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.
Highlights
In wireless transmission systems, orthogonal signals are often used for transmission information
Several different biorthogonal scramble modulation (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, better than orthogonal MCM and OFDM systems
The BOSM systems based on general Fourier series analysis, including Chebyshev series and Legendre series analysis, have higher spectrum efficiency
Summary
Orthogonal signals are often used for transmission information. Biorthogonal CDMA is helpful to improve spectrum efficiency, reduce multiple-access interference and complexity in receiver [3,4]. These systems belong to orthogonal systems because all the biorthogonal signals are orthogonal. In paper [10], we introduced an algorithm to obtain biorthogonal functions based on Fourier-Legendre series. Analysis, and proposed a wireless transmission system of biorthogonal scramble modulation (BOSM) based on such kind of biorthogonal function sets. We introduce a universal algorithm to obtain biorthogonal functions based on General Fourier series analysis. On the condition of flat fading channel, we analyze and compare the BER performance and spectrum efficiency of different BOSM and orthogonal systems. The simulating results show that the BOSM based on General Fourier series analysis has better BER performance, and has higher spectrum efficiency than the BOSM system based on Fourier series analysis
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