Radar System Engineering

SEC. 310] COMPO1’A’D TARGETS 83
The quantity in parenthesis in Eq. (24) will be recognized as the volume
of the region in space [mm which, at a givem ins+.an+.,m%ctd signals can
be received. One must assume, to obtain Eq. (24), that the rain is
distributed over a region larger than this pulse packet and that the
target is smaller than the pulse packet.
The average total power received from all the raindrops that contri-
Imte to the return at a given range is the sum of the return powers of the
individual drops. The return po}vers, not the return fields, must be
addedl be’cauw the random distribution of raindrops in space results in
random phases of the individual contributions.
The cross section uo for raindrops is that of a small sphere of large
dielectric constant (Sec. 32) and is given by
(25)
where a is the radius o’f the raindrops, d their diameter, and the bar
denotes averaging over all drops that contribute to the return. Since
ueither K nor the distribution in drop size is very ~vellknown, it will not
be possible to test this formula experimentally with great precision, but
the existing measurements of average intensity can be explained, assuming
reasonable values of N and =6.
Using Eq. (25) we can now rewrite Eq. (24) as
Average rain-echo intensity = ~50 Rzcr@~
Target-echo intensity .4i%, ‘
(26)
which displays the strong dependence of rain echo upon wavelength and
drop diameter.
What has been said above pertains to the a~erage intensity of the -
rain echo. Actually, the signal received from a given region, being the
vector sum of the ~vaves reflected from the indi~-idual drops, fluctuates
continually in amplitudp as these clrops. shift in position relative to one
:mother. ~ This fluctuation obeys a simple statistical law, which, for our
purpose here, can be stated as follows: the probabilityy of recei~ing, at
P
arly time, an echo of intensity (power) P or greater is just e ~D,where
P, is the a~erage intensity o~-er a time long compared to the fluctuation
time. l’reciscly the same law describes the distribution in intensity of
thermal noise po!rer as amplified by the i-f amplifier of the radar set,
and this is one reason for the striking similarity between rain clutter ancl
receiver noise as seen on a radar oscilloscope. There is, however, onc
LThis point is discussedin greaterdetail in Chap. i’, Vol. 13 of this series.
z‘~he changes of intensitv caused by statistical fluctuationsof the mmber Of
raindropswithin a pulsepacket are small comparedwith thesechanges.