Multi‐beam RF aperture using multiplierless FFT approximation

Abstract

Multiple independent radio frequency (RF) beams find applications in communications, radio astronomy, radar, and microwave imaging. An N -point FFT applied spatially across an array of receiver antennas provides N -independent RF beams at N 2 log 2 N multiplier complexity. Here, a low-complexity multiplierless approximation for the 8-point FFT is presented for RF beamforming, using only 26 additions. The algorithm provides eight beams that closely resemble the antenna array patterns of the traditional FFT-based beamformer albeit without using multipliers. The proposed FFT-like algorithm is useful for low-power RF multi-beam receivers; being synthesized in 45 nm CMOS technology at 1.1 V supply, and verified on-chip using a Xilinx Virtex-6 Lx240T FPGA device. The CMOS simulation and FPGA implementation indicate bandwidths of 588 MHz and 369 MHz, respectively, for each of the independent receive-mode RF beams.

Multi-beam receiver apertures using multiplierless 8-point approximate DFT

“…The two constraints that were imposed on the proposed approximation are: (i) nearorthogonality and (ii) low-complexity. As a result, the following matrix approximation is obtained [13]:…”

“…An 8-point approximate DFT was recently introduced in [13], being capable of small computational error [14]. At the same time, the implied computations are performed without multiplications [13].…”

“…At the same time, the implied computations are performed without multiplications [13]. The multiplicative complexity reduction to zero is a significant achievement for a meaningful DFT estimation.…”

“…The multiplicative complexity reduction to zero is a significant achievement for a meaningful DFT estimation. In this work, we consider the multiplierless 8-point DFT approximation [13] and its associate fast algorithm, based on Cooley-Tukey decimation-in-frequency fast Fourier transform (FFT) approach [15]. The results is a multiplicationfree fast algorithm.…”

“…Such low-cost computation trades the beamformer array pattern accuracy for significantly lower digital arithmetic complexity. The multiplierless DFT approximation [13] allows beamforming with zero power consumption related to power demanding multiplication operations. Thus, the computational framework of associated system is essentially constituted of adders only.…”