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

1012
Assuming the receiving antenna to be a clear circular
aperture of diameter dr, and allowing for losses, equation
(4) may be rewritten as
I01
I
VIOLE1
dr 2
Pr = --
16R 2
rgPeff
(24)
I010
109
I--
3=
I08
I0 7
t
where r/ is the overall quantum efficiency (i.e., the
product of the transmission of both atmospheres, optical
or radio receiving antenna efficiencies, photodetector
quantum efficiency).
Sychronous
Detection
Here, by our definition, we simply set Pr equal to the
total system noise referred to the input. Since we may
wish to synchronously detect signals heterodyned down
from the optical region, we set
I0 6
tO II 1017' 1013 1014 1015 I016
FREQUENCY, HZ
Figure 5-3. Radiation of the Sun versus frequency.
dr2 1"/m
Pr=(_ + $,)B=C,B+
16R2oq 2
,t,(v)B (25)
to be 2.5× 10 _o W/Hz of receiver bandwidth, while at 1/a
the required power would be 7.4X 1011 W/Hz.
RANGE
LIMITS
The maximum range over which communication can
take place with a given system depends on the coding
used and on our definition of an acceptable error rate.
Since our objective is to find expressions for the maximum
range that will enable us to compare different
systems fairly, the exact standards we choose are not too
important so long as we are consistent. We shall assume
that the message is transmitted in a binary code. For
systems using incoherent detection, a "one" is sent as a
pulse and a "zero" as a space. This is known as an
asymmetric binary channel. With a coherent receiver and
a synchronous detector we can detect pulses of either
polarity and can therefore send a "one" as a positive
pulse and a "zero" as a negative pulse. This type of
communication is the symmetric binary channel. The
phase of the transmitted signal is reversed to change
from a on. to a zero or vice versa.
We will define the range limit for a coherent receiver
as the range at which the received signal-to-noise ratio is
unity, and the range limits for all other systems as the
range at which these systems have the same probability
of error per symbol received.
where _ is given by equation (8) using the appropriate
system noise temperature, q_(v) is given by equation (23)
and a_ (which is also a factor included in rT) is the
transmission of the atmosphere of the sending planet.
The coefficient m = ! ,2 is the number of orthogonal
polarizations reaching the detector. If we now define the
star noise background ratio b, as
star noise power m qb(v)B
b. = - (26)
signal power 20qPef f
then we find from equations (24) and (25)
dr eeff(1 - b,)
R = -- (27)
4
,/,./ t 1/2
We note that if b.> 1 the maximum range is imaginary;
that is, there is no real range at which the signal-to-noise
ratio is unity.
Bit Error Rate. We must now determine the bit error rate
for the synchronous detector with unity input signal-tonoise
ratio. Since the output signal to noise power ratio is
2, and the noise is gaussian, the probability density
function when a positive output is present will be
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