Periodic performance of the chaotic spreadspectrum sequence on finite precision*

It is well known that the periodic performance of spread spectrum sequence heavily affects the cor-relative and secure characteristics of communication systems. The chaotic binary sequence is paid more and moreattention since it is one kind of applicable spread spectrum sequences. However, there are unavoidable short cyclicproblems for chaotic binary sequences in finite precision. The chaotic binary sequence generating methods arestudied first. Then the short cyclic behavior of the chaotic sequences is analyzed in detail, which are generatedby quantification approaches with finite word-length. At the same time, a chaotic similar function is defined forpresenting the cyclic characteristics of the sequences. Based on these efforts, an improved method with scramblingcontrol for generating chaotic binary sequences is proposed. To quantitatively describe the improvement of periodicperformance of the sequences, an orthogonal estimator is also defined. Some simulating results are provided. Fromthe theoretical deduction and the experimental results, it is concluded that the proposed method can effectivelyincrease the period and raise the complexity of the chaotic sequences to some extent.