Synchronization-based scheme for calculating ambiguity functions of wideband chaotic signals

This paper develops a synchronization-based scheme for calculating ambiguity function (AF) of a wideband chaotic signal. In the direct implementation, the formulation of the time-scaling chaotic signal takes much computational load and its accuracy determines the quality of the calculated AF diagrams. By exploring the generation of the chaotic signal, the impulsive synchronization theory can be used to produce its time-delay and time-scaling versions. With this observation, the AF diagrams can be accurately obtained by following correlation operation. A distinct characteristic of the proposed scheme is that the generation of the time-delay and time-scaling versions is implemented in an analog way, while the correlation operation can be implemented in a digital way. This mixed analog-digital structure provides the proposed scheme with implementation advantages and practical applicability.