4.6 Article

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

Journal

IEEE ACCESS
Volume 8, Issue -, Pages 96613-96627

Publisher

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/ACCESS.2020.2994550

Keywords

Discrete Fourier transforms; Approximation algorithms; Array signal processing; Signal processing algorithms; Computational complexity; MIMO communication; Fourier transform; discrete fourier transform; approximation; VLSI; DFT; FFT; radix; fast algorithm; beamforming; beamsteering; 5G; MIMO; massive MIMO

Funding

  1. NSF Collaborative Research: Spatially Oversampled Dense Multi-Beam Millimeter-Wave Communications for Exponentially Increased Energy-EffIciency (SpecEES) [1854798, 1731290]
  2. NSF ECCS
  3. Collaborative Research: Wideband Multi-Beam Antenna Arrays: Low-Complexity Algorithms and Analog-CMOS Implementations [1711395]
  4. Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq), Brazil

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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 <= 0.9 dB SNR gain compared to exact 1024-point DFT beamformers (worst case) realizable at using an FFT.

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