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

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Chapter11 in analyzingthe dataprocessing system proposed forCyclops.) Whenthenumberofsamples averaged islargeandthe noiseis uncorrelated, equations (35) and(36) both approachgaussian distributions. Wethencanfind the separation betweenthemeansof thetwodistributions requiredforagivenbiterrorate.If thesamples fromnr receivers are averaged, the star noise will be correlated. If then ns = Br independent samples of this composite signal are averaged, none of the noise will be correlated, and an overall improvement If where b, = P*/Pr m n r n S n 2/?/2 n is produced. b,
Theprobabilitythatthethreshold isnot exceeded in the same observation time r is simply 1 -po(n). The probability that the threshold is not exceeded at any time period r in a much longer time T is then [1 - po(n)] T/r _+ e-Po(T/r), and the probability Pe that the threshold is exceeded in this interval is Having determined _, the range is given by equation (51). I - r _ i i T -po(Ur) Pe = 1 - e (45) which if po(T/r) - ' where "int" means the integer part of. We next require to be such that (47) I __1 m 1) and the background count is large, the distribution approaches the gaussian form with its mean value at no and its standard deviation Oo = x/ no. Simlarly, the distribution of the signal plus background is gaussian with its mean at (fro + n-) and its standard deviation o =-X/-_o+ H. To achieve the desired bit error rate the separation, _, between the means must be some multiple m of the sum of the standard deviations; that is, _= m(o o + o). If we again letff o =7_b + b, n we find _ = m = I1+2b,+2 x/b,(I +b,)+(ffb/m2)] (50) For our assumed error rate (Pe = 0.07865), m = _/'-_-, 47
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(NASA-CR- 11_5) PROJECT CYCLOPS: A
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CR 114445 Available to the public A
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At this very minute, with almost ab
Page 8 and 9: ACKNOWLEDGMENTS The Cyclops study w
Page 10 and 11: COMMUNICATION BY ELECTROMAGNETIC WA
Page 12 and 13: APPENDIX A - Astronomical Data ....
Page 14 and 15: t _ 2
Page 16 and 17: of the living beings evolved by the
Page 18 and 19: Figure2-1. M3I,the great galaxy in
Page 20 and 21: self.Thus,wecaninterpretFigure2-2as
Page 22 and 23: magnitude (low brightness) end, the
Page 24 and 25: Red Giant. The transition from main
Page 26 and 27: tion, as the central part of the cl
Page 28 and 29: TABLE 2-4 SELECTED NEARBY STARS WIT
Page 30 and 31: tideraisingforcesasr--_ where ,v =
Page 32 and 33: 3. Is it possible that living syste
Page 34 and 35: lawsof natural selection, more like
Page 36 and 37: starsthroughout the Galaxyhave also
Page 38 and 39: if the longevity of that life is ty
Page 40 and 41: The imaginative reader will have no
Page 42 and 43: Lookingfar ahead,supposewe aresucce
Page 44 and 45: usuallyterritorial expansion by the
Page 46 and 47: IOO IO 1 [ [ J [ J I J i [ i I i I
Page 48 and 49: order with what Morrison has descri
Page 50 and 51: The quantity gtPt is often called t
Page 52 and 53: which might result from synchronous
Page 54 and 55: 1. Wewillnothavenough resolving pow
Page 56 and 57: normalwith the meanat o x/--2. When
Page 60 and 61: Therangelimitisthenfoundbyequating_
Page 62 and 63: TABLE 5-3 PARAMETER Wavelength Tran
Page 64 and 65: angeanddirectlyasthesquareof antenn
Page 66 and 67: "_ i i i i i p = STELLAR DENSITY AT
Page 68 and 69: I-- g u. O >- I--- .d tit (]O 0 0.
