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.
5x5x5 skewed, dithered array
Annotated version with explanation coming soon.
16x16x16 skewed, dithered array
Annotated version with explanation coming soon.