Project Cyclops

Antenna gain and the free space transmission lawpp. 37–38

A uniformly illuminated aperture of area $A$ has on-axis power gain, and half-power beamwidth,

Power $P_t$ radiated with gain $g_t$ toward a receiving antenna of area $A_r$ at distance $R$ delivers

For fixed antenna areas transmission improves with frequency, but at fixed gain the ${\lambda }^2$ moves to the numerator and favours low frequencies. Practical gain tops out near $g_0\approx 10^{11}$, a beam of about one arc-second, at both optical and microwave wavelengths. For signals not under our control, eqs. (4)–(5) are the right form (p. 38).

Noise in coherent receivers, detection and filteringpp. 38–41

An ideal coherent amplifier has noise power per hertz $\psi$, usually expressed as a noise temperature $T_n=\psi /k$:

With synchronous detection and a matched filter, the output peak signal-to-noise ratio depends only on received energy per pulse $E$ and noise spectral density: $S/N=2E/{\psi }_0$ (eq. 12). Since energy can only grow with signal duration once power is limited, we would expect interstellar contact signals to be highly monochromatic (p. 39). In the search, before a signal is known, square-law (energy) detection must be used: at high signal levels it gives one-quarter the synchronous detector's signal-to-noise ratio, and below the noise the number of averaged samples must grow as the inverse square of the input ratio (pp. 40–41).

The microwave window and star noisepp. 41–43

Three noise sources define a broad quiet region from roughly 1 to 100 GHz that would look nearly the same to observers anywhere in the solar neighbourhood: galactic synchrotron noise falling steeply with frequency, the 3 K cosmic background, and quantum noise rising as $h\nu /k$ (p. 41). An Earth-like atmosphere adds water-vapour and oxygen lines at 22 and 60 GHz. The total sky temperature is about 4 K near the hydrogen line, with a minimum of about 3.6 K at twice that frequency, so the window from 1 to 10 GHz is clearly an attractive region for a ground-based receiver (p. 41).

From the report · Fig. 5-2, p. 41

Pointing at a star adds star noise. Weighting the field by the antenna pattern gives the increase in system temperature, which has the form of the transmission law with the star's projected area $A_{\ast }$ playing the transmitter (p. 42):

Range limits and comparison of several interstellar linkspp. 43–51

For comparison the range limit is defined as the range at which a coherent receiver sees unity signal-to-noise ratio, and every other system is held to the same bit error rate, 0.07865, which is what a synchronous detector gives at unity input signal-to-noise (pp. 43–44). With a clear circular receiving aperture $d_r$ and overall efficiency $\eta$, the received power is $P_r=d_r^2\eta P_{\mathrm{eff}}/16R^2$ (eq. 24), and for synchronous detection

Parallel expressions are derived for square-law detection (eqs. 34, 40) and photon counting (eqs. 50–51). Six point-to-point links are then compared at the same 1 bit/s, the same bit error rate and, to avoid a horsepower race, the same 100 kW wherever continuous operation is possible (p. 48):

Lasers suffer from the higher energy per photon, which raises their effective noise temperature. The report's summary: the sole advantage of lasers is narrow beams from small transmitters, which becomes a disadvantage at a receiver that needs large area; microwave collecting surfaces are cheaper and more durable; Doppler drifts are orders of magnitude smaller; and microwaves work in all weather (p. 51).

Communication rate. At fixed energy per bit the rate falls as the square of range and rises as the square of antenna diameter. A 7-bit convolutional code with Viterbi decoding cuts the error rate from $2.3\times 10^{-2}$ to $10^{-3}$ at 3 dB. Arrays of one to several kilometres at both ends could carry normal communication rates over 100 to 1000 light-years (pp. 51–52).

Probability of contact versus rangepp. 53–55

If each star independently radiates with probability $p\ll 1$, then after interrogating $n$ stars

Allen's density of F0–K7 main-sequence stars, ${\rho }_0=5.4\times 10^{-4}$ per cubic light-year, falls off with height $h$ above the galactic mid-plane as $\rho /{\rho }_0=[1+(h/h_0{)}^2{]}^{-3/2}$ with $h_0=850$ light-years (Fig. 6-1). Integrating over a sphere of radius $R$ gives the number of target stars (p. 54):

Because the range needed varies only as the cube root of $p$, a thousand-to-one uncertainty in $p$ is only ten-to-one in range. Eavesdropping on civilizations that leak megawatts for $10^7$ years ($p\sim 10^{-3}$) means reaching 60–100 light-years; beacons lasting $10^4$ years ($p\sim 10^{-6}$) must be detectable at 600–1000 light-years. Hence: start with a system that can see beacons at about 100 light-years and expand until beacons of reasonable power can be seen at 1000 (p. 55).

