Fast Beamforming for Dynamic, Randomly Configured Antenna Arrays and Metamaterials

We propose methods to determine beam-forming excitation phase profiles for arbitrarily oriented arrays of antennas and scatterers, made of arbitrarily polarized elements. Our generalized analytical phasing (GAP) method provides rapid near-optimal phasing, enabling real-time beam steering with high-element-count, and dynamically configured arrays. In addition, we propose a reduced-order numerical phasing (RONP) method that converts an N-dimensional unknown parameter space (the N unknown phases) to a 2-D space (the optimal beam polarization). Though not as fast as the GAP, this method introduces no reduction in phasing accuracy. Both methods are suitable for a wide range of antenna array and metasurface designs.