A quaternion-valued reweighted minimisation approach to sparse vector sensor array design

In this work, the design of sparse vector sensor arrays is studied based on quaternionic formulations, which is a further extension of the recently proposed compressive sensing (CS) based design methods. As with the traditional case, sparsity of the solution can be improved by converting the problem into a series of iteratively solved reweighted minimisations, where locations with a small absolute coefficient value are more heavily penalised compared to those with a larger absolute value. Moreover, this reweighted scheme is further modified to incorporate a size constraint into the design so that practical antennas with a non-zero size can fit into the designed locations.