Mixed-radix, virtually scaling-free CORDIC algorithm based rotator for DSP applications

• Published in: Integration (Amsterdam) Vol. 78; pp. 70 - 83
• Main Authors: Changela, Ankur, Zaveri, Mazad, Verma, Deepak
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.05.2021; Elsevier BV
• Subjects: Algorithms; Carry-save arithmetic; Commutators; Convergence; Digital computers; Digital signal processing; Digital signal processors; Fast Fourier transformations; Fourier transforms; Higher radix CORDIC; Multipath-delay commutator (MDC) architecture; Read only memory; Read-only memory devices; ROM; Rotation; Scaling; Scaling-free vector rotation; Signal processing; Studies; Taylor series; Trigonometric functions; Two-dimensional vector rotation; Two-dimensional vector rotation; Higher radix CORDIC; Scaling-free vector rotation; Multipath-delay commutator (MDC) architecture; Carry-save arithmetic
• ISSN: 0167-9260; 1872-7522
• DOI: 10.1016/j.vlsi.2021.01.005

In this work, we proposed a novel Coordinate Rotation DIgital Computer (CORDIC) rotator algorithm that converges faster by performing radix-2,4 and 16 CORDIC iterations while maintaining the scale factor implicitly constant. A mixed-radix is used to achieve convergence faster to reduce the computational latency of the CORDIC algorithm. The main concern of the higher radix CORDIC algorithm is the compensation of a variable scale factor. To solve this problem, the Taylor series approximation of sine and cosine is proposed for a higher radix CORDIC algorithm to achieve the scaling-free rotation of the two-dimensional vector. The scaling-free rotation of the proposed CORDIC algorithm removes the read-only memory (ROM) needed to store scale factor of higher radix CORDIC algorithm. Further, the proposed CORDIC algorithm is designed in rotation mode and optimized by removing the Z datapath for the digital signal processing (DSP) applications for which the angle of rotation is known in advance. Finally, the multipath delay commutator (MDC) fast Fourier transform (FFT) algorithm is implemented with the proposed CORDIC algorithm based rotator on FPGA. The proposed design is compared with existing designs. In a comparison between the radix-16 CORDIC rotator based FFT implementation and our proposed implementation, it has been found out that implementation proposed in this article has used 17% fewer resources. •A mixed-radix CORDIC is proposed to achieve the convergence faster.•A problem of complex scale factor in higher radix and hybrid CORDIC algorithm is addressed.•Taylor series approximation for higher radix CORDIC algorithm is proposed to make the vector rotation scaling-free.•A proposed CORDIC algorithm is distinctly optimized for DSP applications wherein the angle of rotation is known in advanced.•Proposed CORDIC algorithm based FFT algorithm implementation shows a significant improvement in resource utilization.