A General Algorithm for Biorthogonal Functions and Performance Analysis of Biorthogonal Scramble Modulation System
- 1
- 2
Abstract
Applying the theorems of Mobius inverse and Dirichlet inverse, a general algorithm to obtain biorthogonal functions based on generalized Fourier series analysis is introduced. In the algorithm, the orthogonal function can be not only Fourier or Legendre series, but also can be any one of all orthogonal function systems. These kinds of biorthogonal function sets are used as scramble signals to construct biorthogonal scramble modulation (BOSM) wireless transmission systems. In a BOSM system, the transmitted signal has significant security performance. Several different BOSM and orthogonal systems are compared on aspects of BER performance and spectrum efficiency, simulation results show that the BOSM systems based on Chebyshev polynomial and Legendre polynomial are better than BOSM system based on Fourier series, also better than orthogonal MCM and OFDM systems.
- R. B. Blizard, “Comparison of biorthogonal and bisimplex codes,” IEEE Transactions on Communications Technology, Vol. 15, No. 4, pp. 657–658, August 1967.
- M. Kim and S. Tretter, “Performance of sequential decoding with biorthogonal modulation and Q-level quantization,” IEEE Transactions on Communications, Vol. 19, pp. 88–92, February 1971.
- S.-H. Hong and J.-S. No, “Performance analysis of CDMA systems by using biorthogonal codes,” IEEE 45th Conference on Vehicular Technology, Vol. 2, pp. 694– 698, July 1995.
- S.-J. Kang, D.-K. Hong, et al., “Constant-amplitude multicode-biorthogonal modulation,” IEEE Transactions on Communications, Vol. 55, No. 1, pp. 69–75, January 2007.
- Y. Wei and N. Chen, “Square wave analysis,” Journal of Mathematical Physics, Vol. 39, No. 8, pp. 4226–4245, August 1998.
- Y. Wei, “Dirichlet multiplication and easily-generated function analysis,” Computers & Mathematical with Applications, Vol. 39, pp. 173–199, 2000.
- N. Chen, “Modified M?bius inverse formula and its applications in physics,” Physics Review Letters, Vol. 64, No. 11, pp. 1193–l195, 1990.
- W. Su, W. Zhang, and J. Wang, “The evaluations of the inverse transform of eight often-used waveforms by M?bius transform—The inverse transform of their Fourier series,” Chinese of Journal Electronics, Vol. 14, No. 3, pp. 513–518, July 2005.
- C. Ling, F. Chen, and W. Su, “The Chen-mobius multi-carriers digital communication system and its simulation,” IEEE International Workshop on Anti-Counterfeiting, Security and Identification, pp. 16–18, April 2007.
- Y. Chen, J. Zhang, and Z. Tan, “A kind of biorthogonal functions based on Fourier-Legendre series and its application in wireless transmission system,” IEEE 9th International Conference on Signal Processing, 2008.
- K. H. Rosen, “Elementary number theory and its application,” 5th edition, Pearson Education Inc. Press, 2005.
- M. R. Schroeder, “Number theory in science and communication,” 4th edition, Springer-Verlag Press, New York, 2006.
- Z. Liu, “Orthogonal function and its application,” National Defense Industry Publisher, Beijing, 1982.