SP-419 SETI: The Search for Extraterrestrial Intelligence

[111] COMPLEMENTARY DOCUMENT 2

NOTES ON SEARCH SPACE

Prepared by:
Charles L. Seeger
SETI Program Office
Ames Research Center

[112] Blank page

[113] NOTES ON SEARCH SPACE

Here we describe briefly some of the major dimensions of microwave search space, not along the way a few physical and technological factors.

FLUX LEVEL

1. A transmitter with an equivalent isotropic radiated power (EIRP)1 of (W) watts will provide a flux level of (S) W/m2 at a receiving site (r) light years away according to the expression

S = 8.89 x 10-34 (EIRP) r-2 (W/m2) (1)

2. A receiver with a predetection noise power bandwidth (Br) hertz, an equivalent input system noise temperature (Ts ) in kelvins (K), and equipped with a power detector at its output, will provide unity signal-to-noise ratio (SNR = 1) after detection and in a time seconds, if the input power is

Pr = kTsBr = 1.38 x 10-23 TsBr (W) (2)

In the microwave region it is practical to choose bandwidths in the range 10-5 < Br < 3 x 108 without appreciably affecting the system noise temperature. A Ts of 10 K or less is achievable on Earth or in space. An ideal microwave receiving system in free space would have a Ts of at least 2.7 K because of the cosmic background radiation.

For optimum SNR with a signal of intrinsic bandwidth Bt,

(3)

Of course, by averaging n observations of duration , the SNR can be improved by (n )1/2, for n >> 1. However, any modulating information of bandwidth Bm > Br/n, will be lost.

We choose a nominal Br = 0.1 Hz for this discussion, and Ts = 10 K. Therefore,

Pr = 1 .38 x 10-23 (W) = -228.6 (dBW) (4)

When Ts and Br are chosen, the gap between equations (1) and (2) can be overcome at the source through choice of Pt and gt. At the receiving end the signal collecting area is the one remaining variable at choice. (The use of n unit observations, or post detection integration, is [114] reserved here for the explicit purpose of providing an adequate false alarm probability. The single objective is to detect the presence of a signal. Decoding any modulation which may be present, is another matter.)

3. For S/N = 1 and effective collecting area Ae in square meters, the range equation is

(m) (5)

or

r = 20 [n100(EIRP-9)]1/2 (ly) (6)

where, n100 is the number of 80 percent efficient 100-m dishes and the unit of (EIRP-9) is a gigawatt (109 W). Equation (6) is plotted in Section II-5, figure 2.

4. One can hope that the transmitting society uses large values of (EIRP).

5. The receiving antenna area is likely to be the single most expensive capital item in a large, passive search system. The 1.5 GHz antenna gains of a few sizes of radio telescope are given in table I below, and were calculated assuming 80 percent efficiency. A 90 percent efficiency should be available. The full half-power beamwidths of these antennas are also indicated in table 1.

TABLE 1. TYPICAL ANTENNA GAINS, EFFECTIVE AREAS, AND FULL HALF-POWER BEAMWIDTHS AT 1.5 GHz

 Telescope diam gr Ae . 25 m 1.25 x 105 = 50.9 dB 3.13 x 102 m2 29' 100 m 1.97 x 106 = 62.9 dB 5.03 x 103 m2 7'.2 213 m 8.96 x 106 = 69.5 dB 2.28 x 104 m2 3'.4

6. A reasonable expectation for the ground-based, zenith noise budget of Ts, assuming a low-noise antenna at a good site, is given in table 2. A space-based system would total at least 2 K less. In and near the galactic plane, or when a discrete radio source is in the beam, Ts will increase appreciably, and particularly so with high values for the gain (gr).2 The atmospheric contribution varies approximately as the secant of the zenith angle.

