The Direct Application Of FFT Algorithms On The Synthesis Of Non-uniformly Spaced Arrays
Free (open access)
A. J. R. Azevedo, X. F. Ren & A. M. E. S. Casimiro
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.