[Server-sky] Thinking about sparse phased arrays

Keith Lofstrom keithl at gate.kl-ic.com
Tue Apr 17 17:57:39 UTC 2012

Testing the list so I'll share an idea I'm working on.

Server sky arrays will be "sparse", with elements spaced much
wider than half a wavelength.   This normally results in
"grating lobes", spurious high gain splatter in the wrong
direction, interfering with other communications. 

But this is for arrays with uniform spacing.  Thinsats do not
need to be uniformly spaced;  as a matter of fact, we will
probably be changing their relative location so they do not
shade each other as the four hour orbit evolves.  We can do
about 30 meters of position shift and return over the course
of one orbit;  with the right 3-D ballet, we probably need
less than one meter, and should be able to "fill" the
illumination area by 25% or so, and fill the "radio
illumination" area by a similar amount. 

An interesting thing happens if the spacing between thinsats
is not uniform - the grating lobes wash out.  The off-direction
broadcast power is still there, but it is scattered over a 
very large area, not focused on a hectare or so, like the 
main beam.  If we are using spread spectrum and correlation
to send and receive our messages, we can correlate out the
unwanted energy (which adds up as root-mean-square) while 
correlating on the main lobe.  If the noise energy is uniformly
splattered over a billion hectares, while the signal energy
is focused on a hectare, we can waste 99.9% of our transmit
energy on splatter and still get a 60db signal to splatter
ratio where we want it.

So the holy grail is finding a 3D thinsat spacing function
that uniformly distributes the splatter, while minimizing or 
eliminating shading, for all transmit angles at all positions
along the orbit.  Surprisingly random spacing works OK, but
does not distribute the splatter as uniformly as I would like,
reducing SNR.  Keep in mind that for one-to-one communication:

  1) we only care about delivering signal power to a
     square-meter-or-so ground antenna, all the rest
     is waste.
  2) we have kilowatts of transmit power available, we
     can waste almost all of it.
  3) we can control relative array positioning to within
     a fraction of a micron.  If we know where we want a
     thinsat in the array, we can position it exactly there.

But then, almost all the transmit power of a big-iron
broadcast comsat is waste, too.  What percentage of the
landscape is covered with satellite dishes?  The rest
of the millions of hectares of the ground spot is just
soaking up the nanowatts per square meter.

Perfect grids are easy to compute phasing for, but trig
computations are very cheap and getting cheaper.  We've
got good computers, the array moves at millimeters per
microsecond, and I/Q channel baseband DSP can make new
samples much faster than that.  We will spend a lot more
fixed-array computation encoding messages and phasing 
them for the destination.


Keith Lofstrom          keithl at keithl.com         Voice (503)-520-1993
KLIC --- Keith Lofstrom Integrated Circuits --- "Your Ideas in Silicon"
Design Contracting in Bipolar and CMOS - Analog, Digital, and Scan ICs

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