Correlation Research On Pseudo-Random Sequences

Pseudo-random sequences are widely used in secret communication,spread spectrum communication system,pseudo-random code ranging,delay measurement,radar navigation and signal synchronization currently.The main indicators that measure randomness properties of a pseudo-random sequence are period,balance,linear complexity and correlation properties.In addition,the cross-correlation properties of pseudo-random sequences are particularly important in code division multiple access systems,different users should use low cross-correlation signals as address codes,the lower the cross-correlation of the two signals,then they are more easily distinguished,and less likely to confuse each other,the interference is also smaller.The work of this paper is divided into two parts.First of all,this paper study on cross-correlation of several binary interleaved sequences based on the interleaving structure u=I(a₀+b（0）,L^{（1/4）（10）+η（a₁）+b（1）,L1/2（a₂）+b（2）,L3/4+η（a₃）+b₃} proposed by Tang Xiaohu and Gong Guang.Secondly,the cross-correlation between m-sequence and its d-sampling sequence is investigated.Main results are as follows:（1）The cross-correlations of the interleaved sequences with above-mentioned structure are studied.The results show that the maximum cross-correlation value is 4N^1/2.（2）This paper selects the sampling factord d=p^3k-p^2k+p^k+(p^4k-1)/2 and gives the distribution of the cross-correlation value between the m-sequence and its d-sampling sequence.The result shows that the cross-correlation property is good in some special cases.（3）This paper verifies the theoretical value of the results that we calculate above by using the Magma soft to write the algorithm.And it shows that the theoretical value and experimental value is consistent.