NAFI TR-lUl+0 



PRELIMINARY DISCUSSION 



To some, the optimization of a conventional system may seem 

 paradoxical since the vrard conventional tends to imply non-optimal pro- 

 cessing; but the concept of optimization is multi-faceted, and the term 

 remains ambiguous until system configuration constraints and criteria of 

 optimality are specified. In tliis paper, an optimum system is one which 

 maximizes the system output signal-to-noise ratio (SNR): from the theo- 

 retical viewpoint of statistical decision theory, this criterion is very 

 limited, and a more satisfactory approach would be to utilize the Bayes 

 decision male ( 1, 2, 3j ^})j however, most engineers are more familiar 

 with the concept of SNE than with Bayes decision rules, and since, for 

 the analytical assumptions imposed upon the following v/ork, the two cri- 

 teria lead to the same optimized configurations,^ the former method is 

 chosen. 



Further, optimization is not an end unto itself. Since optimum 

 systems can never be fully realized in practice, one of the major purposes 

 of mathematical optimization is to determine the limit on achievable per- 

 formance under realistic constraints. In view of this, the primary 

 emphasis of this paper is placed upon the evaluation of a sub -optimum 

 system, i.e., the relative cost (in dB's of output SNF) for utilizing a 

 non-optimum system in place of an optimum system. 



Tlie fundamental constraint imposed upon the following work is 

 that the system configuration remains as shown in Figure 1 for all de^ 

 grees of optimization. The system consists of an array of hydrophones, 

 a simple delay and sum beamformer (with constant multiplicative spatial 

 shading coefficients allowable), and a signal processing unit consisting 

 of a square-law detector. Since such a configuration forms the basis for 

 most contemporary systems, it will be denoted as a conventional system. 

 In contrast to this conventional system are the various "adaptive" systems 

 which continuously modify hydrophone data on the basis of past informa- 

 tion (5, 6, 7, 8); such systems are still in the conceptual state, and 

 are excluded from this analysis. 



*See Appendix D (l) for amplification of this point. 



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