Low-Power Booth Multiplication without Dynamic Range Detection in FFTs for FMCW Radar Signal Processing

Multipliers in DSP applications usually consume a significant amount of power. Studies have shown that power efficiency of the often used Booth multiplier can be improved by dynamically swapping input operands based on the dynamic range of both inputs. However, this requires dynamic range detection logic, which increases the area and delay. Also, no studies have proposed multipliers with dynamic range detection that are larger than
$16 \times 16$
bits. So far, no applications have been identified where statically swapping multiplier inputs leads to increased power-efficiency. In this paper we show that statically swapping Booth multiplier inputs can greatly improve the power-efficiency of FFTs. In the case of automotive FMCW radar systems, where multi-dimensional FFTs are calculated, the intermediate and output values of FFTs are typically sparse. Therefore these values are always given to the partial product generating input of the Booth multipliers, instead of being given the twiddle factors. RTL power-simulation results of a radix-2 FFT implementation using Booth multipliers with swapped inputs show an up to 28.69% decrease in power usage compared to a typical implementation without swapped inputs.