Radar System Engineering

28 THE RADAR EQUATION [SEC.!2.7
limitation down to wavelengths of the order of 3 cm, because ranges that
can be achieved are already very great and are limited usually by the
horizon rather than by the relation expressed in Eq. (14). That is to
say, the condition of free-space propagation, which we have assumed in
this section, often does not apply at the extremity of the microwavebeacon
range.
Long beacon ranges are, of course, a result of the enormous advantage
of one-way over tw~way transmission. If we compare Eq. (14) with
Eq. (4), we see that in signal strength for given transmitted power the
beacon process enjoys the advantage of a factor of 4flJP/G+s. It is
interesting to compute the limiting free-space range for a beacon operating
in conjunction with a radar set of the characteristics assumed in
our earlier radar example. Let us suppose that the gain of the beacon
antenna is 10, and that the tranwnitted power and minimum required
signal power for the beacon are the same as those assumed for the radar
set. Using Eq. (14) we obtain for the maximum range, either for interrogation
or reply, 60,000 statute miles.
In conclusion, we may point out that Eq. (14), although it has been
written in notation appropriate to the radar-beacon problem, applies, of
course, to any one-way transmission problem where free-space propagation
can be assumed. Applications of Eq. (14) are to be found in
the fields of microwave radar relay, radar j amrning, and microwave
communication.
THE MINIMUM DETECTABLESIGNAL
2.7. Noise.—It is well known that despite our ability to amplify
a feeble electrical signal by practically any desired factor, it is still not
possible to discern an arbitrarily weak signal because of the presence of
random elect rical fluctuations, or “noise.” If the true signal entering
any receiver is made weaker and weaker, it subsides eventually into the
fluctuating background of noise and is lost. What is the origin of these
fluctuations, and what factors determine precisely the level at which
the radar signal is hopelessly obscured by them?
Before we attempt to answer these decisive questions, it is worth
while to consider briefly the limit of useful sensitivity of an ordinary
low-frequency radio receiver. This limit is also set by random disturbances,
but in this case the largest random disturbances with which
the signal must compete originate generally not in the receiver itself
but elsewhere in space. Whatever their sourc+and this may range
from a passing trolley car to the mysterious reaches of interstellar
spat-these disturbances enter the receiver by way of the antenna.
The crucial quantity is therefore the ratio of the field strength of the
signal in the neighborhood of the antenna to that of noise or interference.