An Enhanced Adaptive Recoding Rotation CORDIC

Abstract

The Conventional Coordinate Rotation Digital Computer (CORDIC) algorithm has been widely used in many applications, particularly in Direct Digital Frequency Synthesizers (DDS) and Fast Fourier Transforms (FFT). However, CORDIC is constrained by the excessive number of iterations, angle data path, and scaling factor compensation. In this article, an enhanced adaptive recoding CORDIC (EARC) is proposed. It uses the enhanced adaptive recoding method to reduce the required iterations and adopts the trigonometric transformation scheme to scale up the rotation angles. Computing sine and cosine is used first to compare the core functionality of EARC with basic CORDIC; then a 16-bit DDS and a 1,024-point FFT based on EARC are evaluated to demonstrate the benefits of EARC in larger applications. All the proposed architectures are validated on a Virtex 5 FPGA development platform. Compared with a commercial implementation of CORDIC, EARC requires 33.3% less hardware resources, provides a twofold speedup, dissipates 70.4% less power, and improves accuracy in terms of the Bit Error Position (BEP). Compared to the state-of-the-art Hybrid CORDIC, EARC reduces latency by 11.1% and consumes 17% less power. Compared with a commercial implementation of DDS, the dissipated power of the proposed DDS is reduced by 27.2%. The proposed DDS improves Spurious-Free Dynamic Range (SFDR) by nearly 7 dBc and dissipates 21.8% less power when compared with a recently published DDS circuit. The FFT based on EARC dissipates a factor of 2.05 less power than the commercial FFT even when choosing the 100% toggle rate for the FFT based on EARC and the 12.5% toggle rate for the commercial FFT. Compared with a recently published FFT, the FFT based on EARC improves Signal-to-Noise Ratio (SNR) by 8.9 dB and consumes 7.78% less power.