Multi-beam RF aperture using multiplierless FFT approximation

Multiple independent radio-frequency (RF) beams find applications in communications, radio astronomy, radar and microwave imaging. An N-point fast Fourier transform (FFT) applied spatially across an array of receiver antennas provides N-independent RF beams at N/2 log₂N 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 was verified on-chip using a Xilinx Virtex-6 Lx240T field programmable gate array (FPGA) device. The FPGA implementation indicated bandwidth of 369 MHz for each of the independent receive-mode RF beams.