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Space-Diversity Reception

Radobs 21

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
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.
                    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
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
BBOARD No. 334
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
* Dr. Stuart A. Kingsley                       Copyright (c), 1991        *
* AMIEE, SMIEEE                                                           *
* Consultant                            "Where No Photon Has Gone Before" *
*                                                   __________            *
* FIBERDYNE OPTOELECTRONICS                        /          \           *
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* CompuServe: 72376,3545                                                  *
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