Shape Estimation and Pattern Correction of Flexible Phased Arrays Using Local Curvature Measurements

This work presents a general method to estimate the unknown shapes of mechanically flexible phased arrays using strain gauge-based curvature measurements. Such information is crucial to resolve the positions and orientations of the radiators and perform effective beamforming. The procedure is feedback-free, insensitive to electromagnetic interference, and provides a low-frequency modality of shape information. While not limited to a specific size or frequency of operation, this method is demonstrated using a 20-cm, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1\times 8$</tex-math> </inline-formula> phased array operating at 6 GHz, achieving shape reconstruction errors of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\approx 0.052\lambda $</tex-math> </inline-formula> for singly, doubly, and triply bent arrays with curvature radii of less than 3.5 cm. Moreover, we illustrate how the shape information can be utilized to correct the beam pattern of a flexible array and enable beamforming and beam-steering even under severe deformations.