BIRDSALL: COHERENCE 



millihertz to either side of the carrier frequency. That reverberation 

 is part of the 'incoherent' part of the reception; its lack of struc- 

 ture makes it much less useful than the stable signal line. Measure 

 its power and then filter it out; once removed the remainder is the 

 signal that possesses the millihertz stability. That is lesson number 

 one: partially coherent signals may sometimes be separated into coherent 

 and incoherent parts. The separation increases our understanding of 

 propagation. The coherent part is operationally much more effective 

 at low signal-to-noise for detection and identification, and worthy of 

 further study. 



Studies of the isolated stable line showed that life is really not 

 simple. In a multipath situation - and that is the usual situation 

 for many of us - it is common for the amplitude of the line to vary 

 substantially, while the phase of the line (or its instantaneous fre- 

 quency) has such slow variations that it reflects tidal and internal- 

 wave behavior. If one models 'paths' as slowly and independently vary- 

 ing, the model disagrees. However, if one models 'paths' as slowly 

 and dependently varying, reacting to the same global temperature 

 variations, then the model begins to fit. That brings in lesson num- 

 ber two: the propagation may be coherent, that is, complicated but 

 logically consistent and dependent of the same variations, and yet 

 yield some measurements that appear to be incoherent. It is up to the 

 scientist and the sonar designer to seek, recognize, and capitalize on 

 whatever ' coherence ' nature provides . 



NON-MARKOV COHERENCE 



There is a natural tendency to believe that 'coherence' should 

 behave in a Markov fashion in all dimensions. We seek coherence dis- 

 tances, coherence time constants, coherence bandwidths. We ask 'how 

 far apart do receptions have to be before coherence drops to one-over-e?' 

 as if that just has to be an intelligent question. 



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