iXTERMODrLATIOX INTERFERENCE IN RADIO SYSTEMS 



67 



Table I — Number of Potentially Interfering Intermodulation 



Products 

 n = Number of consecutive channels in available band 



Tjrpe of Product 



2A - B 

 A + B - C 



SA - 2B 



SA - B - C 

 2A + B - 2C 

 2A + B - C - D 



A + B + C - 2D 



A + B + C-D-E 



Number of Products 



(n - 1)=^ 

 2 

 if n is odd 



(n - l)(n - 3)(2n -1 ) 

 6 

 if n is odd 



5 (« - 3) 



if n is a multiple of 3 



3(n2 - lln + 32) 



}iin^ - 9n2 + 34/1 - 56) 



3(n - 3) (71 - 5)2 

 f orn > 6 



4(n - 3)(n - 5)^ 



{n -o){n- 6)(n2 - lln + 37) 

 for n 5^ 8 



njn - 2) 

 6 

 if n is even 



njn - 2)(2n - 5) 

 6 

 if n is even 



(n - l)(n - 2) 

 3 

 other n's 



taining ^ consecutive channels. Let us suppose further that the average 

 busy time of the channels is such that T represents the portion of time 

 that an average channel is activated by a transmitter and R represents 

 the portion of time that an average channel is connected to a receiver. 

 The probability of interference, /, may be defined as the probability 

 that one or more of the intermodulation products that are formed when 

 pT channels are transmitting will fall on a specific channel m the operating 

 band. The method used to determine / is based on the assmnption that the 

 distribution of intermodulation products is uniform over the operating 

 band. It is further assumed that the magnitudes of the intennodulation 

 products as encountered at the receiver input, are always strong enough to 

 cause interference. Table III shows formulas for / that have been developed 

 for each t>T)e of third order and fifth order product. Fig. 1 shows plots of 

 p versus / when only 3rd order products are considered and Fig. 2 shows 

 plots of p versus / when both 3rd and oth order products are considered 

 with n and T as independent variables. 



1. Fig. 2a shows that a band in excess of 500 adjacent channels is 

 required to limit the probability of 3rd and 5th order interference to 

 10 per cent (/ = 0.1) when 10 operating channels are picked at random 

 from that band if traffic is such as to fully use these 10 channels, 5 for 



