Adaptive antenna array under directional and spatial derivative constraints

The author examines the beampattern dependency on the choice of phase centre location, when a narrow band beamformer is subjected to directional and spatial derivative constraints. He then presents a technique based on a power response approach, for deriving a new set of constraints for controlling the beampattern spatial derivates. The new set of constraints ensure that the array beampattern is independent of the choice of the phase centre co-ordinate origin. It is shown that for the first-order case, the constraint is linear, but for the second-order case, the constraint is quadratic. The author then presents a technique for approximating the effect of the quadratic constraint by two linear constraints. Finally, he presents a technique for optimising the beampattern with respect to the choice of the phase centre location, when the quadratic constraint is being approximated with linear constraints.