[115] TABLE 2. ORIGIN OF THE SYSTEM NOISE TEMPERATURE WITH THE ANTENNA POINTING AT THE ZENITH FROM A QUIET SITE AT ~ 2000 m ALTITUDE

 Galactic background (minimum) ~4 K Atmospheric radiation ~2 K Maser input amplifier ~2 K Antenna noise due to imperfections ~2 K Ts ~10 K

7. Bandwidth and effective area are inversely related for constant range (r). Clearly one must chiefly count on carrier detection (unless a stunningly powerful signal has been overlooked). That is, the type of signal which is easiest to just detect, is one possessing a high spectral density. For instance, consider UHF TV. About one-fourth of the transmitted peak power is in the steady carrier component, which usually has a bandwidth much less than 1 Hz, when observed for some tens of seconds. The remainder of the TV signal power is spread across about 4 x 106 Hz, and is highly variable as well. Because the system noise is proportional to Br in Equation (2), it is several million times easier to detect the carrier than to detect the modulation.

8. To avoid excessive false alarm signals just due to random background noise peaks, Project Cyclops suggested, in a thorough discussion of detection theory, that about 100 unit observations at should be averaged. This is another way of saying that one must accept a useful limit such that regardless of how it is achieved, via collecting area and/or integration time, when dividing the total instantaneous search band into ~109 channels.

9. To allow for either very long integration times (n >>100) on nearby objects, or more sophisticated signal analysis, one would like a situation where all interfering terrestrial signals produced a receiver input power under -250 dBW. This is 50 - 100 dB below normal communication technology, and it is why a search system on Earth cannot tolerate satellite transmission in (or too near) the search frequency band.

10. Radio astronomy search limits during normal observing procedures, are discussed in Section II-5. Explicit coherent signal searches using normal radio telescope systems, have covered few directions and few frequencies so far (see Section III-12).

11. A useful antenna figure of merit (AFM), in the present context where total collecting area and operating frequency are unspecified is,

(7)

where \$m2 = (total unit antenna dollar cost)/(geometric aperture area in square meters).

[116] SEARCH DIRECTIONS

l. The number of independent pointing directions (n) for an antenna gain g is ng. This and related matters (e.g., all sky area search, target search, and the need for good target lists) are discussed in Sections II-5, III-3, and III-4.

2. A single, one-feed, space-based antenna system can essentially observe in any direction in the whole sky at any time, and in one direction continuously, while a single Earth-based system cannot cover the whole sky nor observe in one direction continuously unless the direction is circumpolar. As a practical matter, it would take five or six Earth-based antenna systems to achieve these capabilities of one range-equivalent space system. Of course, the multiple Earth stations could carry out a given all sky area or target search in one-fifth to one-sixth the time. If, as has been suggested, a large space antenna can be equipped with three feeds, this advantage is reduced by a factor of three.

3. If one assumes merely that transmitting species are randomly distributed among, say, F, G, and K dwarf stars, they will tend to share the distribution pattern of these stars. In the neighborhood of the Sun, the density of these stars seems to be uniform in the galactic plane (so far, perhaps, because the data is yet uncertain), but falls to half density at about ± 650 ly in directions normal to the plane. Then, if one cannot see the entire sky with a given search system, one might sample a given total number of target stars by increasing slightly the range calculated with equation (6), picking more targets from directions near the galactic plane. On this simple assumption, even a system with moderately limited sky-coverage (spherical reflectors in the ground, for instance, like the Arecibo installation) could test such hypotheses as, "There is a 0.95 likelihood of finding one detectable species among a random assortment of (N), F, G, K dwarf stars." The volume of space surveyable varies as the 3/2 power of the quantity inside the brackets of equations (5) and (6).

4. Both these uniformity assumptions are clearly simplistic. Again, not all F, G, K stars are the same age as the Sun: Nor are they equally rich in the heavier chemical elements. Information such as this is needed in order to optimize search strategy; thus there should be an effort to improve the specificity of the target list and to improve our knowledge of the actual distribution of the targets in direction and range. (This matter is discussed further in Section III-4).

FREQUENCY DOMAIN

Search Bands

The arguments in favor of the free-space microwave window and the water hole in particular, are given in Section II-4. As a practical matter, all search bands must be free of wideband RFI for a significant fraction of the observing time. On Earth this means no line-of-sight transmitters, and some relatively minor protection from over-the-horizon systems. This could be arranged, in all [117] likelihood, for perhaps 25 - 35 percent of the spectrum between 1 and 10 or 15 GHz. All bands in which visible satellites are transmitting, or high power surveillance radars are operative, are essentially useless for search purposes from even a so-called quiet site. With a space-based search system, essentially no sharing of the search band with either Earth-based or space-based transmitters is possible, unless an RFI shield separate from the antenna is provided.3 Such a shield should be on the order of two to three times the diameter of the antenna it is protecting, and its edges should be treated to prevent signal currents from propagating on the back surface. So large a diameter is required in order to attenuate, by diffraction loss, interfering signals from the Earth and its vicinity (out to synchronous orbit, at least). The electromagnetic design, physical construction, and cost of such shields needs study.

