The Direct Application Of FFT Algorithms On
The Synthesis Of Non-uniformly Spaced Arrays
Author(s)
A. J. R. Azevedo, X. F. Ren & A. M. E. S. Casimiro
Abstract
In previous work, we presented one efficient method applying the FFT (Fast
Fourier Transform) algorithms to the computation of non-uniformly spaced
antenna array factors, based on the Fourier relation between the array factor and
its source distribution. Using the grid in the spatial domain, the element positions
of one non-uniformly spaced array are set to another equi-spaced array with the
smaller spacing. Then, the conventional IFFT (Inverse FFT) algorithm is used to
compute its array factor. According to the reciprocal property of the Fourier
transform, the direct Fourier transform can be applied in the synthesis problem of
non-uniformly spaced arrays. If the array factor of one non-uniformly spaced
array is completely given in the respective region, the correspondent array
excitation can be obtained by directly applying the FFT after using the sampling
theorem. If it is not, the synthesized array will not be exactly as desired after
directly applying the FFT algorithm. In this case, the array element positions are
chosen to be those where the array element distribution is concentrated. To
achieve the more approximated array factor, we can use some methods to modify
the array element currents, for example, the matrix relation between the array
factor samples and the array element currents. Thus, in this paper we show the
possibility of the FFT algorithm application directly in the synthesis of
non-uniformly spaced arrays and demonstrate how to synthesize one
non-uniformly spaced array from the samples of array factors under the Fourier
relation. Of course, this method can also be used in the synthesis of uniformly
spaced arrays, which is viewed as the particular problem. Due to the application
of the FFT algorithm, the advantages such as fast computation, easy use and so
on are obvious. Furthermore, this method permits the exact array source
distribution of a non-uniformly spaced array to be obtained, given the
corresponding array factor.
Keywords
Related Book
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