Low-Complexity, High-Precision 32-Point DFT Approximation for Multibeam Beamforming Applications - Shi, Peng; Ye, Yinghao (IEEE transactions on aerospace and electronic systems, 2025)
Multibeam beamforming systems employ the N-point discrete Fourier transform (DFT) on time-synchronized samples from a uniform linear array to generate N distinct RF beams, which are essential in applications such as radar, communication, sonar, and medical imaging. Since the direct computation of the DFT for an arbitrary N -point sequence requires \mathcal {O}(N^{2}) multiplications, there is a strong desire to develop multiplierless DFT approximations to minimize hardware resource usage and power consumption. In this work, we introduce a low-complexity, high-precision 32-point DFT approximation along with a corresponding multiplierless fast algorithm. The proposed method achieves higher precision compared to existing 32-point DFT approximations, delivering a normalized Frobenius norm error of 1.7 × 10^{-3} , in contrast to 1.0 × 10^{-2} for the state-of-the-art approach, while maintaining comparable hardware complexity. This advancement offers strong potential for improving performance in applications requiring high resolution spatial information and precise directional localization.