Advances in Radio Science www.adv-radio-sci.net 1684-9965 1684-9973 6 Kleinheubacher Berichte 2007 2008 10.5194/ars-6-89-2008 http://www.adv-radio-sci.net/6/89/2008/ http://www.adv-radio-sci.net/6/89/2008/ars-6-89-2008.html http://www.adv-radio-sci.net/6/89/2008/ars-6-89-2008.pdf 89 94 2008-05-26 Matrix-Vector Based Fast Fourier Transformations on SDR Architectures Y. He K. Hueske klaus.hueske@uni-dortmund.de J. Götze E. Coersmeier University of Dortmund, Information Processing Lab, Otto-Hahn-Str. 4, 44221 Dortmund, Germany Nokia Research Center, Bochum, Meesmannstr. 103, 44807 Bochum, Germany Today Discrete Fourier Transforms (DFTs) are applied in various radio standards based on OFDM (Orthogonal Frequency Division Multiplex). It is important to gain a fast computational speed for the DFT, which is usually achieved by using specialized Fast Fourier Transform (FFT) engines. However, in face of the Software Defined Radio (SDR) development, more general (parallel) processor architectures are often desirable, which are not tailored to FFT computations. Therefore, alternative approaches are required to reduce the complexity of the DFT. Starting from a matrix-vector based description of the FFT idea, we will present different factorizations of the DFT matrix, which allow a reduction of the complexity that lies between the original DFT and the minimum FFT complexity. The computational complexities of these factorizations and their suitability for implementation on different processor architectures are investigated. Berthold, U., Riehmeier, A.-R., and Jondral, F. K.: Spectral partitioning for modular software defined radio, 59th Vehicular Technology Conference (VTC2004), 2, 1218–1222, May 2004. Cooley, J. W. and Tukey, J. W.: An algorithm for the machine calculation of complex Fourier series, Math. Comput., 19, 297–301, 1965. Dillinger, M., Madani, K., and Alonistioti, N.: Software Defined Radio-Architectures, Systems and Functions, Wiley Series in Software Radio, John Wiley & Sons Ltd., 2003. Heyne, B. and Götze, J.: A Pure Cordic Based FFT for Reconfigurable Digital Signal Processing, 12th European Signal Processing Conference (Eusipco2004), Vienna, September 2004. Jeon, C. H. and Reeves, A. P.: The fast Fourier transform on a multicluster computer architecture, Proceedings of the 19th Annual Hawaii International Conference on System Sciences, 103–110, 1986. Schoenes, M., Eberli, S., Burg, A., et al.: A novel SIMD DSP architecture for software defined radio, Proc. of the 46th IEEE International Midwest Symposium on Circuits and Systems (MWSCAS2003), 3, 1443–1446, December 2003. Son, B. S., Jo, B. G., Sunwoo, M. H., and Yong, S. K.: A high-speed FFT processor for OFDM systems, Proc. of the IEEE International Symposium on Circuits and Systems (ISCAS2002), 3, 281–284, May 2002. Van Loan, C.: Computational Frameworks for the Fast Fourier Transform, Frontiers in applied mathematics, Society for Industrial and Applied Mathematics, Philadelphia, 1992.