Research Of An Over-Sampled Discrete Chaotic Spread Spectrum Sequence

Chaos is a deterministic random process in nonlinear dynamic system, this process is non-periodic, not converge but bounded, and is extremely sensitive to the initial value. Chaos is of class random characteristics, very accord with the communications pseudo noise modulation requirements, and because of the sensitivity of the chaos initial value, it can produce numerous and renewable sequence. Therefore, the chaos code applied to spread spectrum system can solve the problem of insufficient address quantity. Meanwhile, because the chaotic sequence used in communications system may not be infinite long, its performance could not reach the ideal state, so we need selecting good chaos sequence to get better performance.Chaos is effectively used in the spread spectrum communication field. As spread-spectrum yards, chaotic sequences need to translate into "0-1" sequence, the traditional way is to use binary quantitative method. But, use binary quantitative method also have drawbacks. Every time produce a "0" or "1" will need to undertake iteration, which gave system has brought great computational efficiency. In order to solve this problem, "many bits method" appeared. Although "many bits method" greatly reduces the computational complexity, but the influence of effective digit quantization still not eliminated. This caused significant hurdles in actual application of chaotic sequence. In order to solve this problem, such as micro interference method, the method of multi-level quantitative hair was advanced, but each has shortcoming. These methods are trying to improve chaotic real value sequence. This paper starting from another way : change real value distribution of the chaotic sequence. Produced by this idea is to add discrete method. So, not only it can reduce the computation cost in a certain degree , but also can improve the complexity, enhance the safety of the sequence.In order to improve the spread spectrum sequence complexity and security, this paper put real value distribution and change sequence had sampling combine, and proposes a way to create "over-sampled discrete chaotic sequence". This over-sampled discrete chaotic sequence producing method may be based on different kinds of traditional chaos mapping. In this paper, it's based on Chebyshev chaos mapping. In the first chapter, we expounds the historical development of ultra-wideband communication background and research status, introduces its research content and chapters arrangement.In the second chapter, through computer simulation, we analyzed the new sequence of chaotic properties, including chaotic attractor and maximum lyapunov index. We Can see the maximum lyapunov exponent is greater than 0, i.e. attractor are strange attractor, it can be concluded that the new sequence is chaotic sequence.In the third chapter, we analysed the initial value sensitivity, autocorrelation, run-length, balance, cross correlation of the new sequence, and compared it with Chebyshev chaotic sequences. Initial value sensitivity analysis shows that, under the same conditions, sampling discrete sequence has separates faster, it has very good initial value sensitivity; in autocorrelation and cross correlation, we can found sampling discrete sequence has good performance, slightly better than the Chebyshev chaotic sequence; Balance aspects, when the sequence's length relatively short, can see obviously, the balance of sampling discrete sequence is better than the Chebyshev chaotic sequences. In actual spread spectrum communication system, spread spectrum code is relatively short, so, as spread-spectrum code, sampling discrete sequence has more advantages; In the run-length analysis, we can see, sampling discrete sequence and Chebyshev sequence are both close to the theoretical value.In the fourth chapter, for further evaluation of the new sequence as spread-spectrum code, a multi-user spread spectrum communication system simulation platform is built. It's required that the channel type, channel parameters, modulation/demodulation method, spread spectrum code, number of users could be changed when need to, so it can simulate different conditions and environments. In order to satisfy the above-mentioned requirements, according to each part function and user requirements, the author made the system multiple level designed and module parted. This makes this simulation platform can not only finish necessary function, but also has a strong opening. It is convenient to change and add new functions , without affecting other modules. In addition, detailed design guarantees the platform prophase distinct and readable.In chapter 5, before using the platform, we tested and verified the effectiveness of the simulation platform, using conventional chaotic sequence as spread-spectrum code. On this basis, we analyze the performance of the new sequence with platform. We can draw the conclusion, in autocorrelation, cross-correlation and performance as spread-spectrum code, sampling discrete sequence is superior to Chebyshev sequence. But, the advantage is not obvious. Over-sampled discrete sequence was proposed to improve safety, so, performance advantage is not the main point, it can regard as a kind of windfall. Analyzed the nature of sampling discrete sequence, the purpose is to prove the sequence can not only improve security, but also can achieve similar performance with traditional sequence. Analysis indicates that the new sequence can be used as spread-spectrum sequence, and performance is slightly better than the traditional sequence.From the generation of the new sequence, we can see that the number of parameters which decide the content of the new sequence is up to six. So, any change of these parameters would bring changes to the sequence. In this way, new sequence is much safer than traditional chaos sequence. Compared with Chebyshev sequence, via discrete and sampling, new sequence changed the real value distribution, making attractor shows the distribution of noise type, if the sequence is used to spread spectrum sequence, can improve communications privacy.Over-sampling discrete method extracts some bits from each iteration result, in this way, improves the production efficiency and reduces the amount of calculation that produce sequence. Especially using "decimal turn binary" method in binaryzation, the effect is more apparent.The sixth chapter summarizes the full text, and puts forward the problems for further research.