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Optimum Bandwidth and Doppler Shifts/Doppler ChirpsRadobs 13The Doppler shift of would be ETI transmissions is due to the line-of-sight relative velocity component, while the Doppler drift or chirp is due to the line-of-sight relative acceleration component. The tables below show the "natural" Doppler shift and Doppler drift components at each end of a link, so taking a worse case scenario, the maximum shift and drifts may be twice as large. The calculations are based on an alien star/planet system assumed similar to Sol/Earth. It is not known what is the radial (line-of-sight) acceleration of the Sun with respect to other stars. One would assume that it is relatively small. The rationale for Optical SETI presupposes that the communication data rates will be considerably larger than presently expected for Microwave SETI, which is typically of the order of 1 Hz. This bandwidth is partially determined by interstellar dispersion effects and the expected microwave Doppler drift rate. At a frequency of a few GHz, interstellar dispersion has been shown to place a lower limit on the usable signal bandwidth. This bandwidth is approximately 1 Hz. It can be shown that the optimum detection bandwidth for a drifting frequency in order to collect the maximum signal energy in each frequency bin, is proportional to the square root of the drift rate. Thus, a 1 Hz bandwidth is just about right for a 1.5 GHz signal with a maximum relative drift rate of 2.24 Hz/s, as might be caused by microwave transmitters and receivers in synchronous planetary orbit (see table below). The potentially higher recovered signal powers afforded by optical communications, would allow for a considerable expansion in bandwidth. Indeed, it is probably one of the main driving forces, besides compactness, preferring optical communications over its radio frequency counterpart. For an optical transmitter or receiver in synchronous planetary orbit (see table below), the maximum relative drift rate is about 682 kHz/s, thus implying an optimum bandwidth of about 26 kHz. As to what that bandwidth would be for chirp- compensated signals which are described below, is unknown, but likely to be determined by date-rate and SNR considerations only. The maximum Doppler Shift is given by: v df = ---.f Hz (1) c where v = maximum line-of-sight velocity (m), c = velocity of light (3 X 10^8 m/s), f = frequency (Hz). The maximum Doppler Drift (Chirp) is given by: w^2.r df' = -----.f Hz/s (2) c where w = angular velocity (rad/s), r = radius of planet or orbit (m). ========================================================================== | INTERSTELLAR DOPPLER SHIFTS Microwave Visible | | 0.20 m 656 nm | | Velocity 1.5 GHz 457 THz | |--------------------------------------------------------------------------| | Transmitter on the surface +/-0.46 km/s +/-2.31 kHz +/-707 MHz | | of a rotating alien planet. | | | | Transmitter in synchronous +/-3.07 km/s +/-15.5 kHz +/-4.68 GHz | | orbit about alien planet. | | | | Transmitter in orbit about +/-29.8 km/s +/-149 kHz +/-45.4 GHz | | alien star. | | | | Relative (radial) motion +/-20.0 km/s +/-100 kHz +/-30.5 GHz | | between alien star system | | and Sol. | ========================================================================== These Doppler shift and drifts will follow simple harmonic motion as the transmitter orbits its star and rotates on or about a planet. For a ground- based transmitter or receiver or ones in planetary orbit, the actually shifts and drifts will be the resultant of separate contributions from planetary or planetary orbital rotation, solar orbital motion, and relative motion between our respective star systems. ========================================================================== | INTERSTELLAR DOPPLER CHIRPS Microwave Visible | | 0.20 m 656 nm | | Velocity 1.5 GHz 457 THz | |--------------------------------------------------------------------------| | Transmitter on the surface +/-0.46 km/s +/-0.71 Hz/s +/-51.4 kHz/s | | of a rotating alien planet. | | | | Transmitter in synchronous +/-3.07 km/s +/-1.12 Hz/s +/-341 kHz/s | | orbit about alien planet. | | | | Transmitter in orbit about +/-29.8 km/s +/-0.03 Hz/s +/-9.05 kHz/s | | alien star. | | | | Relative (radial) motion +/-20.0 km/s +/-0 Hz/s +/-0 Hz/s | | between alien star system | | and Sol. | ========================================================================== The greatest Doppler frequency shifts are produced by a transmitter or receiver in its own orbit about a star, yet the Doppler frequency drifts are a minimum