Density Tapering of Linear Arrays Radiating Pencil Beams: A New Extremely Fast Gaussian Approach

Abstract

In this communication, a very simple and extremely fast algorithm is proposed for the pencil beam synthesis of linear sparse arrays having uniform distribution of the excitations. The key idea is that of selecting, as a desired pattern, a Gaussian function having small standard deviation, so as to obtain a narrow beam. This immediately provides the excitation density of the corresponding continuous array of infinite length. Starting from this result and considering a linear array of length $L$ with $N$ elements having equal excitations, an extremely fast and accurate algorithm based on a density tapering approach is proposed that yields suitable positions of the elements, in such a way as to provide an array factor that well approximates the desired pattern. Numerical examples are presented to show the effectiveness of the developed procedure, also when compared with state-of-the-art algorithms. The proposed approach does not consider the mutual coupling between the array elements, but it is numerically shown that this effect produces quite acceptable degradation on the synthesized patterns. Finally, it is shown that also problems involving thousands of elements can be solved in a very accurate way in few milliseconds.