Twiddle factor generation using Chebyshev polynomials and HDL for frequency domain beamforming

Abstract

Twiddle factor generation is considered a computationally intensive task in generic length, high resolution, FFT operations. In order to accelerate twiddle factor generation, we propose a reconfigurable hardware architecture based on Chebyshev polynomial expansion for computing the cosine and sine trigonometric functions under finite precision arithmetic. We show that our approach presents a flexible 3 decimal digits precision output for variable length FFT operations, since the same design space can be used for any power of 2 FFT length. In particular, this study focuses on communication systems incorporating frequency domain beamforming algorithms for single and multi-beams. The proposed architecture is competitive with classical designs i.e. Coordinate Rotation Digital Computer, CORDIC and Taylor Series by providing low latency, high precision twiddle factors for variable length FFT.