Finally, the chi-squared analogy to equation (38) will be: 



PCfm) - P(fm) 



theoretical SNR = 



where 



cP(fin) 



1.414 , if p(f„) > p(f„) 



0.6465 , if p(fn,) < p (f^,) 

 In terms of the Xt random variable, equation (62) becomes: 



■1 r PC^m) 



theoretical SNR = c " ■{ " - 1} 



Pi^mJ 



r PCfm) 1 

 I P(fm) ' J 



(62) 



(63) 





Hence, the theoretical distribution function for the SNR variables 

 (consistent with the chi-squared assumption) is: 



theoretical ¥^^^ (w) = P ^{x2 " 2J 1 w 1 

 = P X2 1 2cw + 2 

 = F 2 (2cw + 2) = 1 -exp(-cw - 1) 



(64) 



-{ 



1 - exp(-1.414 w - 1) , if w > 



1 - exp(-0.6465 w - 1) , if w < 



(65) 



The theoretical Fj,|^p(w) is graphed in Figures 37 through 48 as a solid 

 line. 



SNR' 



77 



