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

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normalwith the meanat o x/--2. When the signal is negative, the mean will be at -o _ as shown in Figure 5-4. If the a priori probability of either polarity is one •5/0. , , [ PDF, ZERO TRANSNITffD .5/o ° - .41o- I \_ .2/0- - -I/00 I / READ'NOI_j/L l z i i PDF, ONE TRANSWIIIED 4 antenna or array. For n antennas, we find dr eeff (1 - b,) 4 t_B t t 1/2 If successive time samples are averaged we find dr Peff (n-b, 4 f )_11/2 (29) (30) DETECTED SIGNAL AMPLITUDE Figure 5-4. Probability density functions-symmetric binary channel (S/N = 2). 400 500 half, the decision threshold should be set at zero amplitude. The probability of a pulse being incorrectly read is the area of the tail of either distribution that extends across the threshold; that is, _ 1 202 o Pe ex/'_'ff e I ox/Y¢ -5o- -400 -300 -200 - I00 0 I0. 20. 3o- (x- dx so that time averaging (or averaging the signals from sufficiently widely separated antennas) does permit an adverse background ratio to be overcome. In the systems we shall consider, b,
asshownin AppendixD, if thenoisein successive samples isuncorrelated, theprobability thatthisaverage exceeds agiventhresholdvalueofy =YT is n-1 poO, T) = e -YT _ yTkk! (35) k=O If both signal and noise are present, the probability that the same threshold is not exceeded is: n-! pl(yT) = n + Y) ln_l(2nx/"_)dy foYT (Y) 2 e -n(r (36) I i i T I I q a bJ o x LI3 Figure 5-5. Probability that signal plus noise fails to exceed power P. Z Figure 5-5 shows pl(x) plotted against 10 log x for various values of r expressed in decibels. By noting the value of pl(x) for 10 log x = 4.053 dB and plotting this versus the corresponding value of r, we obtain the curve shown in Figure 5-6. We see that if the probability of failing to exceed the threshold is to be 0.07865, then r, the input signal to noise ratio must be 6.06 (i.e., 7.83 dB). Thus for a square law detector with short time averaging (r _ 1/B), the limiting range is IJ ..3 dr Pelf (0.165 - b. R = -- - (34) f I 1/2 4 _B .01 I I I t I I 3 4 5 6 7 B 9 I0 _o log _ where we have written 0.165 for (6.06) -n . The n-bbM Average. lfy = -- _ x i is the average of n i=0 n samples of the output of a square law detector, then, 1 n Figure 5-6. Probability of missing signal. The same graphical method can be used with these expressions that was illustrated with equations (31)and (33) for the case n = 1. (This is the procedure used in 45
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(NASA-CR- 11_5) PROJECT CYCLOPS: A
Page 3 and 4:
CR 114445 Available to the public A
Page 6 and 7: 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 58 and 59: Chapter11 in analyzingthe dataproce
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
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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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