This study deals with the affine transformation that is used to convert the triangular element grid of a planar phased array antenna into a square one. By means of this kind of transformation, it is possible to apply the iterative Fourier transform (IFT) method to synthesise low sidelobe tapers for array antennas featuring a triangular grid. Combination of the IFT method with an affine transformation allows the synthesis of low sidelobe tapers of which the peak sidelobe level does not vary with changing frequency and/or altering main beam position. The considered affine transformation was already briefly addressed in earlier publications of this author. In this study detailed information is given on its use in combination with the IFT method. Examples to demonstrate the effectiveness of the combination affine transformation and the IFT method for triangular grid array antennas are given. It will be shown that the peak sidelobe levels of the obtained tapers are invariant with frequency and scan angle when all far-field directions of the array factor are involved in the low sidelobe taper synthesis.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/iet-map.2019.0050

Affine transformation for synthesis of low sidelobe patterns in planar array antennas with a triangular element grid using the IFT method

This chapter contains sections titled: The Array Factor Uniform Arrays Fourier Analysis of Linear Arrays Fourier Analysis of Planar Arrays Array Bandwidth Directivity Amplitude Tapers z Transform of the Array Factor Circular Arrays Direction Finding Arrays Subarrays Errors Fractal Arrays 
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Array Factor Analysis

In this paper, a hexagonal DFT convenient for triangular grid phased array computations is described. Based on the general theory [4], an algorithm for fast computation has, been developed. Further- more, an algorithm for carrying out the permutations of the input sequence "in place" has also been developed. This is of particular importance in dealing with FFTs of large order as it significantly reduces the-auxilary storage required. The algorithm differs from that of O'neil et al, [3] in that the periodicity lattices in both spatial and spatial frequency domains are identical. A main advantage of this algorithm is that it is remarkably simple to code and requires -about the same number of operations as the vector radix algorithm [2].

/pdf/an-algorithm-for-the-pattern-computation-of-triangular-4kbhteh7ow.pdf

An algorithm for the pattern computation of triangular lattice phased arrays

The invention concerns a method for determining amplitudes and phases of the different channels in an electromagnetic signal transmission network whereof the sources are arranged in a triangular lattice. Said method is characterised in that consists in tiling said lattice with hexagons having six equal sides, the hexagonal tiles formed being distributed on said lattice such that two successive tiles along a direction in the lattice rectangular height equivalent to said triangular lattice are offset by an elementary step along the width direction, and in performing a Fourier transform on the resulting tiling; in selecting on the resulting new lattice the directions corresponding to the transmission directions; in performing an inverse Fourier transform of said directions and in deducing from said inverse Fourier transform the amplitude and phase coefficients to be applied to the transmission network different channels.

Method for determining amplitudes and phases of the different channels in an electromagnetic signal transmission network, such as a telecommunication satellite antenna

Uniform Geometrical Theory of Diffraction (UTD)-based efficient descriptions of the field radiated by electrically large linear and rectangular planar phased arrays have been developed under the hypothesis of uniform current distributions. More recently they have been extended to relatively arbitrary current taperings by resorting to a Discrete Fourier Transform (DFT) representation of the array current excitation. In this paper, the DFT-UTD based technique is extended to deal with the efficient evaluation of the nearand far-field radiated by hexagonal arrays made of free-standing dipoles in a triangular lattice. To face with arrays on hexagonal lattices, the Hexagonal DFT (HDFT) is exploited.

/pdf/utd-fields-radiated-by-electrically-large-hexagonal-arrays-3d5hno96mz.pdf

UTD Fields Radiated by Electrically Large Hexagonal Arrays with Realistic Current Distributions

Modeling triangularly packed array antennas using a hexagonal FFT

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Modeling triangularly packed array antennas using a hexagonal FFT