Cost-efficient mapping of 3- and 5-point DFTs to general baseband processors

Discrete Fourier transforms of 3 and 5 points are essential building blocks in FFT implementations for standards such as 3GPP-LTE. In addition to being more complex than 2 and 4 point DFTs, these DFTs also cause problems with data access in SDR-DSPs, since the data access width, in general, is a power of 2. This work derives mappings of these DFTs to a 4-way SIMD datapath that has been designed with 2 and 4-point DFT in mind. Our instruction set proposals, based on modified Winograd DFT, achieves single cycle execution of 3-point DFTs and 2.25 cycle average execution of 5-point DFTs in a cost-effective manner by reutilizing the already available arithmetic units. This represents an approximate speed-up of 3 times compared to an SDR-DSP with only MAC-support. In contrast to our more general design, we also demonstrate that a typical single-purpose FFT-specialized 5-way architecture only delivers 9% to 25% extra performance on average, while requiring 85% more arithmetic units and a more expensive memory subsystem.