Modified vector rotational CORDIC (MVR-CORDIC) algorithm and architecture

Abstract

The CORDIC algorithm is a well-known iterative method for the computation of vector rotation. However, the major disadvantage is its relatively slow computational speed. For applications that require forward rotation (or vector rotation) only, we propose a new scheme, the modified vector rotational CORDIC (MVR-CORDIC) algorithm, to improve the speed performance of CORDIC algorithm. The basic idea of the proposed scheme is to reduce the iteration number directly while maintaining the SQNR performance. This can be achieved by modifying the basic microrotation procedure of CORDIC algorithm. Meanwhile, three searching algorithms are suggested to find the corresponding directional and rotational sequences so as to obtain the best SQNR performance. Three SQNR performance refinement schemes are also suggested in this paper. Namely, the selective prerotation scheme, selective scaling scheme, and iteration-tradeoff scheme. They can reduce and balance the quantization errors encountered in both microrotation and scaling phases so as to further improve the overall SQNR performance. Then, by combining these three refinement schemes, we provide a systematic design flow as well as the optimization procedure in the application of MVR-CORDIC algorithm. Finally, we present two VLSI architectures for the MVR-CORDIC algorithm. It shows that by using the proposed MVR-CORDIC algorithm, we can save 50% execution time in the iterative CORDIC structure, or 50% hardware complexity in the parallel CORDIC structure compared with the conventional CORDIC scheme.

Design of a variable precision CORDIC coprocessor for RISC-V architecture based on FinFET process

“…To address this problem, Jack E. Volder introduced a fast algorithm in 1959 for calculating trigonometric functions, known as CORDIC [24]. CORDIC is based on vector rotation, which transforms multiplication and division calculations into shifts and additions, making it hardware-friendly [25]. The concept behind CORDIC is to iteratively rotate a vector towards the target angle, either clockwise or counter clockwise, by a pre-calculated angle value that decreases with each iteration.…”

Analog-Digital Partitioning for Low-Power UWB Impulse Radios under CMOS Scaling

“…The rotation phase is estimated by using the correlation results of the I and Q branches. This is traditionally done by a CORDIC module [9].…”

Design and Implementation of DDFS Based on CORDIC in FPGA

“…The CORDIC is widely applied in the fields of DSP and signal generator, such as computer arithmetic, real-time signal processing and signal generator [4]. Since the basic of aim CORDIC algorithm is to computer the trigonometric function such sine function and cosine function, and can computer complex function such as tangent function (sine function division cosine function), the CORDIC can be used for DDFS, which can produce orthogonal sine and cosine signal [5].…”