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Costas阵列因其最优的非周期自相关性而在雷达和声纳波形设计中具有重要作用.在多用户系统中,不同信号之间的最大非周期互相关值需要被限制在远小于阵列阶数的水平,因此构造具有较小最大互相关值的Costas阵列及扩展阵列族具有重要的研究意义.首先,通过将非周期互相关值转化为有限域上三项式方程根的数目,给出了幂置换阵列族最大非周期互相关值的上界估计;其次,对于Welch型Costas阵列和幂置换的扩展阵列族,将非周期互相关值等价于特定Costas阵列主对角线上固定点的计数,由此给出了扩展阵列族最大非周期互相关值的上界估计,从而部分回答Ardalani提出的公开问题.
Abstract：Due to their optimal aperiodic autocorrelation properties,Costas arrays play an important role in radar and sonar waveform design.In multi-user systems,the maximum aperiodic crosscorrelation values between different signals need to be constrained to values much smaller than the order of arrays.Therefore,it is of great interest to construct families of Costas arrays and their extended arrays with small maximum cross-correlation values.First,upper bounds are derived on the maximal aperiodic cross-correlation values of the family of power permutations,by transforming the aperiodic cross-correlation values into the problem of counting the number of roots of certain trinomial equations over finite fields.Second,for the extended families including both Welch Costas arrays and power permutations,an equivalence between the aperiodic cross-correlation values and the number of fixed points on the main diagonal of specific Costas arrays is established,and an upper bound on the maximal aperiodic cross-correlation value is further provided.The open problem proposed by Ardalani is thereby partially addressed.
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基本信息:
DOI：10.16783/j.cnki.nwnuz.2026.01.004
中图分类号:O151.21
引用信息:
[1]刘润丰,王琦.两类阵列族最大非周期互相关值的上界估计[J].西北师范大学学报(自然科学版),2026,62(01):35-40.DOI:10.16783/j.cnki.nwnuz.2026.01.004.
基金信息:
国家自然科学基金资助项目(12371522)
2026-01-15
2026-01-15