Uniform circular array pattern synthesis using second-order cone programming

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 unit-cell boundary conditions. Rotation and translation of that simulated pattern provides embedded element patterns for all elements of the circular array.