Fast Radix-32 Approximate DFTs for 1024-Beam Digital RF Beamforming

TL;DR

This paper introduces three new approximate DFT algorithms tailored for 1024-point digital RF beamforming, significantly reducing hardware complexity and power consumption with minimal impact on signal quality, suitable for future large-scale antenna systems.

Contribution

The paper presents novel hybrid approximate DFT algorithms for 1024-point transforms, optimized for RF beamforming, with efficient hardware implementations and performance comparable to exact FFTs.

Findings

Up to 48.5% reduction in chip area

Up to 66.0% reduction in power consumption

SNR loss of ≤0.9 dB compared to exact DFTs

Abstract

The discrete Fourier transform (DFT) is widely employed for multi-beam digital beamforming. The DFT can be efficiently implemented through the use of fast Fourier transform (FFT) algorithms, thus reducing chip area, power consumption, processing time, and consumption of other hardware resources. This paper proposes three new hybrid DFT 1024-point DFT approximations and their respective fast algorithms. These approximate DFT (ADFT) algorithms have significantly reduced circuit complexity and power consumption compared to traditional FFT approaches while trading off a subtle loss in computational precision which is acceptable for digital beamforming applications in RF antenna implementations. ADFT algorithms have not been introduced for beamforming beyond $N = 32$, but this paper anticipates the need for massively large adaptive arrays for future 5G and 6G systems. Digital CMOS circuit designs for the ADFTs show the resulting improvements in both circuit complexity and power consumption metrics. Simulation results show similar or lower critical path delay with up to 48.5% lower chip area compared to a standard Cooley-Tukey FFT. The time-area and dynamic power metrics are reduced up to 66.0%. The 1024-point ADFT beamformers produce signal-to-noise ratio (SNR) gains between 29.2--30.1 dB, which is a loss of $\le$ 0.9 dB SNR gain compared to exact 1024-point DFT beamformers (worst case) realizable at using an FFT.