OF
Randy Haupt
Department
Electrical Engineering
USAF Academy, CO 80132
I. Introduction.
Large phased array antennas are very expensive to build. A way to cut the costs is to make more efficient feed networks. One efficient feed network for a low sidelobe array consists of amplitude tapering at the subarray level while keeping the individual elements in the subarray uniformly weighted. In this way, subarrays could be mass produced and tested. Unfortunately, grating lobes ruin the low sidelobes in the far field pattern [l]. An improvement to this approach is to find an amplitude taper that is constant for each subamy. Thus, all the elements in a subarray are tapered, but the taper is the same (or a mirr for each subarray [2]. This approach yielded excellent results for a lin
This paper improves the previous approach by using a genetic algorithm to design the amplitude tapers for both the elements in the s outputs for linear and planar arrays. Because genetic large number of parameters, both linear and planar s optimized.
11. Approach.
Amplitude tapers for linear and planar subarrayed antennas will be optimized with a genetic algorithm. The array factor for a symmetric subarrayed linear array lying along the x-axis is given by where k 2n/k h = wavelength
U = cos$ a, = element weight in a subarray b,,, = subarray weight
& = relative spacing of elements within a subarray x, = center-to-center spacing between subarrays
N = number of elements in a subarray
= number of subarrays
The genetic algorithm has M+N parameters to optimize. Element and subarray
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amplitude weights are quantized.
The array factor for a subarrayed planar array that lies in the x-y plane and has symmetry about the x and y axis is given by where
2G = number of subarrays in x-direction
2H = number of subarrays in y-direction b, = subarray weight yys kd&nesin@ y~,, = k&sinecos@
E = number of elements in subarray in x-direction
F = number of elements in subarray in y-direction a,, = element weight vye kdy,sinOsin$
= kd,,sinecos$
dys. dye, dye = the spacings between subarrays (s) and elements (e) in the x and y directions
In this case, the genetic algorithm has GxH+ExF parameters to optimize.
III. Results.
The genetic algorithm optimizes the element and subarray amplitude weights assuming a three bit quantization. It is quite simple to put constraints on the weights and/or far field pattern. The goal in the example presented here is to produce the lowest possible sidelobe levels with no constraints.
Consider a linear array of 10 subarrays with 10 isotropic elements per subarray.
The array is assumed to be symmetric about its physical center. First, the subarray amplitude weights are assumed to be uniformly weighted and the elements in each subarray have the same amplitude taper. A nice bell-shaped amplitude taper is not possible in this case, so good results are
not expected. Figure 1 shows the
optimized far field pattern. Its maximum relative sidelobe level is -14.7 dB. As expected, the sidelobe level shows little improvement over a uniform array. The next step is to optimize the subarray amplitude taper while keeping the elements in each subarray uniformly weighted. Figure 2 shows the resulting far field pattern with a maximum relative sidelobe level of -27 dB. This improvement is significant in that low sidelobes are obtained while keeping the array feed very simple. Each subarray is uniformly weighted, making it much easier to mass produce, test, and maintain. Next amplitude weights are optimized for the 10 elements and
10 subarrays. Figure 3 shows this optimized pattern.
In this case,
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the maximum relative sidelobe level is -29.5 dB. This feed network is more complicated than just amplitude tapering at the subarray outputs, but is much simpler than applying a standard amplitude taper where each element weight is different.
Excellent results can also be obtained for planar arrays. Planar arrays have many more parameters than linear arrays, and the far field pattern must be checked in both the 8 and
+ coordinates. Genetic algorithms can handle the increased computational load, but they take much longer.
IV. Conclusions.
Sidelobe levels can be significantly reduced through a constant amplitude element taper in the subarrays and an amplitude taper at the subarray outputs. These results improve previous attempts at subamay amplitude tapering because constraints can be incorporated, much larger arrays can bc optimized, and quantization of the amplitude weights can be included.
References
[ 11 R. J. Mailloux, "Array grating lobes due to periodic phase, amplitude, and time delay quantization," Vol 32, No. 12, Dec 1984, pp. 1364-1368.
[2] R.L. Haupt, "Reducing grating lobes due to subarray amplitude tapering,"
IEEE AP-S Trans., Vol 33, No. 8, Aug 1985, pp. 846-850.
0
Figure 1.
U
Array factor for a linear array with
U subarrays and an optimized element amplitude taper that is the same for each subarray.
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-1 0
-1 5
0.1 0.2 0.3 0.4 0.5
U
0.6 0.7 0.8 0.9
Figure 2. Array factor for a linear array with uniform element weights and
subarray
1
E -20
E
5
-25
.z m m
-30
-35
-40
0
-5
-10
-15
-45
-50
0 0.1 0.2 0.3 0.4 0.5
U
0.6 0.7 0.8 0.9
Figure 3. Array factor for a linear array with optimized constant element amplitude tapers in the subarrays and optimized subarray amplitude taper.
1
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