Design of Carrier Index Keying-Aided <i>M</i>-Ary Differential Chaos Cyclic Shift Keying for D2D Communications

Device-to-device (D2D) communications can allow different devices to communicate in short range, which greatly meets the demand of effective transmissions. In this paper, a spectral and energy-efficient carrier index keying-aided <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 differential chaos cyclic shift keying (CIK-MDCCSK) system is proposed for D2D communications, where multiple cyclic-shifted <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 information-bearing signals are superimposed and transmitted by a subcarrier, and extra keying bits are transmitted by indices of the selected subcarriers. Furthermore, a carrier keying detection and <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 de-mapping algorithm is proposed to retrieve the information bits transmitted by <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 symbols and indices of carrier keying. The bit error rate (BER) expressions of the proposed CIK-MDCCSK system are derived over the additive white Gaussian noise (AWGN) and D2D channels, and the optimal power coefficient is deduced for performance enhancement. Then, the spectral efficiency, energy efficiency, and complexity of CIK-MDCCSK are analyzed and compared to benchmark systems to show its superiority. Next, the proposed CIK-MDCCSK system is expanded into its enhanced version for more effective transmission without degrading the BER performance. It is demonstrated by performance comparisons that the proposed CIK-MDCCSK system can achieve more than twice energy efficiency and up to 3 dB gain in BER performance compared to state-of-the-art benchmarks.