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

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S B2Ps2 -- = (D16) N f/_ sin 2trrf 2/'°21 (B-f) (nrf)2 df dO In the limit when r >> I/B, this expression approaches (DI5) so the continuous averaging offers no improvement in this case over the discrete average. Sin x/x RF Filter, Output Averaged for a Time r Here we take H(f) = [(sin 7rTf)/lrTf] 2 so that the frequency interval between the first nulls of the RF filter is 2IT. This RF filter takes a running average of the input signal that is T sec long. If no output filter is used and n independent samples of the output taken T seconds apart are averaged so that r = nT, then equation (D13) again applies and N \Po/ T\Po/ (Dl7) If instead we take a running average of the output with the same filter used in the preceding case, we now have (D l 8) In this case there is an improvement from the continuous averaging. Although the discrete samples averaged were statistically independent in the last two cases, the intermediate samples in the third case are so highly correlated with those already taken that no improvement results from their inclusion, whereas in the fourth case the intermediate samples are less correlated and their inclusion improves the SIN ratio. S/N RATIOS IN THE DETECTION OF COHERENT RADIATION The specific combinations of pre- and postdetection filters treated in the last section are presented here once again, but the object now is the detection of the coherent radiation in the presence of the incoherent background. No Postdetection Filtering Again neglecting shot noise, and taking m = equation (D1 O) becomes s er2 H*H = sin 2(rt Tf) sin 20rTf) ('n'T./')2 (rr Tf) _ N 2PrP o + Po 2 (pr/t'o) _ 1 + 2(Pr/P o) (DI9) [H*HIf = 0 = 1 f H*H df = -- _ 1 1 _1 - sin(21rTf)'] OrTf) 2 T L 21rTf j 2 and we obtain from equation (D7) neglecting shot noise: S -- = N Po2T es 2 sin2 _rr[ sin2nTf_ df f (lrrf)----------- T (1- _ /(n-_--f) 2 If r >> T we can use equation (D! I) and obtain Since Pr/Po is the input signal-to-noise ratio, we see that for input signal-to-noise ratios much greater than unity, the square-law detector degrades the input ratio by a factor of two (3 dB). At very low input signal-to-noise ratios we have (S/N) _ (Pr/Po) 2 , and the unfiltered square-law detector doubles the (negative) signal-to-noise ratio expressed in decibels. Signals rapidly become undetectable as they drop below unity input signal-tonoise ratio. Ideal RF Bandpass Filter of Width B, Ideal Low Pass Postdetection Filter of Cutoff Frequency W If W i> B the output filter has no effect except to limit shot noise, and we have from equation (DI 0): S Pr2 -- = (D20) N hvW 2 2(Pr+ Po)-- + -- PrPo + Po: m 190
if B/2 > T we can start instead with equation (DI 2) and obtain __ sin s lrrf + B2 (B-f) 0rr/)2 For r>> I/B, we use equation (DI2) and find (D24) S r Pr: -- = (D29) N r(pr +Po) by2 + --GPo +--&_ 2 77 m 3 191
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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
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ACKNOWLEDGMENTS The Cyclops study w
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COMMUNICATION BY ELECTROMAGNETIC WA
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APPENDIX A - Astronomical Data ....
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t _ 2
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of the living beings evolved by the
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Figure2-1. M3I,the great galaxy in
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self.Thus,wecaninterpretFigure2-2as
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magnitude (low brightness) end, the
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Red Giant. The transition from main
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tion, as the central part of the cl
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TABLE 2-4 SELECTED NEARBY STARS WIT
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tideraisingforcesasr--_ where ,v =
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3. Is it possible that living syste
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lawsof natural selection, more like
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starsthroughout the Galaxyhave also
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if the longevity of that life is ty
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The imaginative reader will have no
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Lookingfar ahead,supposewe aresucce
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usuallyterritorial expansion by the
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IOO IO 1 [ [ J [ J I J i [ i I i I
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order with what Morrison has descri
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The quantity gtPt is often called t
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which might result from synchronous
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1. Wewillnothavenough resolving pow
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normalwith the meanat o x/--2. When
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Chapter11 in analyzingthe dataproce
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Therangelimitisthenfoundbyequating_
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TABLE 5-3 PARAMETER Wavelength Tran
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angeanddirectlyasthesquareof antenn
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"_ i i i i i p = STELLAR DENSITY AT
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I-- g u. O >- I--- .d tit (]O 0 0.
