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

A low-complexity multiplierless approximation for the 8-point DFT is presented for RF multi- beamforming using only 26 hardware adders. The algorithm provides eight simultaneous aperture beams that closely resemble the antenna array patterns of an FFT-based beamformer. The multiplicative complexity is used as a benchmark for comparing the performance-complexity-power trade-offs between the traditional FFT and the proposed approximate DFT algorithms. Metrics based on maximum throughput, chip area, and power consumption are used for the comparison. The paper discusses the theory behind the proposed new algorithm, and the proposed 8-point DFT will be presented in the form of an 8 × 8 matrix. Furthermore simulation examples are provided for both 1-D and 2-D antenna array patters along with synthesized results for 45 nm CMOS technology at 1.1 V supply voltage. Cadence designs show a reduction of 30.6% , 33.2%, 29.0% , 26.1% and 52.0% in chip area, dynamic power consumption, critical path delay, gate-count and area-time and an increase in 45.5% in maximum clock frequency (throughput) for the proposed 8-point DFT approximation in comparison with a traditional radix-2 FFT algorithm, where both algorithms assumed 16-bit input signals.