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Comment:

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Deletions are marked like this.  Additions are marked like this. 
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<:3> $ D = \lambda/2 $ <:3> $ k = 2 \pi / N * L $   <:3> $ D = L/2 $ <:3> $ k = 2 \pi / N * L $  
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... or some variation of that. This assumes the spacing $ L >> \lambda $, a sparse array, so that the antennas do not couple (much).  ... or some variation of that ( I originally tried $ D = \lambda/2 $ , with little effect). This assumes the spacing $ L >> \lambda $, a sparse array, so that the antennas do not couple (much). 
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There will probably be stiff competition for spacing functions, perhaps some trolls will take out patents on them, and in the current US patent climate, with 
Array Phasing
When we randomly dither the position of the emitters in a 3 dimensional phased array, it smears out the grating lobes. I am looking for a better function.
A position dither function to try:
D = L/2 
k = 2 \pi / N * L 

\Delta x = D * ( \sin( k z ) + \cos( k y ) ) 

\Delta y = D * ( \sin( k x ) + \cos( k z ) ) 

\Delta z = D * ( \sin( k y ) + \cos( k x ) ) 
... or some variation of that ( I originally tried D = \lambda/2 , with little effect). This assumes the spacing L >> \lambda , a sparse array, so that the antennas do not couple (much). Try scaling D and k, and also modifying amplitudes across the array like a Hamming window, and see how that changes the sidelobes.
This happens on top of the array of perhaps hundreds of emitters on the thinsat itself, which beamforms to a few degrees of angle, reducing power splattered far from the target.
The signal is broadband, so there is not a well defined \lambda . We may end up making k a function of x, y, and z as well.
There will probably be stiff competition for spacing functions, perhaps some trolls will take out patents on them, and in the current US patent climate, with
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