306 GENERIC TYPES OF RADAR SYSTEMS AND TECHNIQUES 



and an incomplete cross-correlation function as 



^,,{tJ) = ^jjm-^it - r)dt (6-20) 



where 2T is now a finite observation or integration time. 



Autocorrelation of a limited nature, specifically for r = 0, has been used 

 in conventional radar systems almost since the invention of radar. As can 

 be seen from a study of Equation 6-19, the incomplete autocorrelation 

 function as applied to radar for r = consists of (1) obtaining the instan- 

 taneous echo power /i^(/), (2) integrating or summing for a finite time 27", 

 and finally (3) dividing by the period 2T, thus forming an average power. 

 These three steps can be seen to be essentially equivalent to the conven- 

 tional frequency-domain radar processes wherein a square-law second 

 detector converts the echo into instantaneous power and some type of 

 storage provides the required averaging. In early radar sets for echo 

 ranging the averaging was performed aurally by the operator or visually 

 using A-scope presentation. Later the plan position indicator (PPT) used 

 cathode ray tube persistence plus the operator for storage. Finally the use 

 of more sophisticated video integration was adopted. 



The relative merits of autocorrelation (r = 0) and square-law detection 

 versus cross-correlation detection have been studied^ with the results shown 

 in Fig. 6-9. The output-versus-input mean power signal-to-noise ratios are 

 plotted for a bandwidth reduction of 2 : 1 (in going from IF to video, for 

 example), a practical value for echo ranging where the pulses must be 

 retained. These curves apply to a single pulse where there is no integration. 

 Signal enhancement resulting from the integration of pulses is discussed 

 subsequently. It is interesting to note that autocorrelation can be thought 

 of as comparable to postdetection bandwidth reduction, whereas cross 

 correlation is comparable to predetection bandwidth reduction. In Fig. 6-9 

 there is an apparent threshold in the autocorrelation and square-law 

 detection curve starting in the neighborhood of unity signal-to-noise ratio. 

 This threshold is noted by the change from a linear to a square-law relation- 

 ship between output and input sensitivity. Such a threshold does not exist 

 in cross correlation, where a noise-free reference is used. 



Cross-Correlation Radar. As soon as the signal enhancement 

 capability of statistical cross correlation was recognized, applications to 

 radar were considered. In order to obtain the maximum advantage from 

 the process, one of the functions in Equation 6-20 must be noise free. A 

 study of (pi2(r,T) reveals that if /i(/) is the delayed target echo which 

 contains desired information as well as unwanted noise, then Ji{t — r) 

 should be a noise-free reference signal possessing characteristics identical 



^Samuel F. George, Time Domahi Correlation Detectors vs Conventionat Frequency Domain 

 Detectors, NRL Report 4332, May 3, 1954. 



