BAND WIDTH AXD TR.IXS.M fSSIOX PERIORM WTR 593 



Since the two systems occupy the same frequency assignment, we assume 

 that c is not greatly different from zero. Then for fixed 6: 



I\t) = 



(0 = ||'^E ^^rani^2.vsin0 (82) 



Since 6, the frame phase difference, is a random angle we average over its 

 possible values by setting: 



d(t) 



AM = ~ jf ' Jl Ur sin ^^e^ll J'M^- sin 4>) 



_ rV + ^)(2.rr 



7r(2w)!(w!)2 (g3) 



• 2F3(w + i w + ^; 2w + 1, m + 1, w + 1; -4x-'), 



w > 



^_„(.t) = ^m(.v) 



Noting further that for c = 0, mi = -2, m2 = 2, and n = -mN, we have 

 then: 



",2^2 



I\l) = l^ [alAiix) + 4aL^2(x)l (84) 



and 



5// = ^^ [alAiix) + 4aLv^2(-x)r'^ (85) 



For a sinusoidal pulse and rectangular gate of full channel allotment time 

 in duration, c.v = 02.V = 0, /-(/) = 0, and S/I is infinite. If instantaneous 

 sampling is used, 



Go = (In = diN (86) 



and 



S/I = ^tII;^ Ui(.r) + 4^,(.v)]-^'^ (87) 



The curve for similar system interference with instantaneous sampling, Fig. 



14, w^as calculated from Eq. (87). 



For small values of x, we may use the ascending power series: 



-^iW = H' " ?^M ! '■' + 3-4.2'-y-2! •>■'-•■] (8« 



