A Three-Dimensional Non-Constant-Envelope Constellation-Assisted DCSK System With Cyclic Shift Correlator

In this paper, we develop a three-dimensional non-constant-envelope constellation-assisted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm M$</tex-math></inline-formula>-ary differential chaos shift keying (DCSK) modulation system with cyclic shift correlator, named CSC-3DNCEC-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm M$</tex-math></inline-formula>-DCSK system. Particularly, we use a cyclic shift correlator (CSC) to perform channel compensation on the received signal, thereby mitigating the interference of channel fading on the proposed CSC-3DNCEC-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm M$</tex-math></inline-formula>-DCSK system. Meanwhile, the three-dimensional non-constant-envelope constellations (3DNCECs) can increase the minimum Euclidean distance (MED) between adjacent mapped symbols, thus improving the transmission reliability of constellation-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm M$</tex-math></inline-formula>-DCSK systems. We further analyze the theoretical symbol error rate (SER) expressions of the proposed CSC-3DNCEC-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm M$</tex-math></inline-formula>-DCSK system over the additive white Gaussian noise (AWGN) channel and the multipath Rayleigh fading channel. Both the theoretical analyses and simulated results indicate that the CSC-3DNCEC-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm M$</tex-math></inline-formula>-DCSK system is remarkably superior to the existing constellation-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm M$</tex-math></inline-formula>-DCSK systems.