Amplitude Engineering for Beamformers with Self-Bending Directivity Based on Convex Optimization

Paper in proceeding, 2017

Arrays producing self-bending beams were proposed in the literature recently. The self-bending property of the beam is achieved by matching the phase profile that is applied to the array elements to a self-bending wave field. This process is termed phase engineering. It has been unclear how the optimal amplitude profile can be determined as the amplitude distribution of a self-bending wave field is difficult to determine. Previous works employed educated guesses. In this paper, we apply convex optimization to perform amplitude engineering. In other words, we complement phase engineering by determining the purely real amplitude weights that minimize the norm of the amplitude weights for a given maximum beam amplitude in the dark zone around which the beam bends. We show that phase engineering by itself does not narrow down the solution space sufficiently so that the choice of control points in the dark zone has a significant impact on how well the desired self-bending property forms.