The number of resolvable directions and the search range limitpp. 55–56

Accepting 1.1 dB of loss at the beam edge, each pointing covers a solid angle $\Omega =\pi /g$, so the sky holds $N=4\pi /\Omega =4g$ resolvable directions (eqs. 5–6). A single 100-m dish at 20 cm already has $10^7$ fields of view, against about $1.7\times 10^6$ target stars within 1000 light-years: on average 0.17 stars per field, so searching several stars at once is not practical (p. 55).

For a square-law receiver averaging $n=B\tau$ independent samples, setting the output $S/N$ to one gives the conventional range limit (p. 56):

Doppler shifts and rates, and the effect of frequency drift on rangepp. 56–58

Population I stars move at less than 60 km/s relative to the Sun, giving fixed offsets up to $\pm 2\times 10^{-4}$ (eq. 13). Orbital motion and rotation of both planets add sinusoidal shifts. Earth's orbit gives $|\Delta \nu /\nu {|}_{\max }=10^{-4}$, its daily rotation a drift up to $1.1\times 10^{-10}$ per second; a planet with an 8-hour day might drift at $10^{-9}$ per second (p. 57).

A signal drifting at $\dot{\nu }$ Hz/s stays in a channel of width $B$ for $B/\dot{\nu }$ seconds, while the channel needs about $1/B$ seconds to respond, so the narrowest useful channel and the corresponding range are (p. 58)

So a hundredfold cut in drift rate gives the same range with one-tenth the antenna area. With drift near the hydrogen maser's limit, detecting a 1000-MW omnidirectional beacon at 1000 light-years needs an aperture of 2 to 6 km (p. 58).

The magnitude of the search, leakage signals and beaconspp. 58–63

A blind search of $10^{10}$ directions, each with $10^{10}$ one-hertz channels watched for $10^5$ s, would take $10^{25}$ s, or $3\times 10^{17}$ years (p. 58). Three decisions cut this down: search only the million or so likely stars within 1000 light-years, in order of range; analyse all likely channels in a narrow band simultaneously, into $10^8$ to $10^9$ outputs; and assume the signal is either always on or comes from a nearby star. At 1000 s per star, the $1.7\times 10^6$ F–K stars within 1000 light-years take $1.7\times 10^9$ s, about 50 years (p. 58).

Leakage. Earth's TV stations radiate about 50 kW with roughly 13 dB of vertical gain. With a 5-km antenna, 20 K, a 0.1-Hz bandwidth and 1200 s of integration, eq. (11) gives about 50 light-years for one station; another century of broadcasting would make Earth visible to about 100 light-years (p. 59).

Beacons. A single directive beacon visiting $m$ stars in turn replaces $p$ by $p/m$, so with equal effort at both ends $P_c\to 1-e^{-p}$ no matter how hard both races try (eqs. 20–21). Pointing one antenna at each of $m$ stars works up to about 1000–2500 stars, 70 to 100 light-years, but the total power for directive beacons grows as the fifth power of range and eventually meets the omnidirectional line (Fig. 6-6). Long-range beacons will be omnidirectional and high powered (p. 61).

From the report · Fig. 6-6, p. 61

If the efficacy of a beacon–receiver pair is proportional to $P_t{A}_r$ and every race minimises the total system cost (p. 61)

Spending 4 billion dollars on antennas therefore implies beacons of about 2000 MW, and the report expects beacon powers in excess of 1000 MW. Beacons would also transmit continuously, be extremely monochromatic, probably be circularly polarized, and carry information (pp. 61–62). Omnidirectional laser beacons fare poorly: at 1.06 μ, $10^{13}$ W reaches only 0.07 light-years, against 1360 light-years for a $10^9$-W microwave beacon received by a 3-km array (Table 6-2, p. 63).

Likely beacon frequencies: the water holepp. 63–64

Six reasons favour the low end of the microwave window: smaller Doppler shifts, looser stability requirements, more collecting area for the narrowest usable beam, cheaper collecting surface, lower power densities in transmitters, and freedom from oxygen and water absorption. That points to roughly 1 to 3 GHz, still far too wide to comb into 1-Hz channels (p. 63).

