Project Cyclops, A Design... - Department of Earth and Planetary ...

APPENDIXQ
CURVES OF DETECTION STATISTICS
To calculate the range limits of the Cyclops system
for given probabilities of a false alarm and of detection
failure, it is necessary to compute expression (D41)and
to integrate expression (D38) given in Appendix D.
Expression (D41)gives the probability, in an average ofn
samples of the output of a square-law detector, that the
noise alone will exceed a certain threshold, while (D38)
gives the probability that the noise plus signal will not.
Because the curves obtained have rather general
utility and do not seem to be available elsewhere, they
are reproduced here. Figure Q-I is a plot of (D41) for
several values of n. Figures Q-2 through Q-9 are plots of
the integral of (D38) for each of the values of n shown
in Figure
Q-I.
Figure Q-10 shows for various values of n, the probability
of missing the signal as a function of the received
signal-to-noise ratio, when the threshold is set to give a
false alarm probability of 10-12. These curves are
derived from the previous graphs by determining the
threshold for each value of n from Figure Q-l, drawing
these thresholds on the corresponding Figures Q-2
through Q-9 and plotting the probability of missing the
signal at the selected threshold versus the input signal
to-noise ratio.
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Figure Q-I. False alarm probabilities.
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