This is a discussion about the possible use of the PIN photodetector array in ground-based Optical SETI receivers for implementing space-diversity heterodyne reception in the presence of considerable atmospheric turbulence. The definition of the word "space" in this context refers to spatial and not outer-space. Space-diversity reception might be an alternative to laser guide-star adaptive telescopes techniques, or a complementary technique to improved the signal-to-noise ratio.
In the presence of atmospheric turbulence, even if the image of the star wanders a bit across the array, if a signal is present there would be occasions during the sampling of the array when the signal would "pop up" momentarily. In long exposure photography, the "dancing" of the image would cause the photographed image to be smeared and perhaps undetectable. However, with a pixel sampling time of 10 microseconds (for a 100 kHz bin bandwidth), the image scintillation effects would appear momentarily frozen during the brief clear air conditions, and the ETI signal should be detectable if the signal is strong. It would take 164 milliseconds to sample the entire 128 X 128 pixel array if sequential single-pixel sampling was employed. Gross wavefront tilt, which will displace the image across the array, is easy to deal with just by sampling all the pixels rapidly and continuously, perhaps with 16,384 Multi-Channel Spectrum Analyzers (MCSAs), each 10 GHz wide. Just a thought!
ETIs might help us out with in-atmosphere reception, by transmitting a "pilot-tone" with their data. This could consist of a Continuous Wave (C.W.) optical carrier signal, spaced a few MHz to several GHz from the optical carrier that is modulated with the data. The same phase, amplitude and spatial distortions that occur to the data carrier also occur to the pilot-tone carrier. It might thus be possible to apply space diversity pre- detection combining techniques to produce a heterodyne Intermediate Frequency (I.F.) signal with little scintillation in amplitude and phase, and little reduction in signal-to-noise ratio. While photographic and CCD images of faint stars require some integration time, and produce poor images when resolutions better that 0.5 arcsecond are required, the same considerations do not necessarily apply to incoherent or coherent optical communications through a turbulent atmosphere if many photodetectors are employed.
The theory behind the pilot-tone method is as follows, and makes no specific assumption about modulation techniques employed by the ETIs, i.e., whether intensity, polarization, frequency or phase modulation, analog or digital:
Let the pilot-tone carrier at fp be given by:
Ep(t).sin[wpt + dphi] (1)
and the modulated (tone) information signal at fs be given by:
Es(t).sin[wst + phi(t) + dphi] (2)
where dphi = phase disturbance caused by the atmosphere, phi(t) = represents possible phase or frequency modulation.
The phase disturbances dphi, are essentially common to both the signal and the pilot-tone, as they are almost identical optical frequencies and travel the same optical path.
Signal Bandwidth <------------> Ep(t) * ------------ Es(t) * | | * | | Pilot-Tone * | Signal | * | | * | | * | | * | | -----------------------------------------------------------> fp fs Optical Frequency
Pilot-tone system for self-phasing heterodyne detection. The pilot-tone carrier is at frequency fp and has amplitude Ep(t), while the information signal is modulated on to a carrier at frequency fs, with amplitude Es(t). The average intensities of these signals may not be the same. The frequency separation (fs - fp) may be several MHz to several GHz, depending upon the signal modulation bandwidth, and other factors, and fp may be above fs. Typically, (fs - fp) would be about equal to the signal (double-sideband) modulation bandwidth.