Instantaneous Bandwidths

Aside from RFI considerations, several technical factors limit the width of the search that can be simultaneously observed.

1. The cost of a single large collector system drives home the need for antennas with high diffractive efficiency and low dissipative losses, which latter usually cluster in the feed assembly and could, of course, be cooled sufficiently by moderately large cryogenic systems. Besides efficiency, one needs a "low noise antenna." Large antennas today are usually magnified versions of the classical small antennas developed in an era when truly low noise amplifiers were not available. Thus we have, in the main, axisymmetric prime focus or cassegrain systems. None are efficient, i.e., > 0.85, nor are they low noise systems when compared to what can be achieved with modern electromagnetic technology.

Above 1 GHz, the dimensions of practical large antennas are also large when measured in wavelengths, but they are still point-focus devices and the aberration problem is simple compared to that in wide field-of-view optical designs. A low noise antenna needs to be an off-axis device, one with no obstructions anywhere in the wave front path. Avoiding wave front blockage improves efficiency and avoids most structural scattering of unwanted signals and thermal noise into the feed from the surroundings. By shaping all mirrors in the Galindo sense,4 one can achieve both high efficiency and low wide-angle and back lobes-hence a minimal noise contribution from the ground and lower atmosphere.

Optimum feed design needs study. The desirable properties of a feed are low dissipative losses, low spillover past the secondary reflector, and an electromagnetic field geometry, in both intensity and phase, that is nearly independent of frequency and polarization over the instantaneous search band. Furthermore, these properties should remain constant as one changes feeds [118] when changing search bands. Low noise, efficient feeds in current practice, with the exception of the Hogg Horn, tend to have bandwidths less than ~25 percent.

Shaped antenna systems have a long wavelength cut-off in the sense that for, the diffractive performance drops from 90 percent or better, down to the 50 percent level. This occurs when the secondary mirror dimensions are no longer many wavelengths in size, or when the feeds and secondary mirrors required for high performance are no longer practical structures. It is fortunate that for the 100m and up antenna diameter systems, falls outside the long wave boundary of the microwave window, where ultra low noise feed systems are no longer so critically important.

2. Another limit to the instantaneous system bandwidth is set by ultra low noise amplifier technology. Maser designs tend to have a constant gain bandwidth product, and a fractional bandwidth at a given gain that is independent of center frequency. To cover the water hole requires a 0.21 fractional bandwidth. This is difficult to attain with a single maser, though it appears possible after sufficient research and development.

A more attractive solution would appear to be the development of helium-cooled up-converters to feed a maser with the required bandwidth that operates at some frequency in the 20 - 30 GHz region. This scheme has the advantage that only two masers (one for each polarization), each with seven to ten up-converters (all in the same cryogenic package), can cover the entire terrestrial microwave window. This assumes, of course, that one can construct up-converters with Ts < 2 K. Extrapolating experience and current understanding strongly suggests this is a realistic expectation.

3. The possibility of simultaneously scanning two or three well separated frequency bands should be examined, since it would speed the spectral search accordingly. It would be particularly appropriate for the target search mode if it can be done without appreciable damage to the system noise temperatures. (Multiplying the number of simultaneous search bands means, of course, also multiplying the multichannel capability of the receiving system.) If applied to the area search mode so that at the highest frequency one just completes a nonoverlapping full-sky search in time, then the lower bands being scanned at the same time would have covered the sky many times over, in proportion to the ratio, unless one used an interleaved scan strategy with the highest frequency area search and changed the lower frequency scans to adjacent bands whenever a nonoverlapping search had been completed. This strategy would end up with roughly equal flux level limits in each frequency band instead of the relationship when all-sky search times are equal (see Section III-3).

