Low-Complexity, High-Precision 32-Point DFT Approximation for Multibeam Beamforming Applications

• Published in: IEEE transactions on aerospace and electronic systems Vol. 61; no. 5; pp. 13449 - 13458
• Main Authors: Shi, Peng, Ye, Yinghao
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2025; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: 32-Point DFT; Accuracy; Antenna arrays; Approximation; Approximation algorithms; Array signal processing; Beamforming; Complexity; Discrete Fourier transforms; Fast Fourier transforms; Fourier transforms; Hardware; Linear arrays; Matrix decomposition; Medical imaging; multibeam beamforming; multiplierless approximation; Radar beams; Sparse matrices; Spatial data; Vectors
• ISSN: 0018-9251; 1557-9603
• DOI: 10.1109/TAES.2025.3578068

Multibeam beamforming systems employ the N-point discrete Fourier transform (DFT) on time-synchronized samples from a uniform linear array to generate <inline-formula><tex-math notation="LaTeX">N</tex-math></inline-formula> 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 <inline-formula><tex-math notation="LaTeX">N</tex-math></inline-formula>-point sequence requires <inline-formula><tex-math notation="LaTeX">\mathcal {O}(N^{2})</tex-math></inline-formula> 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 <inline-formula><tex-math notation="LaTeX">1.7 \times 10^{-3}</tex-math></inline-formula>, in contrast to <inline-formula><tex-math notation="LaTeX">1.0 \times 10^{-2}</tex-math></inline-formula> 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.