Quantization Effects of Twiddle Factors in FFT for Beamforming Using Planar Arrays

This paper examines the impact of quantization on the twiddle factors in the Fast Fourier Transform (FFT) used for beamforming applications. A comprehensive scenario utilizing a Medium Earth Orbit (MEO) satellite system is developed to analyze these effects. The setup comprises a lOx 10 phased array antenna, where each antenna element consists of a sub array of 5 x 5 elements spaced at half-wavelength intervals, all distributed in a circular aperture. We investigate the influence of 1, 2, 3, and 4-bit quantization on various aspects of system performance, including the overall radiation pattern, the grid of beams gen-erated by a 16-point FFT, and the Signal-to-Interference Ratio (SIR) in a multibeam scenario. Our findings provide insight into the trade-offs between quantization resolution and beamforming efficacy, highlighting the critical role of twiddle factor precision in optimizing satellite communication systems. Finally a set of recommendations is given for selecting the quantization that is most suitable for different cases.