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# 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.

ArrayPhasing (last edited 2021-06-08 17:57:55 by KeithLofstrom)