Cocconi and Morrison had proposed the hydrogen line, and Project Ozma listened there for about 400 hours in 1960 to τ Ceti and ε Eridani. But transmitting and receiving on one natural frequency means self-jamming. What is wanted is a natural contact band, many times wider than the Doppler spread but narrow enough to search half of it at once, free of strong lines and not below the hydrogen line. The band from hydrogen (1420 MHz) to the lowest hydroxyl line (1662 MHz), less 10–20 MHz guard bands, leaves about 200 MHz of clear band (p. 64).

Where shall we meet? At the water hole, of course!Chapter 6, p. 64

Semantics and anticryptographypp. 64–65

Once a signal is found, the sender will have tried to make decoding easy, the reverse of cryptography. Drake and Oliver suggested pictorial messages: a repeated sequence whose length is the square of a prime $p$ invites arrangement as a raster of $p$ lines of $p$ bits. Compared with acquisition, all else is easy (pp. 64–65).

The antenna array and system facilitiespp. 67–68

Each element is steered mechanically to about 10 arc-seconds; the final array beam, of an arc-second or less, is steered electrically by phase and delay. If element cost grows as the $x$th power of diameter, the optimum makes structure cost $2/(x-2)$ times the fixed cost per element; the study found $x$ very near 2, so the elements are the largest fully steerable dishes yet built, 100 m in diameter, on azimuth–elevation mounts (p. 67).

Elements sit about three diameters apart to avoid shadowing at low elevation, in a roughly circular hexagonal lattice. An initial array of 100 or fewer elements (about 1 km clear aperture) would grow at the periphery, or be spread over the full area and filled in. From the air the final system would be a central headquarters amid an orchard of 1000 to perhaps 2500 antennas, 10 km to 10 miles across, linked by service tunnels carrying power, control, standard frequencies and the IF cables (p. 68).

Sky coverage and site selectionpp. 68–69

Noise and shadowing limit observation to elevations above about 20°. At 33° latitude that still covers 80 percent of the sky, against 94 percent at the equator (Fig. 7-1). The site should be geologically stable, dry, calm, large and flat, and remote from habitation and air routes; a remote site in the south-western United States is indicated, and the VLA siting study is pertinent (pp. 68–69).

Receiver system, IF transmission, IF delay, and control and monitoringpp. 69–71

The receivers cover 0.5 to 3 GHz, the low end of the window, using heterodyne conversion at each antenna. Local oscillators are synthesized at each antenna from two standard frequencies distributed from the centre, with phase errors of only a few degrees at 10 GHz. Halving receiver noise is worth doubling antenna area, so the front end is cooled up-converters followed by a fixed-frequency maser, about 20 K; bands change by commanding a new pump frequency. Both polarizations are received (p. 69).

The two 100-MHz IF bands go back on one coaxial cable per antenna, placed symmetrically about a pilot tone and inverted in frequency at the quarter and three-quarter points, so every band edge sees the same mix of frequencies and the cable loss is almost flat; holding the pilot's phase also measures and removes cable delay changes (p. 70). Delays of up to about 50 μs, held to ±1/8 ns, come from stripline, coax and acoustic surface-wave lines, temperature-servoed against the pilot. All antennas normally point and tune together; time-multiplexed control allows independent sub-arrays (p. 70).

Combing the spectrum for signs of lifepp. 71–72

The signal processor is what makes Cyclops a search instrument. Each band is recorded as a raster on film and Fourier-transformed by a lens into its power spectrum, so a coherent signal becomes a needle. Successive spectra are then added with a range of offsets to follow any plausible drift; in the addition that matches the drift, the needle builds into a spike above the noise (p. 71).

Recording 200 MHz for about 1000 s gives 100 spectra at 0.1 Hz resolution. Added about 400 ways, they yield some 100 independent composite signals of $2\times 10^9$ Nyquist intervals per polarization: $4\times 10^{11}$ tests per observation. For a 20 percent false-alarm chance per observation, each test needs about $5\times 10^{-13}$. A signal at unity signal-to-noise in 0.1 Hz, $-93$ dB relative to the whole 200-MHz band, is then missed half the time; 2 dB more brings misses to 1 percent (pp. 71–72).

Imaging the radio sky and the auxiliary optical systempp. 72–73

Because each element's IF signal returns independently, $n$ elements can form $n$ simultaneous beams. The proposed imager re-radiates the signals at their original frequency from a scaled model of the array, 20 m across, onto an image array 40 to 120 m away, inside an anechoic, shielded building about 75 × 75 × 550 ft. Several optical telescopes, including a 1-m Schmidt to survey for target stars, would complete the site (pp. 72–73).

Range capabilityp. 73

For a 1000-MW beacon and 1000 s per star, the range with 1-Hz resolution is simply 100 light-years per kilometer of antenna diameter; 0.1-Hz resolution adds a factor of 1.6 (p. 73).

