Even when the number Ng of stage-B pulses is not constrained by other 

 considerations, it can be optimized for at most only a few adjacent range bins 

 for a target of given cross section. For the particular case graphed in figure 11 



1.0 



0.8 



0.6 



0.4 



0.2 





Ng = 12 ^ 



1 



^OPTIMUM No 



\r (Probability of detecting 

 SN design target if the 

 ^ Ng optimum for that 









T 



particular r 

 is the o 



ange 



ne used.) 











\ 













\\ 

 \\ 

 \\ 

 \ \ 



K 











^ 



S 



s 



0.4 



0.5 



0.6 



0.7 



0.8 



0.9 



1.0 



Figure 11. Single-scan detection probability vs normalized range, for a target 

 of design size. 



(fixed-sample stages; Rice distribution; S^ = dB/pulse; Sir) - -40 log,or; 



M.= 1; N = 1.2; a. a. 



10- 



optimum K'g for each /Vg), the dashed curve is 



a bound for any curve with Ng fixed - a curve for an /Vg somewhat larger than 12 

 would be closer to the dashed curve only at outer ranges. Probably the more 

 practical procedure is to optimize the test for an SNR that corresponds to a 

 chosen value of P^, rather than to optimize it for the SNR that corresponds to an 

 arbitrarily chosen range and design cross section. Figure 12 (fixed-sample 

 stages; M^ = 1; N = 1.2; optimum Kg for each point; P^ varied by changing the 

 SNR) shows how the optimum Ng changes considerably with P„. The correspon- 

 ding optimum values of the stage-A false-alarm probability (optimum a^ = 0.2/ 

 [optimum Ng] when N = 1.2) for these cases are plotted in figure 13. These 



27 



