BAND WIDTH AND TRANSMISSION PERFORMANCE 505 



this reduction of frequency occupancy can be carried very much further 

 when regeneration is practiced. 



We will later assign, for each modulation method, a value for the fraction 

 of the band spacing to which the signal bandwidth must be confined. The 

 frequency occupancy is then given by the product of the following three 

 factors: 



1. The reciprocal of the above factor, to be called U. 



2. The signal bandwidth for the specified number of channels. 



3. The number of frequencies required to operate in the assumed radio 

 situation. 



Inspection of Fig. 4 shows two sources of common frequency interference 

 between East- and Westbound signals: (1) backward radiation from one 

 transmitter into the beam of the other and (2) backward reception of the 

 signal intended for the oppositely directed receiving antenna. Both kinds 

 of interference are suppressed by the front-to-back ratio (assumed as 75 db) 

 compared with the desired signal. The effects occur at every repeater and 

 in a 4000-mi. system with 30-mi. spans, addition of the interfering power 

 contributed by the individual repeaters gives two "equivalent" single sources 

 75 — 10 log 133 = 54 db down. With no fading the two effects combine to 

 form one source 51 db down. The receiver crosstalk is, however, subject to 

 differential fading in adjacent spans. On the assumption that simultaneous 

 deep differential fades on more than one pair of such spans are extremely 

 rare, we base our estimates on a severe fading condition at only one repeater 

 (or a number of less severe differential fades distributed simultaneously over 

 the system having an equivalent effect.) The total interference from the 

 other repeaters is then virtually the same as for 133 non-fading repeaters, 

 while the fading repeater contributes an amount greater than the receiver 

 crosstalk at one non-fading repeater by the depth of the fade expressed in db. 

 We take this differential fade to be 30 db. The total interference from 

 repeater crosstalk is, then, the result of a source 51 db down together with 

 another source 75 — 30 = 45 db down. The combined interference is 

 accordingly 44 db down. It is thus necessary that any long distance system 

 using the repeater plan of Fig. 4 must be operable in the continuous presence 

 of interference 44 db down. Under these assumptions, systems in which 

 bandwidth is not or cannot be expended to gain tolerance to interference 44 

 db down do not allow any frequency to be used more than once in one 

 repeater and therefore a repeater plan must be used which employs four 

 frequencies. 



The four-frequency plan would be necessary in the case of conventional 

 frequency division multiplex because such a system cannot tolerate crosstalk 

 only 44 db down. 



