ECHOES AND TARGETS 313 
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 S,, 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- 
muth. Scanning conditions may be included if de- 
sired. Some factors which affect the signal threshold 
power will now be enumerated, and the magnitude of 
their effects described. 
The first such factor is the noise figure of the re- 
ceiver. In brief, this is simply a multiplicative factor 
which would go with any of the other determinations 
made. The noise figure of the receiver specifically 
measures the amount by which that receiver is noisier 
than the best theoretical receiver. Ordinarily this noise 
figure runs to the order of 10 db, which means that 
the receiver is something like 10 times as noisy as 
the theoretically perfect receiver. As we are dealing 
with signal threshold power in terms of the receiver 
noise power (the latter being a universal parameter) 
it is only necessary to determine the noise figure of a 
given receiver in the field to determine what sort of 
input signal power is necessary. 
The second factor affecting the signal threshold is 
the intermediate frequency or the radio frequency 
bandwidth B of the receiving system. B represents 
specifically the narrower of the two. This bandwidth 
will affect the signal visibility in a way which will be 
discussed presently. The third quantity is the video 
bandwidth 6 of the receiver. At one time it was thought 
that the video bandwidth and the i-f bandwidth were 
equivalent, but this is not at all true. Between the 
i-f and the video systems there is a second detector 
which is a nonlinear element, which causes frequency 
conversion to take place. This causes the video band- 
width to have an entirely different action from that of 
the i-f bandwidth. A third factor is the sweep speed 
of the scope, denoted by small s. The sweep speed has 
an important effect which is nearly equivalent to that 
of video bandwidth. Another parameter is the time 
interval during which the signal is actually presented 
to the observer. This quantity will be represented by 
the letter T and called the signal presentation time. 
In addition to these there are several other factors 
connected with contrast effects in the presentation 
and the scanning variables. 
The first four variables mentioned apply to the 
geometry of the system, and geometrical scaling argu- 
ments can be applied to these quantities. One of these 
variables can thus be eliminated at the start by using 
not the pulse length +, but the product s X + as a 
variable. Similarly, the other variables are B X +, 
b X +r, and N X +. These quantities have a definite 
physica] significance. The sweep speed multiplied by 
the pulse length is simply the length of the signal on 
the scope and can be expressed in millimeters if de- 
sired. B X 7 is the i-f bandwidth times the pulse 
length and turns out to be a simple number. This is 
a number which will affect the signal visibility curves. 
Similarly the video bandwidth b X r is another num- 
ber. The signal power multiplied by the pulse length 
is simply the energy of the signal per pulse, and so 
on. These variables are essentially geometrical para- 
meters. The pulse repetition frequency and the signal 
presentation time are statistical parameters and must 
be treated in a statistical way as will be shown. 
The first geometrical factor to be considered is the 
i-f bandwidth. The interesting factor is the behavior 
of signal and noise. Independently, these are known 
quite well. With respect to noise the power response 
is proportional to the bandwidth. However, the re- 
sponse to a signal of a particular length, once there 
has been obtained a bandwidth which is adequate for 
the transmission of the pulse, will be essentially in- 
dependent of the bandwidth. When the bandwidth is 
very narrow the voltage of the output pulse is propor- 
tional to the bandwidth of the receiver. A curve can 
be drawn which is essentially the signal-to-noise power 
response curve, which for wide bandwidth will be 
proportional to the signal threshold power, while for 
narrow bandwidth it will be inversely proportional to 
the bandwidth. This is exactly the form of curve ob- 
tained experimentally. The optimum bandwidth is 
found to be approximately 1.2 times the reciprocal of 
the pulse length. The noise power in the receiver is a 
very poor single criterion as to how small a signal can 
be seen. For example, with a bandwidth of 1 me for 
1-ysec pulse a signal about 2 db below the noise 
can be seen. But if the i-f bandwidth is 10 me for a 
1-ysec pulse, a signal is visible 7 db below noise. If 
the i-f bandwidth is too small, even a signal equal to 
noise power is invisible. In general, therefore, signal 
threshold power is rated in decibels above the receiver 
noise power for a particular value of B (usually B 
= 1/r), since this provides a universal scale. 
For the video bandwidth the situation is more com- 
plicated. A good deal of theoretical work can be done 
on this problem, but the experimental data do not 
confirm the theory. The reason is that the video band- 
width is already effectively narrowed by the effect of 
sweep speed. Video bandwidth effects can be observed 
when the sweep speed is very fast, where s X + (the 
pulse length on the scope) is of the order of a milli- 
meter or so. Under these conditions video bandwidth 
narrowing always reduces the signal visibility and in- 
creases the signal threshold power. There is a real 
difference between the video bandwidth and the i-f 
bandwidth in the following respect. Decreasing or 
increasing the i-f bandwidth causes the components of 