4. Since the chief, initial search mode in the frequency domain is carrier search, we estimate here some dimensions of the spectral data processor. It consists of two main units, plus the scavenging system that selects and compacts the archival data. These two units are the Fourier transform filter-processor and the pattern detection system.

At the time of Project Cyclops (1971) an optical-photographic-magnetic disk design was proposed as the cheapest feasible system. Digital costs have dropped so far since then that a totally [119] digital system is now cheaper than the optical, as well as less costly to operate and more reliable than a mainly analog system.

Because the search range in carrier search is inversely proportional to the square root of the bin width (Br in eq. (5)) as long as the observed carriers stay within the bin during the time , we estimate a minimum practical bin width to be perhaps 10-2 Hz (see the Cyclops Report, pp. 55-58 (ref. 1) for relevant discussion). We can remove our doppler drift to that accuracy, receiving or transmitting, so we must assume the transmitting species could do as well if they cared to do so. Since they may not, larger bin widths may be needed, as they are for area search procedures and for eavesdropping; or for spotting pulsed signals, or frequency or directionally scanned signals. Thus the multichannel spectrum analyzer should be able to provide bin widths from 10-2 Hz up to perhaps several kilohertz.

Now let us estimate the magnitude of the extreme bit memory requirements of such a system, assuming instantaneous coverage of the water hole.

 Bin width 10-2 Hz Total bandwidth 3.27 x 108 Hz Number of unit observations per target 100 Number of polarizations 6 Bits/bins 16

This comes to 3.14 x 1014 bit memory cells which must be scanned for signal patterns and scavenged for archival data every 104 sec. This may be the largest digital system seriously envisaged to date, but it is feasible within a decade. Even if the bin width is limited to 1 Hz, reducing the scavenging period to 102 sec and the temporary bit memory call to 3 x 10-2, use of such a system with current radio telescopes would improve their carrier search capability by at least 35 dB. In reality, the pattern recognition capability of such a system would improve the "ETI signal identification sensitivity" still further by several orders of magnitude.

At present a 106 complex bin, flexible, modular prototype analyzer is in design, and completion of assembly could be expected within two years after funding. It has these properties:

 Input bandwidth 4 x 106 Hz complex Output bins 220/2m m = 0,1,2,3..... Bits/bin 16 or less Input bits 4 -8 Input sampling rate dual channel and up to 107 Hz Maximum output field 100 x 106 Output bit memory cells 3.2 x 109

This unit is designed to be a test bed for:

1. Acquiring on-air experience and proving (and improving) the economy of the design.

[120] 2. A preliminary look with high resolution at a number of interesting areas and objects in the sky.

3. The development of pattern recognition algorithms.

4. Appraising its suitability for other applications.

5. Determining the response of the design to RFI.

This experimental design uses a variety of available chips and microprocessors. and is economical on this scale at this time. It is not clear whether or not this particular design is suitable for extension to a 109 bin system, now or in the future.

The size of a 109 bin system, the need to retain organizational flexibility so that strategies in data analysis may be changed as experience is gained, and reliability and service needs - all these factors argue firmly for ground-based data processing even if space-based antennas are used.

POLARIZATION DOMAIN

At least two RF channels should be used in each search frequency band, one for each of two orthogonal polarizations. From these two, four additional polarizations may be synthesized at the central processing station to give a total of six: V, H, V + H (or 45°), V- H (or 135°), V + jH (left circular) and V - jH (right circular). If all six are processed, the probable loss for a signal of unknown polarizations, is 0.4 dB or 10 percent, and the maximum loss is 0.7 dB, or 17 percent. If only four polarizations are processed, the probable loss is 0.7 dB and the maximum 3 dB, a factor of 2 and quite equivalent to discarding half the antenna in use. Hence six spectrum analyzers are desirable in a fully built-up system. If fewer processors are available at some stage, one can compensate, assuming constant signals, by sequentially observing with different polarizations, thus trading time for processors. With six processors there may be a small but worthwhile increase in sensitivity if during the 100 unit-target-observations 50 of the unit observations are carried out with the four linear polarizations shifted by 22.5°.

