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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.

BACKGROUND:The number of topside antennas on U.S. Naval ships has almost doubled from the 1980s to the 1990s. The Navy would like to reduce the number of antennas on ships for various reasons including mutual signal interference, ship's signature, manning, spares, and life cycle costs. So, the Office of Naval Research (ONR) has been funding R&D efforts to integrate the many single-function antennas into a few common sets of broadband array antennas. These antennas must provide polarization diversity over large scan angle and broad instantaneous bandwidth.