K is obtained from the following equation (if measured data for K are not available):
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K = 10 39 0003 dN1 sa042
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where dN1 = point refractivity gradient in the lowest 65 m of the atmosphere not exceeded for 1 percent of an average year sa = area terrain roughness The term dN1 is provided on a 15 grid in latitude and longitude in ITU-R Recommendation P453 The correct value for the latitude and longitude at path center should be obtained from the values for the four closest grid points by bilinear interpolation The data are available in a tabular format and are available from the Radiocommunications Bureau (BR) Term sa is defined as the standard deviation of terrain heights (m) within a 110 110 km area with a 30s resolution (eg, the Globe GTopo30 data) The area should be aligned with the longitude such that the two equal halves of the area are on each side of the longitude that goes through the path center Terrain data are available from the Internet, and the Web address is provided by the BR If a quick calculation of K is required for planning applications, a fairly accurate estimate can be obtained from: K = 10 42 00029 dN1 (320)
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For example, a typical value for K over much of Northern Europe is 24 10 4 (dN1 = 200 N-units/km) and as high as 14 10 3 (dN1 = 464 N-units/km) in areas around the Mediterranean Sea
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From the antenna heights he and hr (meters above sea level), calculate the magnitude of the path inclination | p| (mrad) using the following expression: | p| = where d = the path length (km) he, hr = antenna heights ASL (m) The method just shown is used for small percentages of time, does not make use of the path profile, and can be used for initial planning, licensing, or design purposes The general rule is that, the smoother the path, the more likely the occurrence of multipath fading A second method, used for all percentages of time, is suitable for all fade depths and employs the method for large fade depths and an interpolation procedure for small fade depths The method used for predicting the percentage of time that any fade depth is exceeded combines the deep fading distribution and an empirical interpolation procedure for shallow fading down to 0 dB A detailed description of a method for all percentages of time is beyond the scope of this book but can be found in the latest revision of the ITU-R Recommendation P530-xx
Example:
Let s assume that we are designing a 7 GHz link in Northern Europe (or any other region with dN1 = 200 N-units/km, based on ITU maps) and the link length is 40 km Antenna heights above sea level are 200 and 350 m We have to nd the required fade margin if the reliability requirement of the link is 99999 percent
| hr he | [ mrad] d
(321)
First, with the help of basic trigonometry, we will calculate path inclination: | p| = | hr he | 150 m = = 375 mrad d 40 km
The percentage of time that fade depth A (dB) is exceeded in the average worst month is calculated as: P0 = Kd32 (1+| p| 097 100032 f 000085 hL A /10 [%] )
0 P0 = 24 10 4 4032 (1 + 375) 097 100032 7 000085 200 A /10 [%]
P0 = 71 100054 A /10 [%]
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