because of the very large orbital radius. During the early years of SETI, it was believed that ETIs would help us to detect and receive their signals, by compensating for their "natural" local contributions to Doppler shift and drift. In more recent years, that rationale has fallen out of favor as electronic techniques have been developed which allows us to efficiently analyze a microwave spectrum, and observe a signal drifting in frequency. Indeed, the present MultiChannel Spectrum Analyzer (MCSA) systems make it easy to spot a drifting signal even in the presence of considerable noise. Because visible light frequencies are over five orders of magnitude greater than the low microwave frequencies, the Doppler shifts and drifts are increased by the same factor. Fortunately, wider transmission bandwidth systems are better able to cope with large drifts in frequency. However, for Optical SETI we must go back to the earlier SETI rationale, and assume a minimum requirement that the aliens de-chirp their transmission frequency. It may not be necessary to remove some or all of the Doppler shift offset in frequency, if we assume the availability of local-oscillator lasers in the receiver that can be precisely tuned to any frequency. Since we presently don't know the "magic" optical frequencies, it may not matter about precise frequencies being maintained, particularly if the Galactic communications spectrum is not crowded. What is the probability that one ETI signal could interfere with another with so much space and so much spectrum available (the optical cosmic haystack), notwithstanding the important question as to if there are any ETIs out there, let alone many, signalling in our direction? What would the Galactic FCC say about the lack of stability in transmission frequencies! What is far more important, is to remove the Doppler drift or chirp because this smears out the energy over a wide bandwidth, thus making it very difficult to detect. However, once a signal is acquired, the use of automatic frequency control (AFC) on the local-oscillator laser can keep the signal in lock. By not worrying about Doppler shifts, there is then only the requirement to remove Doppler drifts. Since the aliens will know very precisely their transmitter acceleration at any time along the line-of- sight, they can apply a de-chirping signal to their laser which will almost completely cancel the induced chirp. Similarly, we can do the same at our end of the link, and de-chirp the local-oscillator to remove our local component of acceleration along the line-of-sight. Notwithstanding the targeting problem, neither of us needs to know anything about each other's line-of-sight accelerations or even velocities with respect to some galactic frame of reference. It is very unlikely that even ATCs could know our receiver accelerations and velocities because they wouldn't know where on Earth or in space our receiver was located. Many orders of magnitude of de-chirping should be achievable, which would hopefully reduce the residual chirp to something of the order of the linewidth of the lasers and the spectral spreading caused by any interstellar dispersion effects. Thus, the monochromaticity of the received ETI signal will be maintained. Computers controlling the transmitter and receiver can be programmed to vary the amount of de-chirping as a function of direction. In an optical "search" program, we would superimpose our local de-chirp on any tuning strategy that we might adopt to search through the optical frequency spectrum. Even without any de-chirping, it is clear that if aliens wanted to keep the "natural" transmitter frequency drift to a minimum, they would put their transmitter in its own orbit about their star. This may be a requirement anyway if their laser is solar or nuclear pumped. There are also safety considerations with powerful lasers in the MW to GW range, so they probably wouldn't want to locate it close to large populations or in areas with heavy space traffic. December 26, 1990 RADOBS.13 BBOARD No. 287 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Dr. Stuart A. Kingsley Copyright (c), 1990 * * AMIEE, SMIEEE * * Consultant "Where No Photon Has Gone Before" * * __________ * * FIBERDYNE OPTOELECTRONICS / \ * * 545 Northview Drive --- hf >> kT --- * * Columbus, Ohio 43209 \__________/ * * United States .. .. .. .. .. * * Tel. (614) 258-7402 . . . . . . . . . . . * * skingsle@magnus.ircc.ohio-state.edu .. .. .. .. .. * * CompuServe: 72376,3545 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
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