A Low-SWaP 16-Beam 2.4 GHz Digital Phased Array Receiver Using DFT Approximation

A low-complexity approximation for the 16-point DFT and its respective multiplierless fast algorithm is proposed. A receive mode multibeam phased-array experiment was realized at 2.4 GHz employing a 16-element IQ receiver array that uses the proposed approximate spatial DFT in real-time in order to achieve multibeam digital beamforming. The 16-beam digital receiver experiment uses a ROACH-2 based Xilinx Virtex-6 FPGA platform for both digital beam computation as well as to perform the multireceiver analog-to-digital conversion. Receive mode RF beams were measured and compared to the exact DFT (realized with fixed-point multipliers with 8-bit twiddle factors). The measured approximate DFT closely followed the measured beams resulting from the fixed-point conventional DFT implementation. The approximate DFT achieves RF beam performance (mainlobe gain, sidelobes) similar to the DFT at the cost of a small error which would be tolerable for the majority of multibeam phased-array receivers. The 16-point approximate DFT provides a hardware reduction of $\sim$70% with respect to FFTs, setting up a low size, weight and power (SWaP) system.The maximum magnitude error of the filter bank response is 0.106 ($\approx -20$ dB).