Uncertain chaotic behaviours of chaotic-based frequency- and phase-modulated signals

Chaotic signals show many advantages in the application of radar systems. The technique described in this study focuses on the chaotic behaviour of the chaotic-based frequency- and phase-modulated signals. Chaotic-based frequency- and phase-modulated signals are introduced and analysed. Theoretical analysis points out that the initial chaotic map´s phase structure is destroyed by frequency or phase modulation, which may be the direct reason that induces uncertain chaotic behaviours of the modulated signals based on chaos. Furthermore, a sufficient condition for chaotic maps to ensure the chaotic-based frequency-modulated signals remaining chaotic is discussed, and an initial sensitive correlation function for the chaotic-based phase-modulated signals is defined to estimate the possibility of chaotic behaviours remaining. Both theoretical analysis and computer simulation present the uncertain property of chaotic behaviours for chaotic-based signals, which induces better or worse signal performances depending on different chaotic maps and different signal modulation. It is also demonstrated that chaotic behaviours of the modulated signals based on chaos do not certainly provide satisfying performances for radar applications.