The Journal of Korean Institute of Communications and Information Sciences (한국통신학회논문지)

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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A 8192-Point FFT Processor Based on the CORDIC Algorithm for OFDM System

CORDIC 알고리듬에 기반 한 OFDM 시스템용 8192-Point FFT 프로세서

  • Published : 2002.08.01
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Abstract

This paper presents the architecture and the implementation of a 2K/4K/8K-point complex Fast Fourier Transform(FFT) processor for Orthogonal Frequency-Division Multiplexing (OFDM) system. The architecture is based on the Cooley-Tukey algorithm for decomposing the long DFT into short length multi-dimensional DFTs. The transposition memory, shuffle memory, and memory mergence method are used for the efficient manipulation of data for multi-dimensional transforms. Booth algorithm and the COordinate Rotation DIgital Computer(CORDIC) processor are employed for the twiddle factor multiplications in each dimension. Also, for the CORDIC processor, a new twiddle factor generation method is proposed to obviate the ROM required for storing the twiddle factors. The overall 2K/4K/8K-FFT processor requires 600,000 gates, and it is implemented in 1.8 V, 0.18 ${\mu}m$ CMOS. The processor can perform 8K-point FFT in every 273 ${\mu}s$, 2K-point every 68.26 ${\mu}s$ at 30MHz, and the SNR is over 48dB, which are enough performances for the OFDM in DVB-T.

본 논문에서 OFDM (Orthogonal Frequency-Division Multiplexing) 시스템용 2K/4K/8K-point 복소 FFT (Fast Fourier Transform) 프로세서의 구조와 그 구현방법을 제안한다. 제안하는 프로세서의 구조는 긴 길이의 DFT를 짧은 길이의 다차원 DFT로 분할하기 위하여 쿨리-투키 알고리듬에 기반 한다. 전치 메모리, 셔플 메모리, 메모리 합성 방법은 다차원 변환을 위한 메모리의 능률적 조작을 위해 사용한다. Booth 알고리듬과 CORDIC (COordinate Rotation DIgital Computer) 프로세서는 각 차원에서 트위들 팩터 곱셈을 위해 사용한다. 또한, CORDIC 프로세서에는 트위들 팩터를 저장하기 위해 필요한 ROM의 사용을 막기 위해 트위들 팩터 발생 방법을 제안한다. 전체 2K/4K/8K FFT 프로세서는 600,000 게이트를 사용하며, 1.8V, 0.18${\mu}m$ CMOS를 이용해 구현한다. 제안하는 프로세서는 8K-point FFT를 273${\mu}s$마다, 2K-point를 68.26${\mu}s$마다 수행할 수 있으며, SNR은 DVB-T의 OFDM을 위해 충분한 48dB를 넘는다.

Keywords

References

  1. R. Lassalle and M. Alard, 'Principles of modulation and channel coding for digital broadcasting for mobile receivers,' EBU Technical Review, No. 224, pp. 168-190, Aug. 1987
  2. W. Y. Zou and Y. Wu, 'COPDM: An Overview,' IEEE Trans. on Broadcasting, vol. 41, No. 1, pp. 1-8, Mar. 1995 https://doi.org/10.1109/11.372015
  3. L. J. D'Luna, W. A. Cook, R. M. Guidash, G. W. Brown, T. J. Tiedwell, J. R. Fischer, and T. Tam, 'An 8 x 8 discrete cosine transform chip with pixel rate clocks,' The 3rd Annual IEEE ASIC Seminar and Exhibit, PP. P7/5.1-P7/5.4, 1990
  4. K. Kim, 'Shuffle memory system,' 13th Int. Symp. on Parallel and Distributed Processing, pp. 268-272, Apr. 1999
  5. Y. H. Hu, 'CORDIC-based VLSI aichitectures for digital signal processing,' IEEE Signal Processing Mag., vol. 9, No. 3, PP. 16-35, July 1992 https://doi.org/10.1109/79.143467
  6. R. Sarmiento, V. D. Armas, J. P. Lopez, J. A. Montiel-Nelson, and A. Nunez, 'A CORDIC processor for FFT computation and its imple-mentation using gallium arsenide technology,' IEEE Trans. on VLSI Systems, vol. 6, No. 1, pp. 18-30, Mar. 1998 https://doi.org/10.1109/92.661241
  7. A. M. Despain, 'Fourier transform computers using CORDIC iterations,' IEEE Trans. on Computers, vol. C-23, No. 10, pp. 993-1001, Oct. 1974
  8. A. M. Despain, 'Very fast Fourier transform algorithms for hardware implementation,' IEEE Trans. on Computers, vol. C-28, No. 5, pp. 333-341, May 1979 https://doi.org/10.1109/TC.1979.1675363
  9. J. W. Cooley and J. W. Tukey, 'An algorithm for the machine calculation of complex Fourier series,' Mathematics of Computation, vol. 19, No. 90, pp. 297-301, Apr. 1965 https://doi.org/10.2307/2003354
  10. E. Bidet, D. Castelain, C. Joanblanq, and P. Senn, 'A fast single-chip implementation of 8192 complex point FFT,' IEEE Journal of Solid-State Circuits, vol. 30, No. 3, PP. 300-305, Mar. 1995 https://doi.org/10.1109/4.364445
  11. S. H. Park, D. H. Kim, D. S. Han, K. S. Lee,S. J. Park, and J. R. Choi, 'Sequential design of a 8192 complex point FFT in OFDM receiver,' The First IEEE Asia Pacific Conference, pp. 262-265, Aug. 1999
  12. A. V. Oppenheim and R. W. Schafer,Discrete-time Signal Processing, Englewood Cliffs, NJ : Prentice Hall, 1989
  13. S. Winograd, 'On computing the discrete Fourier transform,' Mathematics of Comput-ation, vol. 32, No. 141, pp. 175-199, Jan. 1978 https://doi.org/10.1090/S0025-5718-1978-0468306-4
  14. J. Volder, 'The CORDIC trigonometric computmg technique,' IRE Trans. on Electronic Computers, vol. EC-8, No. 3, pp. 330-334, Sept. 1959
  15. M. Bekooij, J. Huisken, and K. Nowak, 'Numerical accuracy of fast Fourier transforms with CORDIC arithmetic,' Journat of VLSI Sisnal Processing, vol. 25, No. 2, pp. 187-193, June 2000 https://doi.org/10.1023/A:1008179225059
  16. Y. H. Hu, 'The quantization effects of the CORDIC algorithm,' IEEE Trans. on Signal Processing, vol. 40, No. 4, pp. 834-844, Apr. 1992 https://doi.org/10.1109/78.127956
  17. T. Thong and B. Liu, 'Fixed-point fast Fourier tansform error analysis,' IEEE Trans. on Acoust., Speech, Signal Processing, vol. ASSP-24, No. 6, PP. 563-573, Dec. 1976