Efficient Fully-Digital Beamformer for Very-Large Non-Uniform Arrays using Hexagonal Transformations

Digital beamforming is a critical technology for next-generation satellite communications. Conventional solutions in current missions primarily rely on hybrid analog-digital architectures due to the significant power consumption challenges of a fully-digital implementation. For future systems, Fast Fourier Transform (FFT)-based beamforming has been proposed as an efficient digital alternative, especially for managing many beams. However, the use of a FFT beamforming alone is not compatible with non-uniform antennas and beams. This inflexibility poses a significant challenge for modern satellite systems, which require beam reconfigurability to accommodate changing traffic demands. The Non-Uniform FFT (NUFFT) offers the needed flexibility for non-uniform grids, but it involves higher computational costs due to extra processing steps. This paper presents a new method to lower this cost by mapping the spatial samples onto a hexagonal grid instead of the traditional Cartesian grid. Taking advantage of the efficient 2D sampling efficiency of the hexagonal lattice, our approach uses circularly symmetric windows more effectively. This efficiency allows for more accurate signal reconstruction with fewer operations. The hexagonal transformation offers a more power-efficient and adaptable way to achieve real-time, dynamic beam steering required in advanced satellite systems.