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andwidth that will still give near
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acquisitionphasefor otherraces.Supp
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1. They would transmit continuously
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and ¢-Ceti. No signals were detect
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vz .i g)mo PAGE NOr Ir[[,MZ 7. THE
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The price of incomplete sky coverag
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modest size.A largedatabaseontapeor
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THEAUXILIARYOPTICALSYSTEM Althoughn
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edetectedat 20,000light-years byCyc
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feeds must correct for spherical ab
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side of the dish and shade on the o
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TABLE 8-1 UNADJUSTED UNIT COST DATA
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7. Using huge specially designed ji
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9. THE RECEIVER SYSTEM The receiver
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whereP is the radiated power. Divid
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SHADOWED AREA SHADOWED AREA // // /
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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
Page 151 and 152: i --_- i i i i large values of n. T
Page 153 and 154: plottedin Figure11-15for various va
Page 155 and 156: All the1Fsignalswillarrivein phasei
Page 157 and 158: x:(1 +x) x 2 - _ -- (53) If we wish
Page 159 and 160: 3's = unitcostof signal planelectro
Page 161 and 162: where0ma x is the maximum value of
Page 163 and 164: Roughestimates of the costs of buil
Page 165 and 166: 12. CYCLOPS AS A BEACON Although th
Page 167 and 168: 13. SEARCH STRATEGY The high direct
Page 169 and 170: distantgalaxies (oraninertialrefere
Page 171 and 172: wouldfollowtheuppermost linein Figu
Page 173 and 174: persquaredegreeof fieldwouldberequi
Page 175 and 176: starsfrom/'18 to G5 could support a
Page 177 and 178: 14. CYCLOPS AS A RESEARCH TOOL Thro
Page 179 and 180: Only a few such galaxies have been
Page 181 and 182: 15. CONCLUSIONS AND RECOMMENDATIONS
Page 183 and 184: perhapsdecadesand possiblycenturies
Page 185 and 186: APPENDIX A ASTRONOMICAL DATA DISTAN
Page 187 and 188: PLANETARY Planet ORBITS Semimajor S
Page 189 and 190: APPENDIX B SUPERCIVILIZATIONS AND C
Page 191 and 192: ABIOLOGICAL CIVILIZATIONS Many writ
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Page 195 and 196: tqOT APPENDIX C OPTIMUM DETECTION A
Page 197 and 198: to rmsnoise.Wenotethatthematchedfil
Page 199 and 200: APPENDIX D SQUARE LAW DETECTION THE
Page 201: If the output filter is very wide c
Page 205 and 206: Let us now introduce the normalized
Page 207 and 208: where h-- = expectation count of si
Page 209 and 210: APPENDIXE RESPONSE OF A GAUSSIAN FI
Page 211 and 212: APPENDIXF BASE STRUCTURES AZ-EL BAS
Page 213 and 214: ack,it shouldnotbenecessary to prov
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Page 219 and 220: PAGE BLANK NOT APPENDIX H POLARIZAT
Page 221 and 222: APPENDIX I CASSEGRAINIAN GEOMETRY C
Page 223 and 224: APPENDIXJ PHASINGOFTHE LOCALOSCILLA
Page 225 and 226: APPENDIXK EFFECTOF DISPERSION IN CO
Page 227 and 228: APPENDIX L TUNNEL AND CABLE LENGTHS
Page 229 and 230: where r = "Ym/'rs- If we let o-_--o
Page 231 and 232: L-4 we see that the length of IF ca
Page 233 and 234: APPENDIX M PHASING AND TIME DELAY A
Page 235 and 236: andobtain V = 2 (Ps [! + _(Ar)] +Pn
Page 237 and 238: L" D 226
Page 239 and 240: APPENDIX N SYSTEM CALIBRATION The p
Page 241 and 242: APPENDIXO THE OPTICAL SPECTRUM ANAL
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Page 245 and 246: APPENDIX P LUMPED CONSTANT DELAY LI
Page 247 and 248: Thevalueofthefinalcoilonthelineis =
Page 249 and 250: APPENDIXQ CURVES OF DETECTION STATI
Page 251 and 252: 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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