基于线性阵列解析式快速筛选最小冗余线性阵列(MRLA)OA

Minimum redundancy linear arrays(MRLA)are widely used in wireless communication,radar,and other fields.However,obtaining data for large array sizes(with more than 28 elements and a maximum continuous baseline length exceeding 244)poses significant challenges,and there is currently a lack of clear criteria for identifying MRLA.To address this issue,this study delves into the definitions of low-redundancy linear arrays and MRLA,revealing mathematical equivalencies between the numerical values of MRLA and the scale values of perfect sparse rulers,the smallest constrained differences in element counts,and the labeling values of minimal graceful graphs.It is proven that all linear arrays have a redundancy of no less than 1.000 0,and the redundancy is strictly greater than 1.000 0 when the number of elements is 5 or more.For MRLA with a maximum continuous baseline length of L and a number of elements n,the number of elements for an MRLA of length L+1 is no more than n+1.Based on an analysis of large-scale MRLA data,the following hypothesis is proposed:linear arrays with a redundancy of no more than 1.500 0 are MRLA.To tackle the challenge of obtaining MRLA data,this study proposes an efficient screening method based on analytical formulas for linear arrays,successfully identifying four types of infinite configuration patterns for linear arrays with a redundancy of no more than 1.500 0,with a flexible upper limit for screening redundancy.This method enhances the efficiency of obtaining MRLA,laying a solid foundation for their promotion in practical applications.