Real-Time and High-Accuracy Arctangent Computation Using CORDIC and Fast Magnitude Estimation

• Main Authors: Luca Pilato, Luca Fanucci, Sergio Saponara
• Format: Article
• Language: English
• Published: MDPI AG 2017-03-01
• Series: Electronics
• Subjects: real-time; Digital Signal Processing (DSP); Embedded Systems; CORDIC (Coordinate Rotation Digital Computer); ASIC (Application Specific Integrated Circuit); FPGA (Field Programmable Gate Array); IP (Intellectual Property); automotive sensors
• Online Access: http://www.mdpi.com/2079-9292/6/1/22

This paper presents an improved VLSI (Very Large Scale of Integration) architecture for real-time and high-accuracy computation of trigonometric functions with fixed-point arithmetic, particularly arctangent using CORDIC (Coordinate Rotation Digital Computer) and fast magnitude estimation. The standard CORDIC implementation suffers of a loss of accuracy when the magnitude of the input vector becomes small. Using a fast magnitude estimator before running the standard algorithm, a pre-processing magnification is implemented, shifting the input coordinates by a proper factor. The entire architecture does not use a multiplier, it uses only shift and add primitives as the original CORDIC, and it does not change the data path precision of the CORDIC core. A bit-true case study is presented showing a reduction of the maximum phase error from 414 LSB (angle error of 0.6355 rad) to 4 LSB (angle error of 0.0061 rad), with small overheads of complexity and speed. Implementation of the new architecture in 0.18 µm CMOS technology allows for real-time and low-power processing of CORDIC and arctangent, which are key functions in many embedded DSP systems. The proposed macrocell has been verified by integration in a system-on-chip, called SENSASIP (Sensor Application Specific Instruction-set Processor), for position sensor signal processing in automotive measurement applications.