Impact Of The Locations Of The Control Points On Optimal Solutions For Self-Bending Beamforming

Paper in proceeding, 2018

Self-bending beamformers exhibit a sensitivity that bends over space in the nearfield of the array. They were derived from caustic wave fields and have been presented in the literature recently. It is fairly straightforward to obtain an analytic solution for the phase profile that has to be imposed onto the array elements. This approach is termed phase engineering. Deriving the corresponding gain profile is less straightforward. Solutions that have been proposed in the literature so far are educated guesses as well as numerically optimal solutions. The latter are the topic of the presented work. We use a convex approach. We show that the locations of both the (single) target control point in the bright zone as well as the (many) control points in the dark zone have a significant impact on the resulting beam. Particularly, the control point locations in the dark zone have to be chosen carefully so that the desired dark zone actually evolves. Choosing the target control point close to the caustic creates the largest beam gradient along the caustic. A remarkable observation is that prescribing a phase profile onto the elements of the array can also have a detrimental effect, and solving for the complex beamformer weights can yield a better result. Based on the observations we conclude that minimizing the norm of the beamformer weights does not seem to be the most favorable approach for the present problem.