3. Energy per transmission 



4. General class of statistical testing procedure (e.g., fixed-sample-size 

 tests, Wald sequential tests,' etc.) 



5. Number or average number of transmissions 



6. Choice of not quantizing data or quantizing data into any number of levels 



7. Decision statistic 



8. Decision thresholds and, if used, quantization thresholds 



A two-stage detection system having the same radar transmission 

 characteristics in both stages was investigated by Helstrom.' In the system he 

 describes, square-law detected returns from a number of pulses would be processed 

 by superposing them and comparing the accumulation at the end of each stage with 

 the threshold of that stage to see if it exceeds it for any delay, that is, for any 

 range. The second-stage decision would be based on both first-stage and second- 

 stage returns. For convenience in analyzing the process, he supposes that each 

 return is sampled regularly in range, with the number of samples, or increments, 

 equal to twice the product of the bandwidth and the sampling period. Letting the 

 test statistic for each of the range increments be the sum of sampled returns over 

 successive pulses is then analogous to integrating video returns. Two of 

 Helstrom's conclusions as to the performance of this system were that its advan- 

 tage over the ordinary detection system (a fixed-sample single-stage system) 

 decreases as the SNR increases and that at best it achieved about twice the 

 average scanning rate attained by an ordinary detection system. His investigation 

 was not extended to cases with three or more stages since it appeared that little 

 further improvement could be expected and the computations would be much 

 more difficult 



H. M. Finn analyzed an "Energy Variant Sequential Detector" (EVSD)''' 

 and, in a later report,^ a "Resolution-Variant EVSD." For rapidly fluctuating 

 targets (Swerling's' fluctuating target types 2 and 4) the decision statistic at 

 each stage is the sum of square-law detected outputs, generally for three pulses 

 in the first stage and six in the second, while for slowly fluctuating (types 1, 3) 

 and nonfluctuating targets a linearly detected matched-filter output is used, 

 generally with two or three stages of one pulse each. In some of the proposed 

 versions of an EVSD the sum of both first-stage and second-stage outputs is used 

 in the second stage. References 4 and 6 include analytical results on the optimi- 

 zation and performance of some of the EVSD's described, a verification of pre- 

 dicted performance by simulation on a digital computer, and descriptions of the 

 general implementation of EVSD's and RV-EVSD's. One of his conclusions was 

 that in many applications the increased efficiency which would result from 

 employing more than two stages would not compensate for the inconveniences 

 in implementation. 



A more thorough analysis of an EVSD having single-pulse stages is made 

 by Brennan and Hill.*-' They present optimum energy levels and cumulative 

 detection probabilities for various false-alarm probabilities and numbers of range 



