Interleaving Thinned Sum and Difference Linear Arrays
Randy L. Haupt
The Pennsylvania State University, Applied Research Laboratory,
State College, PA 16801, haupt@ieee.org
Introduction
Interleaving elements of multiple arrays is one way to efficiently use aperture
area. In [1] elements in adjacent subarrays are interleaved in order to disrupt the
grating lobes that result when only one phase shifter per subarray is used to steer
the beam. Randomly assigning elements to subarrays reduces the peak sidelobe
level. An array of interleaved waveguide radiators operating at different
frequencies is presented in [2]. An aperture with three interleaved arrays at
different frequencies was successfully built [3].
A thinned array turns elements on and off in a uniform array in such a way as to
produce a spatial taper that results in low sidelobes [4]. Off elements are
connected to a matched load. This paper demonstrates a low sidelobe thinned
difference array. Next, the thinned sum and difference arrays are optimally
interleaved in the same aperture area.
Thinned Sum and Difference Arrays
The sum and difference array factors for symmetric linear arrays with an even
number of elements lying along the x-axis are given by
1 N
∑ an cos ⎡⎣kd ( n − .5) u ⎤⎦
N n =1
j N
D (ϕ ) = ∑ bn sin ⎡⎣ kd ( n − .5 ) u ⎤⎦
N n =1
S (ϕ ) =
(1)
(2)
where
u = cos ϕ
ϕ = angle measured from x-axis
d = element spacing
k = 2π / λ
λ = wavelength
an = sum amplitude weight for element n
2 N = number of elements in the array
The element weights of a thinned array are either "on" ( an , bn = 1 ) or "off"
( an , bn = 0 ). The array taper efficiency is [5]
1-4244-0123-2/06/$20.00 ©2006 IEEE
4773
η ar =
number of elements in the array turned on
total number of elements in the array
(3)
Examples of array factors for a thinned 102 element sum and difference arrays
with d = 0.5λ and bN = 1 are shown in Figure 1 and Figure 2. The thinning
approach is similar to that in [6].
The thinned sum array has the highest density of elements turned on in the center,
while the thinned difference array has few elements turned on in the center. Both
arrays have less "on" elements near the edges. These observations lead to the
possibility of using the elements turned "off" by the thinned sum array for the
thinned difference array. Using the "off" elements from the array in Figure 1 as
elements in a difference array does not result in an acceptable difference pattern.
Assume that the difference pattern consists of the elements turned off in the sum
pattern or bn = 1 − an . Using a GA to find the thinning arrangement that results in
the minimum maximum sidelobe level for both array factors results in an array
having the patterns shown in Figure 3 and Figure 4. The patterns are normalized
to their respective peaks. The peak sidelobe level of the sum pattern is 12.68 dB
below its main beam, and the peak sidelobe level of the difference pattern is 12.5
dB below its main beam. The sum array has η ar = 0.48 and the difference array
has η ar = 0.52 . The entire aperture is 100% efficient, so optimum use is made of
the available space.
Conclusions
It is possible to interleave a thinned sum array with a thinned difference array to
make efficient use of an existing aperture. The GA moderates the sidelobe levels
of both arrays while devoting approximately half the elements to each array.
References:
[1]
[2]
[3]
[4]
[5]
[6]
J. Stangel and J. Punturieri, "Random subarray techniques in electronic
scan antenna design," IEEE AP-S Symp., Vol. 10 , Dec 1972, pp. 17 – 20.
J. Hsiao, "Analysis of interleaved arrays of waveguide elements," IEEE
AP-S Trans., Vol. 19, No. 6 , Nov 1971, pp.729 – 735.
J. Boyns and J. Provencher, "Experimental results of a multifrequency
array antenna," IEEE AP-S Trans., Vol. 20, No. 1, Nov 1972, pp.106-107.
R. Willey, "Space tapering of linear and planar arrays," IEEE AP-S Trans.,
vol. AP-10, 1962, pp. 369-377.
R.J. Mailloux, Phased Array Antenna Handbook, Boston, MA: Artech
House, 1994.
R.L. Haupt, "Thinned arrays using genetic algorithms," IEEE AP-S
Trans., vol. AP-42, 1994, pp. 993-999.
4774
Figure 1. Thinned sum array.
Figure 2. Thinned difference array.
4775
Figure 3. Sum array factor due to interleaved thinned sum and difference
arrays.
Figure 4. Difference array factor due to interleaved thinned sum and
difference arrays.
4776