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.
DTIC page with
link to 3.7 Mbyte PDF
cached PDF (3.7 Mbytes),
- 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.
- DATE OF ENTRY:
May 2011, updated with cached PDF July 2019.