Design of fixed beamformers based on vector-sensor arrays

Vector-sensor arrays such as those composed of crossed dipole pairs are used as they can account for a signal's polarisation in addition to the usual direction of arrival information, hence allowing expanded capacity of the system. The problem of designing fixed beamformers based on such an array, with a quaternionic signal model, is considered in this paper. Firstly, we consider the problem of designing the weight coefficients for a fixed set of vector-sensor locations. This can be achieved by minimising the sidelobe levels while keeping a unitary response for the main lobe. The second problem is then how to find a sparse set of sensor locations which can be efficiently used to implement a fixed beamformer. We propose solving this problem by converting the traditional l1 norm minimisation associated with compressive sensing into a modified l1 norm minimisation which simultaneously minimises all four parts of the quaternionic weight coefficients. Further improvements can be made in terms of sparsity by converting the problem into a series of iteratively solved reweighted minimisations, as well as being able to enforce a minimum spacing between active sensor locations. Design examples are provided to verify the effectiveness of the proposed design methods.