A New Hierarchical $M$ -ary DCSK Communication System: Design and Analysis

Multiresolution <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>-ary differential chaos shift keying (MR-<inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>-DCSK) modulation using non-uniformly spaced phase constellation is a promising technique that can satisfy different bit-error-rate (BER) requirements within one symbol over multipath fading channels. However, the BER performance always deteriorates as the modulation order <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> becomes larger. To overcome this shortcoming, a new hierarchical square-constellation-based <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>-DCSK communication system using non-uniformly spaced distance constellation is proposed, which can be easily extended to other-constellation scenarios, e.g., rectangular, star, and asymmetrical square constellations. Furthermore, an adaptive transmission scheme is designed by modifying the distance between the two constellation points in the last hierarchical level. In addition, theoretical BER expressions of the proposed systems are derived over multipath Rayleigh fading channels, which are consistent with the simulated results. Analytical and simulated results show that the proposed system not only can provide lower energy consumption as compared with the conventional MR-<inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>-DCSK system but also can efficiently adjust BER performance based on the signal-to-noise ratio information. Therefore, the proposed system can serve as a desirable alternative for energy-efficient short-range wireless-communication applications.