Uniform circular array pattern synthesis using second‐order cone programming

Abstract

Here, the authors formulate second-order cone programs (SOCPs) for synthesising 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 signal-to-noise ratio loss relative to ideal by minimising 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 characterised by individual embedded complex patterns, modelled 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 UCAs of directional elements. Design examples assume an antipodal Vivaldi element design with an embedded element pattern obtained through simulation using appropriate unitcell boundary conditions. Rotation and translation of that simulated pattern provides embedded element patterns for all elements of the circular array.

Transmit and receive circular array pattern synthesis for radar applications

“…This is a convex problem, and in [6] it was shown how to formulate such a design as a second-order cone program (SOCP). SOCP is an efficient, structured form of convex optimization that minimizes a linear objective subject to linear and convex quadratic constraints.…”

“…Several SOCP solvers are freely available [12]- [14]. Here we develop a SOCP formulation in the spirit of [6] but with a different normalization.…”

“…The solutions to (6) and (7) are identical and have the form of the unconstrained solution with a particular value of α:…”

“…On receive, digital beamforming allows multiple simultaneous beams to be synthesized, and thus arbitrary regions can be covered with high-gain beams. We use the approach of [6] to formulate the receive beamforming problem as a second-order cone program (SOCP) that trades off taper-loss and sidelobe levels. On transmit circular arrays can form both high-gain and sector beams, similar to linear arrays.…”

2D DOA Estimation of UCA Correlative Interferometer Based on One Dimensional Sorting Lookup Table-Two Dimensional Linear Interpolation Algorithm

“…Because of the advantages of uniform circular array (UCA) such as fewer array elements, the ability of 2-D DOA estimation, non-oriented fuzzy [20] etc., it has been widely used [21][22][23][24]. So, the direction-finding algorithm of UCA interferometer becomes an important issue nowadays.…”