This paper describes a current-mode on-chip analog architecture suitable for multibeamforming of IF band signals from small-to moderate-sized antenna arrays. The architecture uses an approximate discrete Fourier transform (a-DFT) to realize the linear transformation (LT) required for multibeamforming. Compared with the ideal DFT, the a-DFT algorithm exhibits good enough accuracy while only utilizing small integer coefficients, allowing it to be easily realized as a current-mode circuit. The 8-point a-DFT demonstrated in this paper can be used as the core calculation block in a standalone beamforming system and also serve as the key computational block in modularized multi-beamformer systems for larger arrays. The design uses an offset cancellation technique based on a multi-phase dynamic current mirror (DCM) to decrease errors in the generated beam pattern caused by transistor mismatches. The proposed integrated multi-beamformer was realized in the TSMC 180 nm process. Test results show that the chip can support 8-point multi-beamforming with 54 dB dynamic range (DR) and 4.7 Gbps channel capacity. The chip has approximately 40.8% lower power consumption than a fully-digital 8-point a-DFT core synthesized using the NCSU 45 nm PDK. When used within a complete beamforming system, the chip can also save system-level power consumed by the digital blocks, such as reducing ADC power consumption by 69.5% to 92.9% as estimated from the median Walden FoM of recent work.INDEX TERMS Analog beamforming, multi-beamformer, current-mode circuit, dynamic current mirror, analog computing.
Resumo-Este artigo apresenta uma nova representação inteira para números complexos usuais.É mostrado que as raízes da cúbica e sexta da unidade são representadas sem erro empregando apenas os inteiros {0, ±1}. Este resultado torna promissor o uso da representação proposta em algoritmos para a DFT de comprimento 3 e 6. Palavras-Chave-Transformada discreta de Fourier, inteiros algébricos, inteiros gaussianos, inteiros de Eisenstein.
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