c the phases of the main and scattered signals compared. 50/6 Line of sight radio systems Scattered signal terrain with some roughness; 0.25 for mountains, rough or very dry terrain. b is a climate factor and equals: 0.5 for Gulf coast or other hot humid locations; 0.25 for temperate or northern areas; 0.125 for mountainous or very dry areas. f is the frequency in GHz. D is the path length in miles. F is the fade margin in dB. Desired signal The formula assumes, of course, that the path has been designed for adequate clearance and does not take into account effects such as earth bulge, ducting, reflections, etc. The decimal form of U may be converted into time by multiplying by the number of minutes (or Desired signal seconds or hours) per year. This formula and the unavailability Phase difference example formulas following apply to one-way propagation outages. The Scattered signal unavailability time should be doubled for a complete two-way path, since a conservative design would assume that outages in both directions do not occur simultaneously. Figure 50.10 Multipath effect Figure 50.12 illustrates the propagation unavailability for several typical length 6GHz paths as compared to the Rayleigh distribution function. Mathematically, multipath fading is described by the Rayleigh distribution function. Figure 50.11 shows this relationship. Notice Rayleigh that as the permissible fade depth is increased, the probability of cancellation decreases. 50 miles 30 miles 20 miles 6.7 GHz paths a=1 b=.25 non-diversity Depth of fade dB Depth of fade (dB) Figure 50.12 Propagation unavailability Figure 50.11 Raleigh fading At this point it may seem that the system designer, if faced with Now the reason for fade margin should be apparent. With a path an unacceptable outage time for the path, must consider increasing designed for a 40dB fade margin, the probability of a fade deep fade margin, changing to a lower frequency microwave band or enough to reach the receiver sensitivity point and cause the receiver shortening the pat