Research on Chaotic Sequence Autocorrelation by Phase Space Method

Chaotic sequences have been widely used as pseudorandom sequences. But the problem of how to judge the performances of their autocorrelation functions, up to now, has not yet been solved completely. Because of this, the applications of chaotic sequences are limited. In the paper, by method of phase space, we prove that the autocorrelation performance of a chaotic sequence is determined by whether its phase space trajectory is axis symmetrical, and we deduce a theorem that a sequence which phase space trajectory is axis symmetrical has good autocorrelation performance. The theorem is verified by simulations.