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Subarrays in a Large Finite Array For Hybrid Beamforming

Array parameters

Choose number of elements, frequency of operation and the azimuth and elevation angle to steer the main beam of the array.

N = 11;  
fc = 28e9;
az = 30;
el = 20;

Find phase shifts for azimuth control

Design a linear array at the desired frequency. The default element is a dipole. Find the phase shifts to apply on each element of the linear array for controlling the main beam in the azimuthal direction. Note, that the distance of separation is chosen to be half-wavelength to ensure no grating lobes.

l = design(linearArray,fc);
elem = l.Element;
elem.Tilt = 90;
l.NumElements = N;
figure
show(l)

ps_az = phaseShift(l,fc,[az;0]);

Find phase shifts for elevation control

Compute the phase shifts for the steering in elevation. To do this, we modify the geometry of our initial linear array for the echelon configuration along z.

elem.Tilt = 90;
elem.TiltAxis = [0 1 0];
l.Tilt = 90;
l.TiltAxis = [0 1 0];
l.ElementSpacing = 1.05*(elem.Length) ;
figure
show(l)

ps_el = phaseShift(l,fc,[0;el]);

Create subarrays

Create a N x N rectangular array comprising of N, 1 X N linear arrays stacked along the positive and negative z-directions.

l.Tilt = 0;
elem.Tilt = 0;
l.PhaseShift = ps_az;
c = conformalArray;
zposn = fliplr((-N+1)/2:1:(N-1)/2);
for i = 1:N
   c.Element{i} = l;
   c.ElementPosition(i,:) = [0,0,zposn(i)*l.ElementSpacing];
end
figure
show(c)

Assign phaseshifts and plot pattern

Assign the sub-array level phase shifts and compute pattern

c.PhaseShift = ps_el;
figure
pattern(c,fc);

figure
patternElevation(c,fc,az);

Note the actual peak location varies from the theoretical computed due to mutual coupling

Array with Large Reflector Backing

Using the installed antenna capability, allows for an initial approximate analysis of the antenna array by including a large structure in its vicinity. For this example provide an STL file of a large metallic reflector positioned a quarter-wavelength away from the array. The analysis treats the array using a full-wave Method of Moments (MoM) approach and the large reflector is handled using the Physical Optics (PO) approximation.

lambda = physconst('lightspeed')/fc;
ref_offset = lambda/4;
p = platform;
p.FileName = 'GroundPlane.stl';
p.Units = 'm';
p.Tilt = 90;
f = installedAntenna;
f.Platform = p;
f.Element = c.Element;
f.ElementPosition = c.ElementPosition;
f.ElementPosition(:,2) = ref_offset;
f.FeedPhase = ps_el;
figure
show(f)

Approximate Array Pattern

figure
pattern(f,fc)