312 RADIO WAVE PROPAGATION EXPERIMENTS 
that an investigation of the frequency dependence of 
such scatterers would produce useful results. 
THE DEPENDENCE OF SIGNAL 
THRESHOLD POWER ON RECEIVER 
PARAMETERS* 
This paper deals with the effect on the signal thres- 
hold power of various parameters in the receiving 
systems of radar sets, i.e., with the minimum signal 
power necessary for visibility. Although this is a diffi- 
cult problem and all the important factors entering it 
are not known, it is felt that at least qualitatively, 
and sometimes quantitatively, a fairly good answer 
can be given at present. First of all it is necessary to 
define some of the parameters involved in ordinary 
radar reception. When a signal is reflected from a 
target the power entering the receiving system may 
be written in the following form: 
P,Gd?0 
(4)*R4 
where G, A, and o are the antenna gain, radar wave- 
length, and target echoing area or cross section, re- 
spectively. P; is the transmitted power and F the 
target range. This is, of course, the free space formula. 
The propagation conditions can be conveniently lump- 
ed into a multiplicative factor, which in the follow- 
ing arguments is of little concern. To determine the 
maximum range capability 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 capability of the radar set from the above 
formula, on writing it: 
( P,G@2a y 
Rmx=\7Zoap..)¢: 
(4m)8 P, min 
It has been common practice to assume that P, mm, 
or the signal threshold power, 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, mn. . 
A few of the things that affect P, min 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 
are 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, 
°By J. L. Lawson, Radiation Laboratory, M1 T. 
P,= 
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 obtain 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 thres- 
hold signal. 
Two main types of displays are used in radar 
sets, the A-scope display and the plan position 
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 could 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 Sy, (90 per cent signal threshold power) - 
determined. This is the signal power, usually 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 S,, 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, 
however. They depend both experimentally and theo- 
retically on the number of range positions, and it 
becomes necessary to indicate the type of variations 
which cbtain. A “6 position, 90 per cent point” has 
already been defined for this experiment. This is taken 
as the standard of reference denoted by 0 db. Sp, 
for a “1 position” experiment is --0.8 db experi- 
mentally and +1.5 db theoretically. Sj, for an “N 
position” experiment is +-1.0 db both experimentally 
and theoretically. S,, for the “2 position” experiment 
is —2-db experimentally and —'% db theoretically. 
In this last case the experimental improvement is due 
in, part to the statistical difference and in part to 
yhe greater ease with which the observer can con- 
