198 



ECHOES AND TARGETS 



length^ and target echoing area or cross secliun, re- 

 spectivel}'. Pt is tlie transmitted power and /? the 

 target range. This is, of course, the free space formula. 

 The jH-opagation conditions can be couveuiently lump- 

 ed into a multiplicative factor, which in the follow- 

 ing arguments is of little concern. To determine the 

 maximum range capal)ility of the radar set, it is nec- 

 essary to determine how large P,- must be in order to 

 be detectable. It is then possible to calculate the maxi- 

 mum range capal)ility of the radar set from the above 

 formula, on writing it : 



_ / p,(pr-a Y 



It has been common practice to assume that P,- ,ui„. 

 or the signal threshold ]iower, is of the order of magni- 

 tude of the noise power in the radar receiver. This is 

 certainly true; it is of the order of magnitude of that 

 noise power but is not generally equal to it. This 

 paper deals with the various factors in the receiving 

 system and display system which affect P,- n,i„. 



A few of the things that affect P,- u,,,, are 



1. The capabilities of the human observer. 



2. The properties of the display system on which 

 the signal is presented to the observer. 



3. The type of interference which prevents the de- 

 tection of an extremely small signal. 



This interference is not always receiver noise. There 

 ai'e storm cloud echoes and similar interferences, but 

 this discussion will deal only with the case in which 

 receiver noise is the limiting factor. 



It is useful to define the signal threshold power. 

 A good deal of work has been done on this question, 

 both theoretical and experimental, and in the course 

 of events a satisfactory criterion has been developed. 

 There is not a defined minimum threshold power 

 above which the signal is always seen and below which 

 it is never seen. One finds experimentally that if the 

 signal power )S' is plotted against the percentage of 

 cases in which the signal is correctly identified, a 

 "betting curve" is obtained. It takes several times as 

 much signal power to obtain a correlation of 90 per 

 cent as it does to obtaiii a correlation of 10 per cent. 

 In this paper the signal power which permits a cor- 

 relation of 90 per cent will be considered the thresh- 

 hold signal. 



Two main types of displays are used in radar 

 sets, the A-scope display and the plan posilion 

 indicator [PPI] or intensity-modulated display. 

 In the A-scope display there is presented a trace 



in which the apparent range of the target appears 

 as abscissa and the amplitude of the received echo 

 as ordinate. Along the trace the ever present 

 receiver noise appears; where the target is there 

 will be a larger average deflection. In experiments 

 on the A scope an artificial echo of controlled am- 

 plitude and range was introduced into the receiving 

 system. This artificial echo was so introduced 

 that it coidd fall into any one of several fixed 

 range positions. Usually six fixed range positions were 

 used. The observer then attempted to call the position 

 occupied by the signal. "Betting"' curves were then 

 drawn and S^^ (90 per cent signal threshold power) 

 determined. This is the signal power, usiially meas- 

 ured in terms of noise power in the receiver. Between 

 zero correlation and 90 per cent correlation a change 

 in signal power of perhaps 5 db is usually required. 

 This is quite a large spread, and it is very difficult 

 to determine j^'gg accurately because of the statistical 

 fluctuations. Ordinarily in running such a curve a 

 single threshold power measurement requires 50 to 

 100 observations. This laborious and lengthy process 

 of obtaining signal threshold is necessary to remove 

 the subjective element. The results obtained in this 

 way are remarkably constant and consistent among 

 different observers. They do depend on other factors, 

 howe\er. They depend both experimentally and theo- 

 retically on the number of range positions, and it 

 becomes necessary to indicate the type of variations 

 which obtain. A "6 position, 90 per cent point" has 

 already been defined for this experiment. This is taken 

 as the standard of reference denoted by db. /S'go 

 for a "1 position" experiment is -)-0.8 db experi- 

 mentally and +1.5 db theoretically. *S'go for an "N 

 position" experiment is -|-1.0 db both experimentally 

 and theoretically. .S'gf, for the "2 position" experiment 

 is — 2 db experimentally and — V2 db theoretically. 

 In this last case the experimental improvement is due 

 in part to the statistical difference and in part to 

 the greater ease with which the observer can con- 

 centrate on the range positions. 



In spite of these variations it is felt that any one 

 of these definitions is representatively good. For con- 

 venience the Sc,o for the "6 position" experiment has 

 been chosen, since it gives a sufficient number of posi- 

 tions so that statistical determination of S^^ can be 

 obtained with reasonable ease. It is possible to make 

 the same correlation trials for the intensity-modulated 

 PPI as for the A scope. The signal is put at any of 

 a number of range positions which are fixed in azi- 