From the report · Fig. 7-2, p. 73

The cost of Cyclopspp. 73–74

Costs are plotted against clear aperture, about one-third of the physical array diameter. Tunnels, receivers, IF delay and imager scale with the number of elements; IF transmission scales as its 3/2 power. The signal detector is a fixed 160 million dollars (optical analyzers with time-bandwidth product $10^7$ and 1000 s per star), or 45 million dollars with $10^6$ and 100 s; engineering is a rough 100 million dollars, buildings 10 million dollars and the optical system 2 million dollars (p. 73).

From the report · Fig. 7-3, p. 74

Above a few hundred metres of aperture the antenna structures dominate: here is where creative innovation would really pay. Lowering the elements' top frequency from 10 to 3 GHz might halve their cost (pp. 73–74).

A comparison of the Cyclops and Ozma systemspp. 74–75

A signal Ozma could have seen at τ Ceti or ε Eridani, 10–11 light-years away, Cyclops could see at 20,000 light-years, or a signal 1/400 as strong at 1000 light-years. Those stars would have needed about $10^{13}$ W of effective radiated power to move Ozma's pens; Cyclops would detect 2.5 MW. Cyclops also searches two million times the band, for a spectrum search rate 200,000 times faster (pp. 74–75).

Confusion limitation. Going from one 100-m dish to 1000 dishes over 10 km raises sensitivity $10^3$-fold but resolving power $10^4$-fold, so the array becomes confusion-limited only if the log N–log S curve is steeper than $-4/3$, which the authors consider unlikely (p. 75).

The detection of narrow band signalspp. 123–126

The aim is a receiver with $10^8$ to $10^9$ channels of 1 or 0.1 Hz watching the whole 100-MHz IF band at once (p. 123). Alternatives are examined first. Total-power detection of a signal that doubles the noise in one 1-Hz channel would need $10^{16}$ samples, about three years of integration. Cross-power detection between two half-arrays also correlates the sky background and star noise and halves the area. A Golay detector carries no more information than a simple square-law detector, and a scanning analyzer wastes all but $\Delta f/B$ of the data (pp. 123–125).

A hard-wired fast Fourier transform of $N$ points takes $T_0\approx 2(N{\log }_{2}N)10^{-6}$ s (eq. 5). For real-time 1-Hz resolution one unit handles about 11,000 Hz, so two 100-MHz bands would need some 18,000 units at about 4.5 billion dollars, which leads to the optical approach (p. 126).

The optical spectrum analyzerpp. 126–129

The IF signal, biased positive, modulates a laser that writes a raster on moving film. In the analyzer's gate a lens transforms the film's transmission into its power spectrum, which appears in the back focal plane, itself in raster form: each line spans a band equal to the scanning frequency. A gate holding a signal duration $T$ resolves (p. 128)

From the report · Fig. 11-5, p. 127

Power spectrum processingpp. 129–136

A weak drifting signal is invisible in any one spectrum but appears as a slanting trace in a stack of them, like the pulsar record of Fig. 11-7. The spectra are scanned by a high-resolution vidicon, stored on head-per-track magnetic disks (about 120,000 dollars per second of observing, so 120 million dollars for 1000 s), then played back together down tapped video delay lines whose taps, in slanting rows, form the composite signals (pp. 130–133).

From the report · Fig. 11-8, p. 133

If the true drift differs from the nearest composite by $x_0$ resolution intervals across the stack, the detection efficiency is (p. 133)

Costing the storage, analyzers, delay lines, taps and detectors (eq. 21) for 100-MHz channels and 1000 s gives 264 million dollars for 1-Hz channels with $N=10^6$ analyzers, 480 million dollars for 0.1 Hz, and 135 dollars and 158 million dollars with $N=10^7$: from 125 dollars to 500 million dollars in round numbers (pp. 135–136). The authors present this as a sort of existence proof, expecting better or cheaper methods (p. 136).

Statistics of the detection processpp. 136–140

The analyzer's output brightness has the statistics of a square-law detector. If $y$ is the average of $n$ samples, normalised so that the mean noise is 1, then with noise alone (Appendix D, p. 137)

An observation holds $N_d=2Bn/\Delta f=2B{T}_0=4\times 10^{11}$ independent data for $B=200$ MHz and $T_0=1000$ s (eq. 27). If false alarms may lengthen the search by $k_{fa}=1.25$, then $q_{n0}=\ln (k_{fa})/N_d=0.55\times 10^{-12}$; the report uses $10^{-12}$ (eqs. 28–30, pp. 137–138). With signal-to-noise ratio $r$ in one resolution bin, $y$ follows

After 80 averages a unity (0 dB) signal is missed half the time at a $10^{-12}$ false-alarm rate; after 150, only 1 percent of the time; and beyond $n=10$ two decibels take the miss rate from 50 to 1 percent. With $\Delta f=0.1$ Hz and $n\approx 100$, a coherent signal 90 dB below the total noise power in the 100-MHz band can be found (pp. 138–139).

