Chaotic phase shift keying in delayed chaotic anticontrol systems

Based on the delayed feedback chaotic anticontrol systems, a new chaotic phase shift keying (CPSK) scheme is proposed for secure communications in this paper. The chaotic transmitter is a linear system with nonlinear delayed feedback in which a trigonometric function cos (·) is used. Such system can exhibit rich chaotic behavior with the choice of appropriate parameters. For an M-ary communication system where M = 2ⁿ, each of these M possible symbols (n-bits) is firstly mapped to 2(m-1)π/M (with m=1, 2,⋯,M) which is used as the phase argument for the cos(·) function in the nonlinear feedback. Two different kinds of signals can be transmitted. In the first one, an appropriate linear combination of state variables is chosen as the transmitting signal based on the observer theory. In another one, a nonlinear component in the transmitter state equation is chosen. In both schemes, only a scalar chaotic signal is transmitted through the channel. Demodulation is based on the synchronization of the transmitter and the receiver, and different decoded phases correspond to different information signals.