This work shows that chaotic signals with different power spectrum and different positive Lyapunov exponents are robust to linear superposition, meaning that the superposition preserves the Lyapunov exponents and the information content of the source signals, even after being transmitted over non-ideal physical medium. This work tackles with great detail how chaotic signals and their information content are affected when travelling through medium that presents the non-ideal properties of multipath propagation, noise and chaotic interference (linear superposition), and how this impacts on the proposed communication system. Physical media with other non ideal properties (dispersion and interference with periodic signals) are also discussed. These wonderful properties that chaotic signals have allows me to propose a novel communication system based on chaos, where information composed from and to multiple users each operating with different base frequencies and that is carried by chaotic wave signals can be fully preserved after transmission in the open air wireless physical medium, and it can be trivially decoded with low probability of errors.
Bibliographical noteOpen access via Springer agreement
Data Availability StatementThe online version contains supplementary material available at https://doi.org/10.1007/s11071-021-06644-4.
- Ergodic theory
- Information theory
- Signal analysis