If we heterodyne a local-oscillator laser operating at frequency wo with both these signals, we obtain the difference frequency signals (see RADOBS.17) or first I.F. from the photodetector proportional to:
Ep(t).Eo.sin[(wp - wo)t + dphi] (3)
Es(t).Eo.sin[(ws - wo)t + phi(t) + dphi] (4)
The pilot-tone signal as stated by Equ. (3), may be passed through a narrow- band filter and amplifier, to produce what is effectively a strong electrical (second) local oscillator (L.O.) signal for an electrical mixer. It may also be used to lock a narrow-band Phase Locked Loop (PLL) whose Voltage Controlled Oscillator (VCO) is used as the strong, amplitude-stable and clean 2nd local oscillator. The information signal as stated by Equ. (4), may be passed through a wide-band filter and applied to the other port of this electrical mixer. The difference frequency output of the electrical mixer or second I.F. is proportional to:
Ep(t).Es(t).Eo(t)^2.cos[(ws - wp)t + phi(t)] (5)
------- sin[(wp - wo)t + dphi] | | ----- k.cos[(ws - wp)t + phi(t)] --------------------------->| Mixer |-->| LPF |----------------------------> (30 MHz) | | ----- (70 MHz) ------- ^ To Summer -----> | (100 MHz) sin[(ws - wo)t + phi(t) + dphi] | --------------------------------
Second I.F. produced after the low pass filter (LPF) has all the atmospheric-induced phase noise eliminated. The frequencies given in brackets are arbitrary, and used to help clarify the technique. Each array pixel has one of these circuits whose in-phase outputs are simply added and taken to the MCSA.
The phase disturbances dphi introduced by the atmospheric turbulence have been eliminated by the process of electrical mixing. Thus, if the image of the transmitter is instantaneously or sequentially smeared out over many pixels, all the second I.F. contributions are in phase, and may be simply summed to provide pre-detection diversity combining and a substantial reduction in amplitude instability (scintillation). It also provides the best type of predetection summation in the form of maximal-ratio combining. Those pixels producing the weakest signal also produce the lowest quantum or Planckian noise contributions, so that the summed signal power is not degraded by noise from pixels with little or no signal. Only a single MCSA would be required, which would be effectively continuously "looking" at the combined outputs of all 16,384 pixels. We would have only one MCSA, but 16,384 electronic front-end systems for predetection combining, based on the mixing technique partially illustrated above.
If as to be described in RADOBS.22, we need to use a local-oscillator pixel sampling technique to overcome heat dissipation problems in the array, we might find that we couldn't implement this maximal-ratio combining technique over so many pixels.
The MCSA would not detect directly any Planckian starlight noise from a star in the field-of-view alone, only that which overlapped and mixed with an ETI signal on one or more pixels. Thus, it may not be possible with this signal-processing technique to eliminate Planckian starlight noise due to it being smeared out over many pixels along with the signal. Also, if there were significant interstellar or atmospheric dispersion effects between the signal and pilot-tone, the technique wouldn't work. This consideration may affect the choice for the value of (fs - fp) and the modulation bandwidth. Of course, to use this technique anyway requires the cooperation of the ETI.
Would they be so obliging? It would be difficult to justify building such a receiving signal processing system without foreknowledge that ETIs employ this technique - this could be said to be putting the cart before the horse!
I have some experience with fiber-optic versions of optical space-diversity receivers. I have used four-quadrant photodetectors in the far-field radiation pattern from multimode fiber, to substantially reduce fading in "Fiberdyne" (modal-noise) sensors and communication systems. The far-field mode radiation pattern of a multimode optical fiber is similar to the spatial mode patterns produced by atmospheric turbulence. There is a bit of serendipity here in reference to my previous fiber-optic work. When I first looked at multimode fiber radiation patterns some 18 years ago, and how we might more reliably extract differential phase modulation signals between the modes, I likened the situation to the spatial modes induced on free- space beams by atmospheric turbulence. Thus the wheel may be turning full circle.
There might be several other good reasons for ETIs to use the pilot-tone technique, particularly if they are employing wide bandwidth transmissions. Firstly, the monochromaticity of the pilot-tone would ease the detectability problem for Emerging Technical Civilizations searching the Optical Cosmic Haystack. The pilot-tone, would in effect be the ETI beacon, and might even contain some low-bandwidth data telling us how to demodulate the wideband information signal. Secondly, any residual Doppler chirp (drift) either cause by the transmitter and/or receiver, would be eliminated at the second I.F. frequency (fs - fp). This might be important if frequency modulation or coherent final detection is employed, since the common-mode chirp would be canceled, thereby eliminating spectral broadening of the information signal. This would also overcome noise problems associated with any spectral broadening caused by the finite linewidths of the transmitting laser or the receiving local-oscillator laser - sort of killing several birds with one stone!
January 24, 1991 RADOBS.21 BBOARD No. 334
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