N average number of pulses per beam position when noise alone is 



present, for a two-stage detector 



NiS) average number of pulses per beam position occupied by a target, 



for a two-stage detector 



E{n), E^in) average number of pulses in a sequential stage-A, £„{«) in the 

 noise-alone case 



a, a^, ag false-alarm probability per test — same for every range bin in that 

 stage; a^ is stage-A false-alarm probability when M^^ = 1 



(3, P^, (3g miss probability per test (therefore per stage) 



1' ^A> 9b quantization level against which sample voltage x is compared; 

 level may vary with range 



p prob \x > q\ for the sample voltage x corresponding to any particular 



stage and range bin 



Po value of p when noise alone is present 



PA' Pb specific cases of Po 



piS), Pji^iS), value of p for particular values of the SNR 

 Pb(S) 



K, K^, Kg decision threshold of a fixed-sample-size test 

 C • parameter specifying a sequential test 



General Description 



The detection scheme to be investigated here is a binomial two-stage 

 system featuring coarse resolution in stage A and fine resolution in stage B. The 

 properties of the stages are listed below. Binomial quantization is performed by 

 comparing each of the sample voltages with a quantization level chosen for that 

 particular stage and range bin. 



STAGE A 



1. Long pulses, generally few range bins. The long pulses result in radially 

 wide range bins; thus the surveillance zone is divided in range into a relatively 

 small number M^ of bins per beam position. 



2. One stage-A decision per stage-A bin per beam position. There are M^ 

 stage-A tests per beam position, each having the two possible decisions, alarm 



