弱半bent正交序列集的构造

Constructions of Weakly Semi-bent Orthogonal Sequences Sets

扩频通信系统的码序列在近些年一直是备受关注的研究课题之一,扩频通信序列目前已经被广泛应用于军事以及民用通信.对于扩频序列,相关值决定了系统的抗干扰性,它要求具有良好的互相关性质,为满足越来越密集的人口通信,还需要保证每个蜂窝里的用户数量足够大.本文提出弱半bent布尔函数和弱半bent序列集的定义,并利用Maiorana-McFarland类密码函数构造技术,构造出弱半bent正交序列集.与半bent正交序列集相比,利用弱半bent序列集可以使单个蜂窝内用户的数量更多.本文还给出弱半bent序列集的两种优化方案.第一种优化方案仍然是以增大单个蜂窝用户数为主要目标,在某些情况下数量比目前最优结果大一倍.第二种优化方案是用弱半bent正交序列集构造出半bent正交序列集,使不相邻蜂窝间的用户干扰较弱半bent正交序列集更低,并且没有减小单个蜂窝内的用户数.弱半bent正交序列可用于同步CDMA系统的蜂窝用户码,可以实现用户数量和抗干扰性的较好折中.

Spread-spectrum technique has been widely applied both in military and in civilian communications. The design of the codewords in the spread-spectrum communication systems is one of the most concerned topics in sequence design. The correlation value of the spread-spectrum sequences determines the ability of the anti-interference of the system. Thus the sequences should have desirable cross-correlation properties. In order to meet the communication demand for increasingly dense population, the sequences also need to ensure a sufficient number of users in each cell. In this paper,the definition of weakly semi-bent Boolean functions and weakly semi-bent sequences are presented.A class of weakly semi-bent orthogonal sequences has been constructed by using Maiorana-Mc Farland cryptographic Boolean function construction technique. Weakly semi-bent orthogonal sequences can be assigned to regular tessellation of hexagonal cells, the number of users per cell is larger than that by the currently best known method. Two optimization schemes of the weakly semi-bent sequence sets are designed. The first optimization scheme is to increase the number of individual cellular users as the main target, and in some cases it is twice as large as the current optimal result. In the second optimization scheme, the semi-bent orthogonal sequences sets are constructed based on the weakly semi-bent orthogonal sequences sets, making the interference between non-adjacent cells smaller than weakly semi-bent orthogonal sequences sets without reducing the number of users in each cell. Weakly semi-bent orthogonal sequences can be assigned to regular tessellation of hexagonal cells, which is typical for certain code division multiple access（CDMA） systems, it can achieve a compromise between the number of users and the anti-interference performance.