Thinned Interleaved Linear Arrays
Randy L. Haupt
The Pennsylvania State University
Applied Research Laboratory
P. O. Box 30
State College, PA 16804-0030
haupt@ieee.org
Abstract.
Thinned interleaved linear arrays have aperiodic spacings that are integer
multiples of a set minimum element spacing. The arrays fit together such that the
resulting aperture appears to be uniform but actually consists of two separate
arrays. These arrays are optimized to have a narrow main beam without high
sidelobes.
Introduction.
When antennas occupy the same area, they are known as shared aperture aperture
antennas. Shared aperture arrays have elements from each array interspersed or
interleaved. Most of the time, the arrays are of different frequencies [1], [2]. This
paper presents an approach that interleaves two arrays of the same frequency.
Both arrays are highly thinned. They have narrow beamwidths and no grating
lobes in spite of some of the large element separations.
Interleaved Array Model.
A linear array with an even number of elements lying along the x-axis has an
array factor given by
AF ( u ) =
where
1
2N
2N
∑a e
n =1
jkd ( n −1)u
n
u = cos ϕ
ϕ = angle measured from x-axis
d = element spacing
k = 2π / λ
λ = wavelength
an = sum amplitude weight for element n
2N = number of elements in the array
0-7803-9068-7/05/$20.00 ©2005 IEEE
(1)
Figure 1. Diagram of two interleaved arrays.
The element weights of a thinned array are limited to "on" or an = 1 and "off" or
an = 0 . Figure 1 is a diagram of two interleaved linear arrays. An array taper
efficiency can be calculated from
η ar =
number of elements in the array turned on
total number of elements in the array
(2)
A genetic algorithm (GA) was used to optimize the placement of the elements to
minimize the sidelobe level of the interleaved arrays. The two arrays are
antisymmetric in that when one array has an element on/off the other array has the
same element off/on. The amplitude weights are represented as
a = [ a1 , a2 ,… , aN ,1 − aN ,… ,1 − a2 ,1 − a1 ]
(3)
a′ = 1 − a
(4)
and
Adding a and a′ yields a vector of all ones which implies η ap = 100% . Each array
has η ar = 50% . The symmetry associated with a and a′ insures that 50% of the
elements will be turned on for each thinned array.
Results
The first example is an array with 20 elements across the aperture. The elements
are equally spaced at d = 0.5λ with uniform weighting. After optimizing the
thinning of two 10 element arrays, the element assignment is given by
11111111101000000000
The "1" indicated that particular element is connected to the feed network for the
first array and the "0" indicates the element is connected to the feed network for
the second array. Figure 2 is the array factor associated with the two interleaved
arrays. The maximum sidelobe level is -14 dB below the peak of the main beam.
The second example is an array with 100 elements across the aperture. The
elements are equally spaced at d = 0.5λ with uniform weighting. After
optimizing the thinning of two 50 element arrays, the element assignment is given
by
01010011111011010010000110011011001111000101
10110011001001011100001100100110011110110100
100000110101
Figure 3 is the array factor associated with the two interleaved arrays. The
maximum sidelobe level is -13.26 dB below the peak of the main beam.
These optimized arrays have the narrow beamwidth of the full aperture and have
the same peak sidelobe level of a uniform array. Thus, it is a compromise between
the side-by-side uniform array and the every-other element interleaved array.
Conclusions.
Two interleaved arrays at the same frequency have narrow beamwidths without
high sidelobe levels. Interleaving can be extended to two dimensions at the
expense of a more complicated cost function. Mutual coupling is always
important, but given that the arrays are relatively large, equally spaced, and
uniformly weighted, isotropic point source approximations are adequate
approximations.
References
[1]
J. Hsiao, "Analysis of interleaved arrays of waveguide elements," IEEE
AP-S Trans., Vol. 19, No. 6 , Nov 1971, pp.729 – 735.
[2]
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.
Figure 2. Array factor associated with two 10 element interleaved arrays.
Figure 3. Array factor associated with two 50 element interleaved arrays.