A Improved Algorithm Of Generating Chaotic Sequences Base On Chebyshev Map

Chaos system is one kind of complex nonlinear dynamic system that exhibit many wonderful phenomenon, it changes the way people think about the uncertainty of the world. After half a century unremitting efforts, the chaos research has gone from simply observed phenomenon to using the mathematical analysis that research the profound essence of the chaos system. Chaos science research has been integrated into every aspect of the natural science and social science,a lots of scholars show great enthusiasm that apply the chaos theory to engineering field.Chaos system has lots of special properties, which are sensitive to the initial value, excellent correlation properties, long time unpredictability and no regular non-periodic motion within bounded convergence. These characteristics is very useful for the SSC (Spread Spectrum Communication). Communication scholars want to get one kind of spread spectrum sequences form chaos system, which has enough code number, easy to generate and the performance is better than the tradition one. However, the chaos system work on computer will rise chaotic dynamics degeneration caused by finite precision effect, which contain the short-cycle sequence in the chaotic spread spectrum sequence. It follows that the chaotic spread spectrum sequence can’t use in actual SSC system.This paper analyze the characteristics of chaotic iteration mapping that work on computer at first. And show imperfection of the traditional way to improve chaotic dynamics degeneration, for example the iterative numerical perhaps out of range when add random perturbations and the random perturbations is hard to control compare with the chaos system. Therefore, we present a method that construct a chaotic switch to control random perturbations to improve chaotic dynamics degeneration. Compare with the traditional way, the Switch-Perturbation has better control performance than the common perturbation and increase the complexity of the system through another chaotic switch. Using this method get chaotic sequence and verify its correlation property, balance property and run length characteristic through simulation experiments at MATLAB.This paper present a new generation method of k-order Chebyshev map at last. Traditional way of digitize the Chebyshev map in digital circuit will face to the complex trigonometric calculations, and occupied a lot of hardware resources as a result. We converse k-order Chebyshev map to the multiplicative form by mathematical transformation. This method can optimize iterative process and reduce calculation in hardware. Finally use Verilog HDL and ModelSim to verify the rationality of this method.