Uniform circular array pattern synthesis
using second-order cone programming
W. Mark Dorsey,
Jeffrey O. Coleman, and
William R. Pickles
Here we formulate second-order cone programs (SOCPs)
for synthesizing complex weights for far-field
directional (single-point mainbeam) patterns for
narrowband arrays. These formulations, while
constructed here with the uniform circular array (UCA)
in mind, are actually quite general in that they
control the arbitrary-pol sidelobe level (SLL) and
co-pol SNR loss relative to ideal by minimizing either
while upper-bounding the other. The SLL can be
addressed in either an L-infinity sense or an L1
sense, and elements are assumed characterized by
individual embedded complex patterns, modeled or
measured, and so need not be identical. Conformal
arrays are the obvious application, but we leave that
for others and here instead apply the SOCPs to uniform
circular arrays of directional elements. Design
examples assume an antipodal Vivaldi element design
with an embedded element pattern obtained through
simulation using appropriate unit-cell boundary
conditions. Rotation and translation of that simulated
pattern provides embedded element patterns for all
elements of the circular array.
- ONLINE VERSIONS:
In the preprint the plots use color, making it easier reading than the official IEEE/IET version.
- MINOR CLARIFICATIONS:
This appears in the first paragraph of Section 2.3 [preprint: II-C]:
Rather than "In this paper..." it should have been "In 2.3.1 [preprint: 1)] below..." Further, to the end of the above, as modified,
it would have been appropriate to add "In 2.3.2 [preprint: 2)], peak SLL is replaced with an approximation of the L1 norm
of the array's sidelobe response."
In this paper, we show two SOCP formulations for synthesizing
narrowband directional patterns from a phased array. The first method
maximizes SNR while upper bounding SLL, and the second method lower
bounds SNR while minimizing peak SLL.
In Section III [preprint: 3]:
- "Synthesized patterns are shown in Fig. 3(a)..." should refer to Fig. 3, and "results obtained using SOCP (4)" should refer to SOCP (4) with the point bounds removed.
In the Fig 3 caption, "with SLL minimization formulation" should be removed.
"The pattern in Fig. 4 was synthesized... using SOCP (4)" should refer to SOCP (4) with \delta replaced with \delta_s to apply different SLL bounds in different sidelobe regions.
"The sidelobes for \phi > 0 ... \phi < 0 " should refer to 8 deg rather than 0. The same is true for the Fig 4 caption.
In the sentence before "Section IV Conclusion," the remark "(shown in Fig. 2)" should really be "(magnitudes shown in Fig. 2)."
In the Conclusion, "straightward" of course should be "straightforward."
- Published in IET
Microwaves, Antennas, and Propagation, June 2015, vol. 9, no. 8, pp. 723-727.
- DATE OF ENTRY:
July 2015. Clarifications added December 2020.