Large Minimum Redundancy Linear Arrays: Systematic Search of Perfect and Optimal Rulers Exploiting Parallel Processing

Minimum Redundancy Linear Arrays (MRLAs) are special linear arrays that provide the narrowest main lobe in the radiation pattern possible for a given number of antennas. We found that the calculation of MRLAs is the same as for the mathematical problem of perfect sparse rulers. Finding perfect rulers (or MRLAs) is a hard problem, as there is no proven mathematical rule to design them. They can only be found by constructing ruler candidates via an exhaustive search while ensuring that no ruler with less redundancy exists. We revisited the problem of sparse ruler construction and used two exhaustive search algorithms to compute longer rulers than previously published. Further, we present an approach to accelerate the execution by distributing the recursive search algorithms over multiple computers. Our compute cluster found perfect rulers with all lengths up to 244 in 443 years of combined CPU time. All found rulers are provided to the research community. Additionally, we confirm previously known Low Redundancy Linear Arrays being MRLAs. Our results show that larger perfect rulers do not always require equal or more marks (antennas) but can sometimes be constructed with fewer marks than the previous ruler.