INTRODUCTION 



A theoretical analysis was made of the performance of some binomial two- 

 stage radar detectors which use low range resolution in the first stage and high 

 range resolution in the second stage. In the first stage of the detection procedure, 

 one or more pulses are transmitted while the antenna beam is in a given position, 

 and a tentative decision is made for each of the wide range bins as to whether or 

 not a target is present. If no alarm occurs in the first stage, the antenna beam is 

 moved to the next position; otherwise, the beam is held fixed and pulses of the 

 second-stage type are transmitted. In the latter case, the regions corresponding 

 to first-stage alarms are then re-examined by collecting and processing the high- 

 range-resolution data, after which the antenna beam is moved to the next position 

 for a new first stage. 



The two-stage detectors reported on here belong to a class of multiple-stage 

 radar detectors requiring beam agility and versatile transmission and reception 

 capabilities. After a brief description of this class of multiple-stage detectors and 

 a mention of particular versions considered by others, the binomial high-resolution 

 two-stage detectors are investigated and their performances compared with that of 

 a conventional detector. 



HISTORICAL BACKGROUND 



The large body of literature on sequential analysis reveals a wide variety 

 of hypothesis-testing situations in which a statistical test of the sequential type 

 will require fewer observations, on the average, than a fixed-sample-size test with 

 the same probabilities of error. With the development of electronic scan antennas, 

 the application of sequential testing procedures to radar detection has become 

 practical; in many detection situations it is possible to design sequential pro- 

 cedures which promise appreciable energy savings over procedures limited by the 

 constant rotation rate of a mechanically scanning antenna. 



In the study of sequential radar detection the usual assumption has been 

 that successive observations (detected returns from a particular range gate) are 

 obtained under nearly identical circumstances (identical transmitted waveforms, 

 same receiver characteristics, etc.) and the testing procedures considered have 

 typically consisted of operating on the acquired sequence of measurements of a 

 matched-filter receiver output with the same rule of procedure after each trans- 

 mission. In particular, earlier work was generally with Wald's' sequential prob- 

 ability-ratio test of two statistical hypotheses, the optimum nature of which can 

 be realized in cases with a single resolution cell (or a single decision) per 

 antenna-beam position. Later applications to radar involved modifications of the 

 classical Wald test and various schemes for using sequential tests in multiple- 

 resolution element situations. 



'See list of references at end of report. 



