A General Algorithm for Biorthogonal Functions and Performance Analysis of Biorthogonal Scramble Modulation System

Yueyun Chen, Zhenhui Tan

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DOI: 10.4236/wsn.2010.23026                

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.

Keywords

Biorthogonal Functions, Biorthogonal Scramble Modulation, Generalized, Fourier Series, Mobius Inverse, Wireless Transmission

Conflicts of Interest

The authors declare no conflicts of interest.

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