两类阵列族最大非周期互相关值的上界估计OA

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.