From the report · Fig. 11-14, p. 139

Low frequency time anomaly detector and Drake ensemble signal detectionpp. 140–141

For pulsed or swept signals such as pulsars, one analyzer can cover the whole 100-MHz band at 100-Hz resolution and 0.01-s integration, watched by vidicon, for perhaps 300,000 dollars (p. 140). Drake's ensemble method cross-correlates two successive power spectra to detect many weak narrow-band signals collectively. Its gain over a conventional detector depends on the fraction of occupied channels: about 0.70 for Earth's UHF television band and 1.25 for the FM band; it is recommended as an inexpensive addition (pp. 140–141).

Wide band imaging of the radio skypp. 141–152

With 1000 dishes over 10 km at 10 cm there are about $1.5(\pi d/\lambda {)}^2=1.5\times 10^{11}$ resolvable directions: 5000 years to map the sky at one second per point with one beam, or 5 years with 1000 simultaneous beams (p. 142). Radiative imaging must be done at, or near, the received frequency to avoid lateral chromatic aberration (eqs. 52–53). Delay-line, acoustic and optical imagers are compared; a microwave imager with plane signal and image arrays focused by paraboloidal delay is preferred, at about 9.2 million dollars including its shielded building (pp. 143–151).

Undesired signals. Unlike radio astronomy, Cyclops must work outside protected bands. UHF television would overload any reasonable receiver, low-power stations would be detectable for several hundred miles, and any flying object out to lunar distances. Options include a concentric secondary beam to subtract interference, a catalogue of known transmitters, or a quiet zone around the array (p. 152).

Key assumptions

• Other civilizations communicate with electromagnetic waves and favour the same low end of the microwave window, and plausibly the water hole, for the same physical reasons (Chs. 5–6).
• The most detectable signals are intentional, continuous, highly monochromatic and probably circularly polarized beacons of about 1000 MW or more; leakage is detectable only from nearby stars (pp. 59–62).
• Target stars are F, G and K main-sequence stars within about 1000 light-years, about 1.7 million of them from Allen's density and the 850-light-year scale height (pp. 53–55).
• The reference performance assumes a 20 K system, 1000 s per star, a false-alarm rate of 10⁻¹² per datum, and drifts of at most one resolution interval per spectrum (pp. 73, 134–138).
• Antenna structure cost scales as diameter squared (1156 d² dollars, 1970 prices) over 25–150 m, so the largest steerable dish, 100 m, is chosen; mass production saves 30 to 60 percent (pp. 82–84).
• Subsystem designs use 1971 technology: film-based optical spectrum analysis, analog disk storage, coaxial IF cables and cooled up-converters with masers (Chs. 9–11).

Where further work would help

• Antenna cost law. The whole system cost rests on the $d^2$ exponent fitted to seven designs and on the mass-production factor. The report itself calls a large study of element cost the first order of business (p. 84); a wider set of designs would show how sensitive the optimum element size and total cost are to that exponent.
• Beacon power and duty. Range scales with the square root of effective radiated power, and the 1000-MW figure comes from a cost-balancing argument (eqs. 22–23). How the search time changes across a wider range of assumed powers, duty cycles and drift rates would bound how far the 1000-light-year design target can be relied on.
• Signal processing. The detection statistics assume independent spectra, a rectangular analyzer gate and a fixed drift per observation. Testing with real interference, non-constant drift and the continuous-averaging variant (about 1 dB better, p. 139) would show how the 90-dB sensitivity holds up in practice.
• Target list. The search order depends on knowing spectral class and distance for about a million stars, and the report notes that no rapid method yet existed (p. 160). The effect of an incomplete or diluted list on the time to contact is not quantified.
• Terrestrial interference. Chapter 11 estimates that television and aircraft would be strongly detectable (p. 152). How much of the 0.5–3 GHz range, and of the water hole itself, remains usable at a real site would set the practical bandwidth.
• Sky and noise models. The sky-noise curves of Fig. 5-2 are described as approximate and elevation dependent (p. 41), and the range figures take the receiver at 20 K; site measurements would show how far the quoted ranges extrapolate to low elevations and the band edges.