There is no predicting what polarization schemes another species might employ, except (probably) in the case of signals expected to be received at great interstellar distances by antennas of unknown rotational orientation. Magnetoionic plasmas in planetary atmospheres and in interstellar space, particularly in the region of the Galactic plane, will rotate the plane of polarization of a plane polarized wave (the Faraday effect), and for maximum response the polarization of the receiving antenna must equal that of the incident wave. The polarization of a circularly polarized wave, on the other hand, will only be altered under most exceptional circumstances, to the best of our observational knowledge. Furthermore, the response of a circularly polarized antenna of the proper sense is independent of the rotation angle around the bore sight axis. Thus one would expect intentional, long distance signals to be circularly polarized at the point of origin.

[121] MODULATION

Electromagnetic waves may be modulated in any one of these ways-in amplitude, in phase and/or frequency, or in polarization -- or in any combination of these. We have used all these degrees of freedom to some extent. It is not absolutely necessary to have strong carrier components present with the modulation sidebands, but carriers or subcarriers, bearing an appreciable fraction of the total power in very narrow bandwidths within the total signal, are the general rule in our technology. The redundancy inherent in carriers simplifies coherent detection of the information in the modulation. Sometimes we suppress carriers somewhat in order to save power, but these vestigial carriers, as they are called, are prominent compared to individual frequencies in the sidebands. In order to make most efficient use of the radio spectrum, we have found it increasingly advantageous to thoroughly stabilize these carriers, hence they have very narrow frequency spectra. At the least, many of our signals are relatively easy to detect, if not to decode.

What a technologically advanced species might find most useful in the complex modulation domain, is unknown. Since there is only one electromagnetic spectrum, our experience would suggest that they may use it efficiently, in the Shannon sense. If they do, carriers may not exist in the prominent fashion to which we are, so far, generally accustomed. If this is the situation, attempts to eavesdrop over a few tens or hundreds of light years will be more difficult by unknown orders of magnitude. What appears patently clear is just this. The basic EM communication physics of our Universe seems to be fairly well understood by us here on Earth. Thus, if we or another species want to make signals detectable at great distance, very stable, high spectral density signals will be provided. Similar signal characteristics are eminently desirable if we are to eavesdrop on unintentional, intraspecies transmissions.

TIME FACTORS

Signals that appear at regular or irregular intervals, perhaps due to special scanning, time schedules or frequency programs or schedules, are a form of modulation, of course, but are separately discussed here for convenience of emphasis.

1. A way to produce high flux level signals at great distance is to use a very directive antenna. There are at least two obvious and simple strategies here. Intentionally, such powerful signals may be scanned over a part or the whole of the sky, appearing in a given direction at regular intervals in the form of a strong pulse of some appreciable duration. Or the transmitting species may have determined by means presently beyond us, that there are only a small set of likely directions within (their) reasonable range and they confine their transmissions, simultaneously or sequentially, or irregularly, for short or long sampling periods, to these directions.

The possibilities one can visualize depend on our imagination, but we should be able to rank them in an order of estimated likelihood and be on the lookout for the more distinctive time [122] patterns. At the moment there seems to be no way to avoid this large range of time dimensional possibilities.

2. It has been suggested occasionally by some radio observers who have suffered interference from swept frequency transmissions by ionosounders, chirp radar, and the like, that an ETI beacon might be systematically swept in frequency in order to assist with its identification as an artifact, and to make less demanding the frequency-search aspect of SETI at the receiving end.5 The apparent attractiveness of this tactic is diminished by recognizing that unless one can derive a singular frequency sweep rate from obvious and likely, universal, physical arguments, it requires increasing the receiver bin width, which increases the signal power required for detection. Then, too, if the receiving frequency-search effort is to be significantly reduced, still more power (costly to us at any rate) must be continuously supplied per hypothesized signal detection possibility, and a minimum observing time interval is established by the frequency sweep repetition rate. To recognize and identify an ETI signal requires more than a single, band limited pulse.

Similar arguments pro and con, can be hypothesized with respect to the possibility that ETI beacon signals might be pulsed in amplitude. So far, only one thing seems clear, and two others rather persuasive, as a result of human experience.

a) A frequency stable signal is much easier to detect than a signal of the same power v is gyrating in time and/or frequency in an unknown way.

b) Unless the transmitting society knows where we are and the likely state of our technology (which they might, of course, if they have observed our radiations), beacon maintenance is a power consuming operation. There, as here now, there may be a need to conserve energy.

c) They may, also, have a strong interest in spectrum conservation because of their own interference problems; and then a stable signal, narrow in frequency, would seem a more likely choice.

