On Optimization of Mixed-Radix FFT: A Signal Processing Approach

Abstract

In order to achieve higher transmission rates and system capacities, fifth generation (5G) systems as well as 802.11 ad/ay systems consider higher frequency bands (24GHz-70GHz), the so-called millimeter wave frequencies. These systems rely heavily on Orthogonal Frequency Division Multiplexing (OFDM) approach in order to realize the transmitted signal. The Fast Fourier Transform (FFT) and inverse FFT (IFFT) blocks are vital signal processing components in synthesizing the OFDM signal. Towards the objective of designing a low-complexity, small area, and low-power consumption FFT blocks, this paper proposes an extension of the algorithmic level approach, known as COordinate Rotation DIgital Computer (CORDIC)-Friendly FFT in [1], to a more practical higher order FFTs and mixed-radix FFTs. Moreover, it introduces the first quantization error analysis of a generalized mixed-radix FFT. The error analysis is used to find the optimal modified twiddle factors that reduce the FFT hardware complexity. Additionally, this paper shows that any type of CORDIC considered in the proposed framework outperforms the conventional FFT in terms of Signal-to-Quantization-Noise Ratio (SQNR), for a given silicon area budget. The proposed framework offers up to 50 dB SQNR gain compared to the conventional FFT for different FFT sizes when CORDIC rotators are employed. If Single-path Delay Feedback (SDF) pipeline architecture is used, the achieved SQNR gain is obtained at no additional hardware cost.