Radar System Engineering

266 RADAR BEACONS [SEC. 89
not favored. This simple system can lead to occasional unnecessary
interference of one interrogator with another. Let us assume, for
example, that there are but twointerrogators and that the beacon could
readily reply to both steadily. If the dead time is long, there will nevertheless
be times when the interrogations from one beacon will arrive in
the dead time following the reply to the other. A more complicated system
that avoids this defect has been used. The dead time is normally
short but is arranged to increase, as needed, with increasing average rate
of interrogation. Too short a dead time can be troublesome, for it may
lead to multiple interrogation by the same interrogator pulse that has
reached the beacon not only directly, but also by other and longer paths
involving reflection.
If W represents the probabilityy that the beacon will reply to an interrogating
pulse of sufficient strength, it is easy to show by a statistical
argument that
w>J-
(6)
I+nr
and
w<
1
l+(n– 1),
In these expressions, n is the number of like interrogators having almost
equal recurrence rates, and 7 is the ratio of the dead time to the total
interval between interrogating pulses. Thus r is the fraction of the time
that the beacon is insensitive to a second interrogator if it is replying
fully to a first one. If the recurrence rates of the interrogators were
exactly equal, there would be a fixed phase relationship between pulses
and the statistical argument would be inapplicable. When interrogating
radars have crystal-controlled repetition rates that are almost exactly
equal, the radar that first emits its pulses may for a time steal the beacon
completely away from a second radar that emits its pulses somewhat
later. Equation (6) results from assuming complete randomness of
interrogations, and gives a result that is absurd when there is but one
interrogator. Equation (7) results when we assume that the probability
of reply to a particular pulse from one interrogator is completely uninfluenced
by the existence of the other interrogations by that interrogator.
This assumption is false since there is indirectly such an influence. The
exact expression for W is cumbersome but this is of little practical consequence
since it need not be used. The two values obtained from Eqs.
(6) and (7) bracket the true value and differ from each other unimportantly
in practical cases. A useful approximation for W is given by
(7)
w=
1
1 + (n – W)7’
(8)