()10 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 



When the path profile consists of a single sharp obstruction that can 

 be seen iVoni both terminals, the signal level may approach the value 

 predicted by the knife edge diffraction theoiy.'^ While several interest- 

 ing and unusual cases have been recorded, the knife edge or "obstacle 

 gain" theory is not applicable to the typical but only to the exceptional 

 paths. 



As in the case of line-of-sight transmission the fading of radio signals 

 beyond the horizon can be divided into fast fading and slow fading. The 

 fast fading is caused by multipath transmission in the atmosphere, and 

 for a given size antenna, the rate of fading increases as either the fre- 

 quency or the distance is increased. This type of fading is much faster 

 than the maximum fast fading observed on line of sight paths, but the 

 two are similar in principle. The magnitude of the fades is described by 

 the Rayleigh distribution. 



Slow fading means variations in average signal level over a period of 

 hours or days and it is greater on beyond horizon paths than on line-of- 

 sight paths. This type of fading is almost independent of frequency and 

 seems to be associated with changes in the average refraction of the 

 atmosphere. At distances of 150 to 200 miles the variations in hourly 

 median value around the annual median seem to follow a normal proba- 

 bility law in db with a standard deviation of about 8 db. Typical fading 

 distributions are shown on Fig. 10. 



The median signal levels are higher in warm humid climates than in 

 cold dry climates and seasonal variations of as much as ±10 db or more 

 from the annual median have been observed.'* 



Since the scattered signals arrive with considerable phase irregularities 

 in the plane of the recei\'ing antenna, narrow-beamed (high gain) anten- 

 nas do not yield power outputs proportional to their theoretical area 

 gains. This effect has sometimes been called loss in antenna gain, but it 

 is a propagation effect and not an antenna effect. On 150 to 200 miles 

 this loss in received power may amount to one or two db for a 40 db 

 gain antenna, and perhaps six to eight db for a 50 db antenna. These 

 extra losses vary with time but the variations seem to be uncorrelated 

 with the actual signal le\'el. 



The bandwidth that can be used on a single radio carrier is frequently 

 limited by the selective fading caused by multipath or echo effects. 

 Echoes are not troublesome as long as the echo time delays are very 

 short compared with one cycle of the highest baseband frequency. The 

 probability of long delayed echoes can be reduced (and the rate of fast 

 fading can be decreased) by the use of narrow beam antennas both 

 within and beyond the horizon.'^' -<' Useful bandwidths of several mega- 



