MATLAB: Directivity did not match our expectation

antenna array arrangementdirective gaindirectivityPhased Array System Toolbox

As we know, 1X16 linear antenna array arrangement should have larger peak directive gain than 4X4 square array, because the former's beamwidth is narrower which can consentrate beamforming resolution in a given direction.
However, in the phased array system toolbox, this truth cannot be proven… Here is our code,
if true
  % code
figure
ha = phased.ULA('NumElements',16);
phased.ULA('Element',ha,'NumElements',16,'ElementSpacing',0.5 * lambda);
plotResponse(sArray,'RespCut','Az','Format','Polar','Unit','dbi');
hold on;
ha = phased.URA('Size',[4 4]);
phased.URA('Element',ha,'Size',[4 4],'ElementSpacing',0.5 * lambda);
plotResponse(sArray,'RespCut','Az','Format','Polar','Unit','dbi');
hold off;
end
if we find the peak values for 1X16 and 4X4 in the figure, 4X4 always has the higher gain value…
Thanks, Ralph

Best Answer

Hi Ralph,
In this example you are using an isotropic antenna element. So even though in this cut the beam is more focused, it has strong lobe all around the array axis, so in some sense the energy is not well focused.
If we change the element type to a more realistic pattern, such as cosine antenna pattern, then you can see the directivity of the ULA starts to be better than the URA
figure
ha = phased.ULA('NumElements',16,'Element',phased.CosineAntennaElement);
plotResponse(ha,3e8,3e8,'RespCut','Az','Format','Polar','Unit','dbi');
hold on;
ha = phased.URA('Size',[4 4],'Element',phased.CosineAntennaElement);
plotResponse(ha,3e8,3e8,'RespCut','Az','Format','Polar','Unit','dbi');
If you use a Hertzian dipole, the ULA is also better
figure
ha = phased.ULA('NumElements',16,'Element',phased.ShortDipoleAntennaElement);
plotResponse(ha,3e8,3e8,'RespCut','Az','Format','Polar','Unit','dbi');
hold on;
ha = phased.URA('Size',[4 4],'Element',phased.ShortDipoleAntennaElement);
plotResponse(ha,3e8,3e8,'RespCut','Az','Format','Polar','Unit','dbi');
In short, I'm not saying that you are wrong since I don't really have a theoretical result to back me up. But I'm also not convinced that the toolbox is giving the wrong answer. If you do have a number that I can compare to, please let me know and I'd love to take a look.
Thanks
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