The optimization of the conventional system in Figure 1 is 

 further restricted to the optimal specification of the shaping filter, 

 I r(f ) ; the array configuration and beamformer design are assumed fixed, 

 and square-law detection is used throughout. In the non-optimal system 

 which is evaluated, the shaping filter is used only to v/hiten the noise 

 and bandlimit the input to the square-law detector; the performance of 

 this system is compared to three different optimum systems,, the three 

 optimizations resultinR from different sets of imposeol contraints. 



In the first optimization, it is assumed that the designer has 

 no a priori knowledge of the signal spectral characteristics, except, 

 perhaps, a vague knowledge of the expected extreme limits. In this case, 

 it is generally assumed that the best one can do is to whiten the noise 

 and appropriate Ij- bandlimit the input;** thus, this optimal system differs 

 from the non-optimal system only to the extent that the bandwidth is 

 (somewhat artifically) optimized. In fact, the procedure followed is to 

 evaluate the performance of the non-optimal system as a function of band- 

 width, and to denote that the bandwidth which maximizes the output SI>ffl 

 for a particular (but unknown to the designer) signal spectrum as optimum. 

 The procedure may appear strained and artificial until it is remembered 

 that the main purpose is not to determine a strictly mathematical opti- 

 mum system but to evaluate the relative performance of the non-optimal 

 system. The results will show the cost, in dbs of output SKR, for 

 utilizing an incorrect bandwidth for a particular signal spectrum; per- 

 haps more important physically, the results also show how the performance 

 of a fixed bandwidth non-optimal system deviates from optimum as the 

 input spectrum varies between certain limits. 



The second optimization makes use of the well known Eckart 

 filter (6, 8, 9). In this second case, it is assumed that the designer 

 does have prior knowledge of the signal spectrum; this knowledge can be 

 effectively utilized to determine a form of the shaping filter which 

 maximizes the output SNR. Such a filter specification depends upon both 

 signal and noise spectral characteristics, and can be viewed as the 



**For discussion, see Appendix D (2) 



3 



