COHERENCE 



Theodore G. Birdsall 



Cooley Electronics Laboratory 

 University of Michigan 



My theme is that much of the randomness in underwater 

 acoustics is not "inherent" randomness, but rather is the 

 manifestation of complicated deterministic phenomena. 



INTRODUCTION 



What is "coherence" and, more important, what good is "coherence?" 

 Definitions can be "sticky." The pun is intentional. Coherent means 

 to consist of parts that stick together, that are logically consistent. 



In various disciplines coherence has taken on special meanings, 

 often related to techniques of quantifying (measuring) the degree of 

 coherence. Quantification is necessary, but it can carry hidden 

 assumptions that can confuse and even impede progress. For example, 

 a correlation coefficient and its decay in time or space is most 

 appropriate for first order Markov processes. The more sophisticated 

 "coherence function" is most useful for wide-sense stationary 

 Gaussian random processes. 



This paper is concerned with underwater acoustic propagation, 

 with "coherence" meaning the consistency of reception across time, 

 frequency, and space. The viewpoint is that of a signal processor, 

 concerned with extracting information from acoustic receptions. This 

 means information about propagation, or extracting operational infor- 

 mation about targets or false targets. 



Signal coherence is most important in weak signal situations; 

 that is, when the signal power is small compared to the noise power 

 or the signal's own reverberation power. The sub-discipline known as 



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