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 smear function to try:
D = \lambda/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. This assumes the spacing L >> \lambda , a sparse array, so that the antennas do not couple (much). We can scale D and k, and also modify amplitudes across the array like a Hamming window, and see how that changes the sidelobes.