西北师范大学学报（自然科学版）2026，Vol.62Issue(1)：35-40,6.DOI:10.16783/j.cnki.nwnuz.2026.01.004
两类阵列族最大非周期互相关值的上界估计
Upper bound on the maximum aperiodic cross-correlation values for two families of arrays
摘要
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 cross-correlation 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.关键词
Costas阵列/幂置换/互相关值/阵列族/Welch构造Key words
Costas array/power permutation/cross-correlation value/family of arrays/Welch construction分类
数理科学引用本文复制引用
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(1):35-40,6.基金项目
国家自然科学基金资助项目(12371522) （12371522）
