A Pre-Coded Multi-Carrier<i>M</i>-Ary Chaotic Vector Cyclic Shift Keying Transceiver for Reliable Communications

Abstract

In this paper, we propose a pre-coded multi-carrier <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary chaotic vector cyclic shift keying (PC-MC- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -CVCSK) transceiver for reliable information transmissions. In this design, we exploit the principle of diagonalization to combat noises and interferences. At the PC-MC- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -CVCSK transmitter, we propose to precode the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary modulated symbols based on the discrete Fourier transform (DFT) and the reverse matrix of an eigenvalue matrix. Meanwhile, the chaotic generator outputs chaotic sequences, which are then cyclically shifted and used to modulate precoded symbols. At the receiver, reverse operations are conducted to recover the data. Moreover, we prove that a circulant matrix can be constructed by selecting the cyclic shift length, while the DFT aided processing will diagonalize the circulant matrix. Thanks to the diagonalization design, the inner product of information-bearing chaotic vectors becomes zero, thus signals can be orthogonalized to suppress interferences. Furthermore, theoretical performances of the proposed transceiver, including the bit error rate (BER), the symbol rate, the energy efficiency and the spectrum efficiency, and the computational complexity are analyzed. Simulation results validate the exact analysis. Furthermore, the results demonstrate that the proposed PC-MC- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -CVCSK system outperforms the counterpart schemes, which can provide <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary high symbol rate transmission services with enhanced reliability performances.