Study On Chaotic Spread Spectrum Communication Technology And Its Application

In digital code division multiple access (CDMA) mobile communication, the selection of address code is a key technology. Nowadays, two-level pseudo-random code is used as the de-spread spectrum sequence for all spread spectrum system. Although it has perfect self-correlation property, its mutual correlation function is not ideal, which has more serious multi-access interference and the amount of address code is limited, whose capacity is restricted, and the code itself is easy to be decyphered. Therefore, it is an urgent project for communication researchers to explore a practical spread-spectrum sequence. The chaotic phenomenon refers to the deterministic and random like process appearing in the non-linearly dynamic system. This process is non-convergent but bounded. It has sensitive dependence on the initial value and the external parameter, that is, the little difference of the initial condition will separate each other according to the Lyapunov exponential rule with time passing by. And at last it will turn into two tracks with absolutely distinct track of motion or feature. Therefore, two sequences originating from close initial values will be non-correlated in short time. Meanwhile, chaotic system has very complex track of motion, which will never close, as long as the time is long enough. The chaotic track will traverse the entire suction factor, and the properties of the chaotic sequence express high random behavior. The chaotic power spectrum has continuous broadband property as well, which is the reason why the chaotic spread sequence can resist the noise well. This characteristic of chaotic phenomenon is much suitable for noise camouflage modulation in communication, which is chaotic spread spectrum code division multiple access communication and security communication. On theory, the self-correlation function of chaotic sequence is δfunction, and the mutual-correlation function is zero. Moreover, the chaotic sequence is numerous; it can be generated by a map function and an initial value, and it is not needed to store each sequence value. Consequently, if we use chaotic sequence as the spread spectrum sequence in spread spectrum communication, it cannot only provide necessary conditions for multi-user communication but also achieve encryption for the information. It has wide application future in multi-access communication and security communication. In this paper, we will focus on the application of chaotic in communication and explore an optimal chaotic sequence, in order to provide certain theoretical reference for the appropriate application of chaotic in communication system. This paper mainly discusses the application of chaotic in communication, which includes several sections as following: 1. We analyze the theory and method of generating chaotic sequence by using Logistic-Map, and iterate the map to get the sequence. From the academic view, we focus on the Chebyshev-Map to discuss ordinary one-dimensional time discrete chaotic system and its measure, and conclude their relationship. Moreover, we analyze the fixed measure, self-correlation mutual-correlation of the two-phase chaotic sequence, and verify these properties by simulation. As we see from the calculation, the mean of chaotic sequence iterating by the Logistic-map is zero, self-correlation is δfunction, and mutual-correlation is zero, its probability statistic property is consistent with white noise property. Therefore, the Chebyshev-Map chaotic sequence can be used as noise modulation, and is appropriate to be applied as spread spectrum sequence in spread spectrum communication. Analyzing results show that chaotic sequence is sensitive to the initial value, easy to generate, rich in sequence code, and better than conventional pseudo-random sequence, which is suitable to be used as spread spectrum sequence in communication system. 2. We discuss various properties of the chaotic sequence generated in practice. First, we judge whether the chaotic is perfect by checking its correlation property. Second, we discuss how to choose its initial value. And we use the numeric method to analyze the properties of chaotic sequence, especially how the sequence length influences the correlation properties, furthermore,we get its fitting formula. Then, we analyze the performance of balance of three kinds of chaotic sequence generating by Logistic-Map, Chebyshev-Map, and Tent-Map separately. For Logistic-Map, the fractal parameter of two-phase chaotic spread spectrum sequence has great influence on its performance of balance, and we obtain that the degree of balance E=0, when r=3.848,3.856,3.969,3.978,4, which offers reference for us to choose the proper fractal parameter to meet the performance of balance of the sequence. When r=4, we get the best performance of balance. The initial value affect the performance of balance seriously on several peak points, that is when X is 0.25,0.5,0.75 and E is 0.998, -0.996,1 respectively, therefore, these points should be avoided when constructing the sequence. For Chebyshev-Map and Tent-Map, we also discuss how their fractal parameters, initial values, and sequence periods affect the performance of balance, and find out the non-balance points which should be avoided when constructing sequence, which provides theoretical reference for the application of chaotic to the communication system in the way of performance of balance. Finally, we compare the performance of balance for the three kinds of sequence. Analyzing results indicate that, the Chebyshev sequence has the best performance of balance, and Logistic sequence is after it. However when the sequence length is longer than 800, all the above three kinds of sequence can meet the performance of balance ,it is E%<0.02, which is available for the CDMA. 3. Based on the theory of spread spectrum communication, and the former researches, we construct four-phase chaotic spread spectrum sequence with unequal length, and testify the correlation properties of this kind of sequence. The numerous simulation results show that its self-correlation and mutual-correlation are all superior to that of the two-phase sequence, the correlation distribution of four-phase sequence is not sensitive to the selection of map initial value and the correlation distribution of different sequences generating by different initial values is approximatly the same, which means we can get a great deal of spread spectrum sequence by changing initial values randomly. If choosing two four-phase chaotic sequences with different sequence length but similar initial values to analyze the correlation property, we can get correlation property of the sequence with unequal length. Also, the absolute values ofgeneralized odd mutual-correlation of four-phase spread spectrum sequences with period p mp accord with the Rayleigh distribution with root-mean-square value 1/mp, where m is a natural number. Four-phase chaotic spread spectrum is fit for quaternionic modulation in CDMA, and it can also increase linear complexity of the sequence, which has a bright future in spread spectrum communication and security communication. 4.We propose TOCS (Two-dimensional Over-sampled Chaotic Sequences),and introduce the generation method of sequence in detail. We prove the self-correlation and mutual-correlation of sequence and compare to the original sequence. We also discuss the performance of balance for TOCS, and analyze the signal to noise ratio and the multi-access interference bit error rate of TOCS in CDMA multi-user communication system further. Analyzing results show that the TOCS has chaos locus for all initial values, the ideal complexity and optimal performance of balance under the situation of sampling times P=2,the Lyapunov's index value is twice of the source mapping. Due to more bits are lost in the each iteration. And the shortened prediction time the bit error rate may meet the need of 10-3 , which minimums the power of multi-access interference in DS-CDMA and improves SNR easily. Thanks to more bits are lost in each iteration and the superior security aspect to original chaos mapping sequence,it is the optimal choice for CDMA spread spectrum sequence .It is much suitable for communication system, especially for secure communications. 5. Along with multi-user digital mobile communication system, we put forward the performance measure rule for spread spectrum sequence, and construct the standard to determine the optimal sequence. Meanwhile, we complete the optimal choice for TOCS, and point out that if the optimal choice is performed according to given method, the performance of chaotic spread spectrum sequence will be improved. The basic idea is: "screening method". First we generate M sequences by chaotic map. Then we check the performance measure rule to take away the unfitted sequences, the final result is just the optimal sequence. Afterwards, the performance of the asynchronous code division multi-access system can be efficiently improved to make use of the optimum seeking method to screen the TOCS. We compare it with the conventional pseudo-random sequence and four-phase sequence with unequal length, the results indicate that the chaotic sequence, which has been selected, has numerous...