DYER: FLUCTUATIONS: AN OVERVIEW 



In many cases the probability density for amplitude, P(A), for 

 fast fading results from a phase random process and for the intensity 

 is exponential, while for the rms pressure it is Rayleigh. These are 

 equivalent statements and for the logarithmic distributions, the mean 

 is depressed by 2.5 decibels and the standard deviation is 5.6 deci- 

 bels. This result assumes enough paths (10 or more) to justify an 

 asymptotic limit. 



For this distribution, the fading range (throwing away 5 percent 

 of the extremes) is about 21 dB, which is consistent with short 

 observation periods (under 2 hours) for the frequency of 400 Hertz. 



The next step (Figure 10) is to describe the amplitude statistics 

 for a longer period of time than that which just corresponds to each 

 of the fast-fading segments. 



If the probability densities of the individual processes are 

 known, the final probability density is found by averaging P(A) over 

 the variation of the mean itself, P (y ) . For example, for fast fading 

 alone, the probability density of the mean is a delta function, yield- 

 ing back the phase random process. For predominantly slow fading, 

 variations in the mean may be reasonably given by a Gaussian process 

 which generates a sufficiently large spread in the mean that the 

 probability density of the logarithmic amplitudes approach a Gaussian 

 distribution. There is evidence that, in fact, this occurs when data 

 are included from experiments over time periods of 30 to 40 days. 



In the intermediate fading-rate case, the results are not so 

 easily described. Figure 11 shows results obtained by John Clark (1974) 

 and his colleagues last year, where the signal histograms (essentially 

 the probability densities) are plotted as a function of time. Each 



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