512 BELL SYSTEM TECHNICAL JOURNAL 



Fig. 10— PPM-AM, CW and Similar System Interference 



The curve of Fig. 10 for marginal ratio of pulse power to CW interfering 

 power has the same shape as the corresponding curve of Fig. 9 for marginal 

 power over tluctuation noise. There is a shift of 9 db in ordinates, however, 

 because the peak factor of the CW interference is 9 db less than that of 

 fluctuation noise. The interference from similar systems follows a different 

 law because of the "exposure factor" arising from the finite probability that 

 the interfering pulse does not overlap the wanted pulse. A straightforward 

 probabiUty calculation taking into account the distribution of pulse voltages 

 in an interfering system occupying the same radio frequency band yields the 

 curve shown on the assumption that the repetition frequencies are asyn- 

 chronous. As the bandwidth is increased the pulses become shorter and 

 their coincidences less frequent, leading asymptotically to a 9 db per octave 

 slope instead of the 6 db per octave of the CW interference. 



Fig. 11— PPM-FM, Fluctuation Noise 



In the transmission of PPM by FM there are two sources of advantage 

 over noise. One is the ordinary FM advantage and the other is the sheer 

 advantage of PPM acting on the noise remaining in the FM output. There 

 are, likewise, two separate conditions for system failure; one a breaking of 

 the limiter and the other a breaking of the sheer. A certain amount of radio 

 power will result in marginal operation of the limiter for a certain frequency 

 swing. The corresponding deviation ratio is the quotient of the frequency 

 swing and the baseband width; this ratio is maximum when the baseband is 

 least. Except in the region near the minimum PPM band, advantage 

 accrues faster with bandwidth in FM than in PPM. It is apparent, there- 

 fore, that most of the radio bandwidth should be devoted to FM advantage. 

 The optimum proportioning occurs when the baseband width has a small 

 value but not so small as to invoke an unsurmountable penalty by not 

 providing for any position modulation. Mathematical analysis given in 

 Appendix IV shows that the optimum baseband for the pulse position modu- 

 lation varies with radio bandwidth in the manner shown in Fig. 11 by curve 

 1. Curve 2 shows the audio signal-to-noise ratio vs. radio bandwidth when 

 the baseband width follows curve 1 and the FM limiter is marginal. It is of 

 interest to compare curve 2 with the poorer performance of the dashed curve 

 3 which is calculated for the case in which both the FM limiter and the PPM 

 slicer are marginal. The baseband width for the double marginal condition 

 follows curve 4. Curves 5 and 6 show audio signal-to-noise ratio vs. band- 

 width for constant radio power and optimum baseband. The curv^e of 

 marginal amount of radio power is not given in Fig. 11, but is the same as the 

 one given later in Fig. 13. 



