MULTIPLE-RANGE-BIN FIRST-STAGE 



In most of the practical applications of two-stage systems, it will be 

 necessary to use at least several first-stage bins to cover the search zone. 

 Figure 21 presents plots of P„ vs S for a Rice distribution for various combinations 

 of M^ and /V, where FAR = 3xFRFxM^Mg xlO"^ As mentioned in the dis- 

 cussion of figure 3, for a fair comparison of cases having different values of 

 M^, the M^ bins must cover the same search zone and M^Mg must have the 

 same value. From a comparison of these figures the following observations 

 can be made. 



1. An increase of about 0.6 to 1.0 dB/pulse in the SNR (the SNR required 

 for a single-scan detection probability of 0.5) is necessary as M^ is quadrupled 

 (under the assumptions made in the earlier discussion under "Resolution"). This 

 same observation was mentioned in connection with figure 3. The amount of this 

 increase tends to be smaller for the larger values of M^. 



2. For fixed N (and Pq = 0.5), the decrease in the optimum value of A/g 

 with an increase in M^ is often considerable. 



3. For fixed M^, the optimum value of /Vg increases with /V; this is con- 

 sistent with the results for M^ = 1 shown in figure 6. 



4. The optimum value of Ng decreases with an increase in Pq (equivalently, 

 with an increase in S), as was shown for the M^ = 1 case in figure 12. 



One important conclusion drawn from these figures is that often an Ng 

 considerably smaller than the optimum iVg can be used without significant loss 

 in detectability; this is fortunate, since a small value of iVg is desirable in 

 situations involving occasional clutter or high target density. 



38 



