RADIO PROPAGATION FUNDAMENTALS 601 



Severe fading may occur over water or on other smooth paths because 

 the phase difference between the direct and reflected rays varies with 

 atmospheric conditions. The result is that the two rays sometimes add 

 and sometimes tend to cancel. This type of fading can be minimized, if 

 the terrain permits, by locating one end of the circuit high while the 

 other end is very low. In this way the point of reflection is placed near 

 the low antenna and the phase difference between direct and reflected 

 rays is kept relatively steady. 



Most of the fading that occurs on "rough" paths with adequate clear- 

 ance is the result of interference between two or more rays traveling 

 slightly different routes in the atmosphere. This multipath type of fad- 

 ing is relatively independent of path clearance and its extreme condition 

 approaches the Rayleigh distribution. In the Rayleigh distribution, the 

 probability that the instantaneous value of the field is greater than the 

 value R is exp [ — {R/Ro}], where Ro is the rms value. 



Representative values of fading on a path with adequate clearance are 

 shown on Fig. 4. After the multipath fading has reached the Rayleigh 

 distribution, a further increase in either distance or frec^uency increases 

 the number of fades of a given depth but decreases the duration so that 

 the product is the constant indicated by the Rayleigh distribution. 



Miscellaneous Effects 



The remainder of this Section describes some miscellaneous effects of 

 line of sight transmission that may be important at frequencies above 

 about 1,000 mc. These effects include variation in angles of arrival, 

 maximum useful antenna gain, useful bandwidth, the use of frequency 

 or space diversity, and atmospheric absorption. 



On line of sight paths with adec^uate clearance some components of 

 the signal may arrive with variations in angle of arrival of as much as 

 ^° to 1° in the vertical plane, but the variations in the horizontal plane 

 are less than 0.1°.*' ^ Consequently, if antennas with beamwidths less 

 than about 0.5° are used, there may occasionalh^ be some loss in received 

 signal because most of the incoming energy arrives outside the antenna 

 beamwidth. Signal variations due to this effect are usually small com- 

 pared with the multipath fading. 



Multipath fading is selective fading and it limits both the maximum 

 useful bandwidth and the frequency separation needed for adequate 

 frequency diversity. For 40-db antennas on a 30-mile path the fading 

 on frequencies separated b}'' 100-200 mc is essentially uncorrelated re- 

 gardless of the absolute freciuency. With less directive antennas, uncor- 

 related fading can occur at frequencies separated by less than 100 mc.^' ^ 



