NAFI TR-lkkO 



II. THE PASSIVE SONAR SITUATION 



For the purposes of this analysis, the passive sonar situation 

 can be depicted as shown in Figure 2. The quantities on the left are 

 generally beyond the control of the sonar engineer, and may be considered 

 as inputs. The target which is sought radiates noise of spectral con- 

 tent T(f), The signal spectrum received, at the detecting platform is 

 T(f) as modified by the propagation loss H(R,f). Masking the target 

 radiated noise are both environmental and platform generated (self) noise; 

 it is assumed that these two noise processes are independent so that their 

 power spectra combine additively. This total noise is reduced by the 

 array gain, so that the resultant signal and noise spectra into the shap- 

 ing filter are* 



S^,(R f) :. TCf) H(a,-^) 0) 



The spectral characteristics of the quantities on the right of 

 equations (l) and (2) can, of course, be rather complex; however, in 

 regions of interest, the following trends are generally exhibited : ■'<-'*■ 



T(f) : spectral slope of approximately -5db/oct. 



H(R,f): highly variable spectral slope, depending upon mode of 

 propagation, range, and. environmental conditions; typical slopes vary 

 between Odb/oct and -20db/oct. 



Ns(f), NeCf): spectral slope of approximately ■ -5db/oct. 



A(f): spectral slope of approximately +6d -b/oct for planar and 

 volumetric arrays, +3db/oct for line arrays-**-** 



*This formulation assumes the target is on the major response axis of the 

 beam; an off axis target would naturally have its spectrum modified by 

 the frequency dependence of the beam response. 



♦♦These values are presented only to give a physical feeling for the 

 problem being treated. They can be ignored from a mathematical standpoint, 

 since the problem can be viewed simply as an optimization exercise. That 

 the stated trends are representative can be determined by examining refer- 

 ences 12 and 13. 



i^Arrays assumed to be in their aperture response region, i.e., less 

 than half wave length spacing of the elements. 



