# Low Sidelobes from Identically Thinned Subarrays Introduction Randy L. Haupt

```Low Sidelobes from Identically Thinned Subarrays
Randy L. Haupt
The Pennsylvania State University, Applied Research Laboratory,
State College, PA 16801
Introduction
Large phased array antennas have many desirable characteristics but are
extremely expensive to build. The large array can be broken into smaller
subarrays and the amplitude or phase weighting can be done at the subarrays to
save the expense of placing them at every element. Unfortunately, this approach
results in unacceptable grating lobes [1].
A tradeoff exists between sidelobe performance and simplicity of design. One
approach amplitude tapers the subarray outputs and the element outputs in such a
way that the element amplitude tapers are identical for every subarray of a linear
array [2]. In this way, the resulting amplitude taper is a better approximation to
the desired taper than subarray tapering alone. All the subarrays are identical, so
the feed design remains very simple A genetic algorithm (GA) has been used to
design optimum amplitude tapers for both the elements in the subarrays and the
subarray outputs for linear and planar arrays [3].
This paper extends the previous work by amplitude tapering identically thinned
subarrays to minimize the sidelobe level. A mixed integer genetic algorithm is
used to find the optimum configuration.
Cost Function Formulation
The cost function returns the maximum sidelobe level of the array, and the GA
minimizes the cost. Optimization variables are the subarray amplitude weights at
the subarray outputs and the amplitude weights of the elements in the subarrays.
All elements within a subarray have the same amplitude weights, other than half
the subarrays are mirror images of the other half. In the previous papers, the
amplitude weights assumed array values between zero and one. In this paper the
amplitude weights are either zero or one.
Figure 1 is a diagram of a 256 element square array divided into 16, 4x4 element
subarrays. Dark circles indicate that the element has an amplitude of one, and
white circles indicate that the element is terminated in a matched load and
receives an amplitude of zero. Note that the subarrays are either identical or are
mirror images.
1-4244-0123-2/06/\$20.00 &copy;2006 IEEE
4217
Figure 1. Planar array with identically thinned subarrays.
The cost is the maximum relative sidelobe level is calculated from the array factor
given by
Ne
cost = ∑ an cos [ kxn sin θ cos ϕ ] cos [ kyn sin θ sin ϕ ]
(1)
n =1
where
an = product of element weight and subarray weight for element n
k = 2π / wavelength
( xn , yn ) = location of element n
(θ , ϕ ) = look direction
The example here has 6 &times; 6 = 36 subarrays with each subarray having 5 &times; 5 = 25
elements. The element spacing in both directions of the square lattice is one half
wavelength.
Results
A GA is used to find the optimum weights. If the subarray weights are optimized
with all the elements uniformly weighted, then the maximum sidelobe level is
found to be -18.4 dB. The directivity is 28.3 dB with a taper efficiency of 75%.
These results are relative to a uniform aperture with a directivity of 29.5 dB and a
maximum sidelobe level of -13.2 dB. If the subarray weights are uniform and the
elements of the subarray thinned, then the directivity is 27.3 dB, the maximum
sidelobe level is -15.3 dB, and the taper efficiency 60%.
When the element thinning and subarray weights are simultaneously optimized,
then the optimized element weights are shown in Figure 2 and the optimized
subarray weights are shown in Figure 3. When multiplied together, the effective
element weights for one quadrant of the array are shown in Figure 4. This taper
4218
has an efficiency of 54.5%. The resulting array factor appears in Figure 5. Its
directivity is 26.9 dB and the maximum sidelobe level is -22.9 dB. Sidelobes that
are 4.5 dB lower than the optimized subarray weighting come at a cost in taper
efficiency and loss in directivity.
Figure 2. Optimized element weights in one subarray.
Figure 3. Optimized subarray weights for one quadrant of the array.
4219
Figure 4. Optimized effective element weights in one quadrant of the array.
Figure 5. Optimized array factor.
Conclusions
Using identical subarrays decreases the complexity and cost of construction and
testing. Thinning has the advantage of a simple, uniform feed network. Obtaining
slightly lower sidelobes comes at a cost in aperture efficiency.
References:
[1]
R.J. Mailloux, Phased Array Antenna Handbook, Artech House, Boston,
MA, 2005.
R. Haupt, &quot;Reducing grating lobes due to subarray amplitude tapering,&quot;
[2]
IEEE AP-S Trans., Vol 33, No. 8, Aug 1985, pp. 846-850.
R. Haupt, &quot;Optimization of subarray amplitude tapers,&quot; IEEE AP-S
[3]
Symposium, Jun 1995, pp. 1830-1833.
4220
```