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Description of the IFT method for low sidelobe pattern synthesis
Will P.M.N. Keizer
ArraySoft, Netherlands
INTRODUCTION
The iterative Fourier technique (IFT) uses the property that for an array with uniform spacing
of the elements, an inverse Fourier transform relationship exists between the array factor (AF)
and the element excitations. Because of this relationship, a direct Fourier transform performed
on AF will yield the element excitations. The underlying approach relies on the repeatedly use
of both types of Fourier transforms. At each iteration, the newly calculated AF is adapted to
the sidelobe requirements, which then is used to derive a new set of excitation coefficients.
Only those excitation coefficients constituting the array are used to calculate a new AF.
A key characteristic of this iterative synthesis method is that the algorithm itself is very
simple, highly robust, and easy to implement in software requiring only a few lines of code
when programmed in MATLAB. The computational speed is very high because the core
calculations are based on direct and inverse fast Fourier transforms (FFTs).
The presented results are related to linear arrays consisting of 100 elements located in
periodic grid with half wavelength inter-element spacing.
FORMULATION OF THE IFT METHOD
The far-field F(u) of a linear array with M elements arranged along a periodic grid at distance
d apart, can be written as the product of the embedded element pattern EF and the array factor
AF
=
(1)
=
1
=0
(2)
where A
m
is the complex excitation of the mth element, k is wavenumber (2/λ), λ is the
wavelength, u = sinθ and θ angular coordinate measured between far-field direction and the
array normal.
Equation (2) forms a finite Fourier series that relates the element excitation coefficients A
m
of
the array to its AF through a discrete inverse Fourier transform. AF is periodic in u-dimension
over the interval d/λ. Since AF is related to the to the element excitations through a discrete
inverse Fourier transform, a discrete direct Fourier transform applied on AF over the period
λ/d will yield the element excitations A
m
. These Fourier transform relationships are used in an
iterative way to synthesize low sidelobe pattern for arrays with a periodic element
arrangement.
The synthesis procedure starts with the calculation of AF using an initial set for the M element
excitation coefficients. The calculation of AF is carried out with a K-point inverse FFT with
K>M and using zero padding. This is followed by an adaptation of the sidelobe region of AF
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