Page 70 and 71: andwidth that will still give near
Page 72 and 73: acquisitionphasefor otherraces.Supp
Page 74 and 75: 1. They would transmit continuously
Page 76 and 77: and ¢-Ceti. No signals were detect
Page 79 and 80: vz .i g)mo PAGE NOr Ir[[,MZ 7. THE
Page 81 and 82: The price of incomplete sky coverag
Page 83 and 84: modest size.A largedatabaseontapeor
Page 85 and 86: THEAUXILIARYOPTICALSYSTEM Althoughn
Page 88 and 89: edetectedat 20,000light-years byCyc
Page 90 and 91: feeds must correct for spherical ab
Page 92 and 93: side of the dish and shade on the o
Page 94 and 95: TABLE 8-1 UNADJUSTED UNIT COST DATA
Page 96 and 97: 7. Using huge specially designed ji
Page 99 and 100: 9. THE RECEIVER SYSTEM The receiver
Page 101 and 102: whereP is the radiated power. Divid
Page 103 and 104: SHADOWED AREA SHADOWED AREA // // /
Page 105 and 106: Corrugatedhornssupportingbalancedhy
Page 107 and 108: o 50 ----- - _ T i 20 _,o 5 ,,,5 09
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TABLk ?- I A COMPARISON OF VARIOUS
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CENTRAL POINT STATION LSB LINE FREQ
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A02 .... + No (25) (i C 1 where No
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COAXIAL LINE DIRECTIONALCOUPLER FRE
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DeJager, J.T.:IEEETrans.onMicrowave
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pR_ING PA6E BLANK HOT FILMF_ 10. TR
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o-------------o_ _ o o o o ing of t
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addedto theother IF channel. The tw
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INPUT MHZ _PF 500 MHZ i : 575 T1 92
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azimuth _) has a delay (2a/c)sin 0
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stripline. For 2 _< k _< 6, appropr
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mation are common to all antennas i
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A cable pair costs about 20 cents/m
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11. SIGNAL PROCESSING The Cyclops s
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1.0 T t t I I r .9 -8 asynchronousl
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collimated coherent light. A simple
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power of the film and associated op
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samples simultaneously onto the sam
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outputs is assumed. COMPOSITE SIGNA
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SPECTRUM I n LINES M n LINES U SPEC
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signal andyet have a tolerable fals
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i --_- i i i i large values of n. T
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plottedin Figure11-15for various va
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All the1Fsignalswillarrivein phasei
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x:(1 +x) x 2 - _ -- (53) If we wish
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3's = unitcostof signal planelectro
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where0ma x is the maximum value of
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Roughestimates of the costs of buil
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12. CYCLOPS AS A BEACON Although th
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13. SEARCH STRATEGY The high direct
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distantgalaxies (oraninertialrefere
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wouldfollowtheuppermost linein Figu
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persquaredegreeof fieldwouldberequi
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starsfrom/'18 to G5 could support a
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14. CYCLOPS AS A RESEARCH TOOL Thro
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Only a few such galaxies have been
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15. CONCLUSIONS AND RECOMMENDATIONS
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perhapsdecadesand possiblycenturies
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APPENDIX A ASTRONOMICAL DATA DISTAN
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PLANETARY Planet ORBITS Semimajor S
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APPENDIX B SUPERCIVILIZATIONS AND C
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ABIOLOGICAL CIVILIZATIONS Many writ
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182
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tqOT APPENDIX C OPTIMUM DETECTION A
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to rmsnoise.Wenotethatthematchedfil
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APPENDIX D SQUARE LAW DETECTION THE
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If the output filter is very wide c
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if B/2 > T we can start instead wit
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Let us now introduce the normalized
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where h-- = expectation count of si
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APPENDIXE RESPONSE OF A GAUSSIAN FI
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APPENDIXF BASE STRUCTURES AZ-EL BAS
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ack,it shouldnotbenecessary to prov
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204
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206 i
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PAGE BLANK NOT APPENDIX H POLARIZAT
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APPENDIX I CASSEGRAINIAN GEOMETRY C
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APPENDIXJ PHASINGOFTHE LOCALOSCILLA
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APPENDIXK EFFECTOF DISPERSION IN CO
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APPENDIX L TUNNEL AND CABLE LENGTHS
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where r = "Ym/'rs- If we let o-_--o
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L-4 we see that the length of IF ca
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APPENDIX M PHASING AND TIME DELAY A
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andobtain V = 2 (Ps [! + _(Ar)] +Pn
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L" D 226
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APPENDIX N SYSTEM CALIBRATION The p
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APPENDIXO THE OPTICAL SPECTRUM ANAL
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232
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APPENDIX P LUMPED CONSTANT DELAY LI
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Thevalueofthefinalcoilonthelineis =
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APPENDIXQ CURVES OF DETECTION STATI
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I I I I LE :E oo
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APPENDIX R RADIO VISIBILITY OF NORM
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io 3 - l rlrllll I I I ]l+,ll_ I _f
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