- Volume 47 Issue 9
Performance Comparison of Taylor Series Approximation and CORDIC Algorithm for an Open-Loop Polar Transmitter
Open-Loop Polar Transmitter에 적용 가능한 테일러 급수 근사식과 CORDIC 기법 성능 비교 및 평가
- Kim, Sun-Ho (School of Electronic Engineering, Soongsil University) ;
- Im, Sung-Bin (School of Electronic Engineering, Soongsil University)
- Received : 2010.06.17
- Published : 2010.09.25
A digital phase wrapping modulation (DPM) open-loop polar transmitter can be efficiently applied to a wideband orthogonal frequency division multiplexing (OFDM) communication system by converting in-phase and quadrature signals to envelope and phase signals and then employing the signal mapping process. This mapping process is very similar to quantization in a general communication system, and when taking into account the error that appears during mapping process, one can replace the coordinates rotation digital computer (CORDIC) algorithm in the coordinate conversion part with the Taylor series approximation method. In this paper, we investigate the application of the Taylor series approximation to the cartesian to polar coordinate conversion part of a DPM polar transmitter for wideband OFDM systems. The conventional approach relies on the CORDIC algorithm. To achieve efficient application, we perform computer simulation to measure mean square error (MSE) of the both approaches and find the minimum approximation order for the Taylor series approximation compatible to allowable error of the CORDIC algorithm in terms of hardware design. Furthermore, comparing the processing speeds of the both approaches in the implementation with FPGA reveals that the Taylor series approximation with lower order improves the processing speed in the coordinate conversion part.
Supported by : 한국연구재단
- J. Groe, "Polar Transmitters for Wireless Communications," IEEE Communications Magazine, Vol. 45, no. 9, pp. 58-63, Sep. 2007.
- J. E. Volder, "The CORDIC Trigonometric Computing Technique, " IRE Trans. Electronic Computers, Vol. EC-8, no. 3, pp. 330-334, Sep. 1959. https://doi.org/10.1109/TEC.1959.5222693
- J. S. Walther, "A Unified Algorithm for Elementary Functions," in Proc. Spring. Joint Computer Conference, Vol. 38, pp. 379-385, 1971.
- R. Andraka, "A Survey of CORDIC Algorithms for FPGAs," in Proc. of the 1998 ACM/SIGDA Sixth International Symposium on FPGA, pp. 191-200, Monterey, CA, Feb. 1998.
- J. Valls, M. Kuhlmann and K. K. Parhi, "Evaluation of CORDIC Algorithms for FPGA Design," Journal of VLSI signal processing, Vol. 32, no. 3, pp. 207-222, Nov. 2002. https://doi.org/10.1023/A:1020205217934
- Y. Hu, "CORDIC-Based VLSI Architectures for Digital Signal Processing," IEEE Signal Processing Magazine, Vol. 9, no. 3, pp. 16-35, Jul. 1992. https://doi.org/10.1109/79.143467
- D. E. Milos, T. Lang, Digital Arithmetic, Morgan Kaufmann, Jun. 2003.
- W. F. Loke, Y. W. Chia and P. Y. Chee, "Phase Wrapping Digital Polar Transmitter for Multi-band OFDM Ultra Wideband System," in Proc. of MTT-S International Conference, pp. 401-404, Jun. 2009.
- W. F. Loke, Y. W. Chia and P. Y. Chee, "Design Considerations for Multi-Band OFDM Polar Transmitter of UWB System," Electronics Letters, Vol. 43, no. 8, pp. 466-468, Apr. 2002.
- R. S. Murray, L. Seymour, L. John, Schaum's Outline of Mathematical Handbook of Formulas and Tables, McGraw-Hill, Oct. 1998.