3. As yet, we have no generally useful algorithm for recognizing coherent signals when the SNR/Hz is appreciably less than unity, except the simple one of long integration time and precision examination of the relative level of one part of the spectrum compared to the spectrum levels on either side. Again, a frequency stable signal is much easier to detect.

4. Finally, we note that intrinsically stable signals launched uncompensated from rotating planets revolving about a central star do show distinctive, informative, Doppler drift patterns.

[123] PATTERN RECOGNITION

1. The need for pattern recognition in the frequency-time domain is a pervasive theme in search strategy discussions. How should one best seek to recognize the presence of an almost infinite class of coherent patterns in a finite noise field and at low SNR? Can powerful and rapid algorithms be developed to answer this question?

The human eye, ear, and brain are probably our most versatile pattern perceivers, so far. But the human being is fallible, pattern selective, imprecise, subject to fatigue and hallucination, and above all in this context, too costly.

Fortunately, there are algorithms for recognizing simple lines and bands in a frequency-time data field, for recognizing spectral lines and the like. Figure 1 is a famous picture which here simulates a slowly drifting carrier in a noisy frequency-time field. Eye or machine recognition for such a pattern is straightforward. In the figure, imagine frequency increasing to the right, and time increasing downward.

Figure 1. Signature of a pulsar produced by simultaneous observation on adjacent frequency channels. (Photograph courtesy of Martin Ewing, Calif. Inst. of Technology.)

We do not wish to overstress or understress the importance of pattern recognition studies in the development of search strategies. A major research effort seems worthwhile. But for a significant class of signals which we think are very likely signals, we do not have search procedures already defined, and our concern is mainly to find the most efficient procedures.

2. A visual pattern display with pedestal blanking and coordinate compression capability is clearly needed for diagnostic purposes and for pattern recognition studies. It should be possible to [124] "zoom" a 103 x 103 point display at will over the stored data field, and with adjustable magnification (or compression). Assistance might be sought from those who have been studying visual pattern recognition problems. This visual display should be given an early priority and, at least in prototype form, be used with the earliest high frequency-resolution observations, the better to bound the problem area for the first automatic scanners to be developed.

3. Multicomponent natural spectral line signals should be recognizable and probably fitted to compact descriptions by multicomponent Gaussian approximations. Likewise, it should be possible to recognize pulsing signals, narrow band, broadband, and showing dispersion. Since the search system must be gain stable, the galactic background noise level as a function of frequency, should be recorded with minimal redundancy.

4. There should be algorithms for recognizing carefully defined categories of RFI, coherent or not. Following up false alarms is tedious, subtracting directly from search time, and a practical balance must be struck between sensitivity and false alarm rate.

5. To summarize, the field of pattern recognition is an important and rich one to study.

Table 3 lists a number of the most powerful radars operating in the territories of the United States and some other nations. It is tantalizing to realize that if another intelligent species should somehow recognize the solar system as a likely site for intelligent life, then it would be trivial to illuminate it with an easily detectable signal from enormous distance.

TABLE 3. LOCATION, FREQUENCY, AND EIRP OF MOST POWERFUL RADARS IN 1000-2500 Mhz BAND.

 Location Frequency, Mhz Power (EIRP), W Number . Areciboa 2380 7.4 x 1012 1 Goldstone, Calif.a 2100 3.2 x 1012 1 Goldstone, Calif.a 2388 7.9 x 1011 1 Westford, Mass.a 1295 1.6 x 109 1 Stockholm, Sweden 1315 5.7 x 109 1 Argentina (Ezeiza) 1324 2.2 x 109 1 Bahrain 1795 2.0 x 109 1 Bahrain 1825 2.0 x 109 1 United Arab Emirates 2105 2.0 x 109 1 United Arab Emirates 2075 2.0 x 109 1 Roetgen, Germany 2353 1.3 x 109 1 Roetgen, Germany 2395 1.3 x 109 1 Goldstone, Calif. 2100 1.2 x 109 4 Madrid, Spain 2101.8 1.2 x 109 2 Madrid, Spain 2106.4 1.2 x 109 2