Beamforming with distortionless co-polarisation for conformal arrays based on geometric algebra

Abstract

This study presents a general and systematic method for three-dimensional pattern analysis and beamforming with distortionless co-polarisation for arbitrary conformal arrays. The method is based on the mathematical framework of geometric algebra and is able to consider element patterns which are both directional and polarised to produce a compact representation of the array pattern. As well as being simpler and more direct than derivations in the current literature, the method provides a visually intuitive means of dealing with the many frame conversions necessary in conformal array analysis. Geometric algebra provides us with an analysis tool, which is simpler and more practical than the traditional Euler rotation and matrix representations. Here a space-polarisation filter based on a conventional delay-and-sum structure is proposed for the pattern beamforming for conformal arrays. Filters assigned to each antenna are used to acquire the overall array pattern and the authors use the co-polarisation component to realise beamforming. In addition to the new derivation, the authors compare with traditional methods and present simulations on a cylindrical conformal array.