Reverse-time Chaos based Scheme for Calculating Wideband Ambiguity Functions of Chaotic Signals

This paper develops a reverse-time chaos based scheme for calculating wideband ambiguity function (WBAF) of a 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 reverse-time chaos theory, it is found in this paper that the time-delay and time-scaling versions of chaotic signal can be generated directly by linear system. With this observation, the WBAF 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 analog way, while the correlation operation can be implemented in digital way. This mixed analog-digital structure provides the proposed scheme with implementation advantages and practical applicability.