This is for a simulation. I have a 10x10 array that I'm using to time domain beamforming. The look-angles are polar (theta 0-90) and azimuthal angle (phi=0). My problem is this. The beamformer works fine when the source is on phi=0 axis; however the further I move from this axis, the worse the direction of approach prediction becomes. Is this expected? Or is beamforming expected to work when the source is far from the phi look-angle axis too?

Beamforming will work far from the phi look-angle axis but as you move away the phi look-angle axis, sidelobes areanincreasing problem. This is one of the areas of beamforming the depend significantly on the algorithm used for combining beams and on the windowing algorithm employed. So the short answer is yet it should work but as you would expect it gets complicated.

Okay, I'll look into this. Thanks for your response. 

I think that the distance of the source and the size of the array are important as beamforming, in the simplest implementation, assume planar waves coming from a far source. In case the coming waves are significatively curve you need to consider different delays ...

What you may be running into is boundary conditions which we address with spacial windows called shading functions.

The second problem in the near field the expanding spherical surfaces are close enough that you can see their curvature. The spacial sums are used to focus the beams while in the far field we can't see their curvature, we see planal waves, so we steer the beams.

subtle difference in the two processes,

fred h

Examination of real-world antenna arrays indicate they deteriorate quickly beyond 60-70 deg off-normal. Not only does the SLL increase, but the main lobe reduces in gain, widens and becomes lop-sided eg. Fig. 12, Microwave Journal April 2019, Vol. 62 pp.64-79. I'd suggest this effect doesn't help the resolution of your AoA.

I just thought of the third cause of your problem. The broadside beamwidth of a line anteanna is the ratio of antaenna length to wavelength (lamba) (L/lambda). as you steer off of broadside, lets say 45 degreea, half way to end fire, the projection of the anteanne length onto th steering driection is reduced by the cosine of the steering angle. The shorter antennae length, normal to the steering direction, has a wider beamwidth by the sqrt(2). You can see this in the succession of widths between the zeros of the sidelobes in the beam pattern.

fred h 

Thanks Fred. I will look into the array dimensions with respect to wavelength and shading functions.