The Improvement Of Chaotic Spread Spectrum Sequence And Its Application In CDMA Communication

In code division multiple access mobile communication, the selection of address code is a key technique, and the spread spectrum sequence used as address code directly influence the properties of communication system, such as the system capacity, anti-jamming capability, the ability of keeping secret, connecting rate, switching rate and so on. Nowadays, most spread spectrum sequence used for the spread spectrum system is generated by the shift register, such as m sequence, gold sequence etc. M sequence is easy to produce, but it has some disadvantages, for example, its complexity is low and the ratio of its maximal mutual correlation function value to its maximal auto correlation function value is very large. Gold sequence has relatively better correlation properties, but its random-like perfomance is not good. Besides, the amount of address code is limited, which restricts the system capacity. Chaotic sequence is sensitive to the initial value and the external parameter, so it has very good random perfomance. Therefore, chaotic sequence provides a new method for the produce of the spread spectrum sequence.The chaotic phenomenon is a deterministic and random-like process appearing in the non-linearly dynamic system. This process is non-period, non-convergence but bounded. It has sensitive dependence on the initial values, that is, the little difference of the initial conditions 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. This random-like characteristic of chaotic phenomenon is very suitable for disguising modulation as noise in communication. And it is most important that chaotic system can provide signal which is plentiful, uncorrelated, random-like, deterministic and being easy to generate and regenerate because of the sensitive dependence on the initial values. Therefore, chaotic sequence has a good application foreground in communication domain especially in the generation of pseudo random spread spectrum code because of these especial characteristics.In this paper, we will focus on the application of chaotic sequence used as spread spectrum code in CDMA communication system. We propose the two-dimensional over-sampled chaotic sequence on the base of the combination of time discrete chaotic system and over-sampled theory in communication. This paper mainly research on the various properties and application of the binary over-sampled chaotic sequence, which includes the following aspects:1. We define the concept of OSCM (Over-sampled Chaotic Map), generate the over-sampled chaotic sequence by using improved Logistic-Map, Tent-Map, Chebyshev-Map, and analyze their sensitive dependence on the initial values. The numerous simulation results show that when the initial value difference is only 10-6, the two tracks separate only after four iterations, and at last the two tracks become absolutely different. Analysis shows that over-sampled chaotic sequence is sensitive to the initial value,easy to generate, rich in sequence code. Therefore, we can make use of the over-sampled chaotic sequence to implement muti-access.2. We analyze detailedly that how each parameter of improved Logistic-oscm-Map, Tent-oscm-Map, Chebyshev-oscm-Map influences the balance perfomance of the over-sampled chaotic sequence. Simulation results show that: the over-sampled parameter P of each OSCM doesnot affect greatly the balance perfomance and there is no peak value. Using the balance guidelines we select the optimal over-sampled parameter value, such as: Logistic-oscm-map: P=5, the balance value E%=3.694740e-003; Chebyshev-oscm-map: P=5, the balance value E%= 1.627604e-002 ;Tent-oscm-map: P=3, the balance value E%=6.510417e-002. The initial value parameter of each OSCM affects smally the balance perfomance, but all have several peak value points, such as: Logistic-oscm-map: x0=-1,-0.5,0,0.5,1, the balance value E%≥0.5; Chebyshev-oscm-map: x0=-1,0,1, the balance value E=1; Tent-oscm-map: x0=0.9, the balance value E=1. So we should avoid these points when we generate chaotic sequence. The balance perfomance of each OSCM tends to balance gradually along with the increase of the sequence length. Besides, power series k of Chebyshev-oscm-map affects smally the balance perfomance, and we select k=4 inthis paper. Coefficient a of Tent-oscm-map affects smally the balance perfomance, but the balance value has a high peak value when a is 0.50, and the balance value has a low peak value when coefficient a is 0.156, 0163, 0.201, 0.224 and 0.246 respectively, and the balance value E=0 when coefficient a is 0.89 and 0.92. Finally, comparing to the simulation results of the original map we can conclude that OSCM has a better balance perfomance than the original map, and OSCM can improve the secrecy perfomance of communication system.3. we analyze detailedly the self-correlation, the mutual-correlation, the odd-correlation, and the even-correlation of improved Logistic-oscm-Map, Tent-oscm-Map, and Chebyshev-oscm-Map. Simulation results show that the self-correlation of the above three OSCM is perfect, the absolute value of the mutual-correlation of the above three OSCM is near in 0.05, and the ratio of the maximal mutual-correlation value to its maximal self-correlation value is smaller, that is, the OSCM has a good anti-mutipath-interference ability. The absolute value of the odd-correlation and the even-correlation of the above three OSCM are less than 0.04, and the value become small along with the increase of the sequence length, but the value keeps basically identical when the sequence length is greater than 4000. Therefore, it is appropriate that we select the sequence length from 2000 to 4000. Simulation results tell us that over sampled chaotic sequence has good anti-mutiaccess-interference and it can increase greatly the capacity of the communication system.4. we analyze detailedly the run distribution perfomance of the above three OSCM, simulation results show that the simulated run distribution curve is basically identical to the ideal run distribution curve, that is, the over sampled chaotic sequence has good run balance, therefore, the over sampled chaotic sequence has good pseudo random perfomance, it is very appropriate to the disgusting modulate as noise in the spread spectrum communication.5. On the base of MATLAB software simulated platform we construct CDMA communication system model in which we simulate the mobile radio channel asRayleigh fading channel and AWGN channel. We analyze and simulate the bit-error-rate of the above three over sampled chaotic sequence applied in the CDMA communication system, then compared to the traditional spread spectrum code such as m sequence, gold sequence. Simulation results show that the over sampled chaotic sequence can relatively reduce the bit-error-rate and improve the system transform perfomance. Meanwhile, when the over sampled chaotic sequence is applied in the CDMA communication system as spread spectrum code, the bit-error-rate dose not go up along with the increase of the number of the parallel users. That is to say, the over sampled chaotic sequence used as spread spectrum code can commendably stand against the muti-access interference, and improve the channel capacity.