J. O. Coleman

Planar Arrays on Lattices and Their FFT Steering, a Primer
J. O. Coleman
This is a primer for practicing design engineers on two topics. The first is the theory of the simplest planar receive arrays, those positioning identical antenna elements on a point lattice and using terminated guard elements at the array periphery. The second is multi-beam phase-shift steering of such arrays using generalized Cooley-Tukey FFT structures. Array theory here largely avoids electromagnetics and instead uses classic LTI-system arguments from signals and systems. The FFT realization of the general multidimensional DFT for beam steering is developed using nested sublattice chains. The needed lattice basics are covered in detail, and the usual coset decompositions are avoided in favor of a simpler geometric approach based on tiling the element-position and beamspace (direction cosine) planes. Example array architectures use the hexagonal lattice (equilateral triangular grid) with the classic optimal zero-aliasing spacing.
Shortly after (3) the statement that "Our basis-choice strategy will be to use B and B^+ respectively as bases for array-plane row vectors and column vectors" has row and column reversed. Actually B is used as a basis for column vectors, and pseudoinverse B^+ is used as a basis for row vectors.
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Published April 29, 2011 as NRL Formal Report 10207 (or more formally, NRL/FR/5320--11-10,207). Approved for public release; distribution is unlimited.
May 2011, updated with cached PDF July 2019.