Design of Orthogonal Golomb rulers with applications in wireless localization

Orthogonal Golomb rulers (GRs) are useful in a vast number of applications across various areas of engineering such as coding theory [1], radio astronomy and communications [2] and pulse phase modulation [3]. Yet, the design of sets with multiple mutually orthogonal GRs is a problem that finds no solution in current literature. In this paper we present a genetic algorithm to solve this long-standing problem. Our solution is based on a modification of a classic GR-generation algorithm [4], which allows the construction of GRs out of constrained sets of marks, such that multiple orthogonal rulers can be obtained iteratively. A complete pseudo-code of the new algorithm is offered, along with examples that not only demonstrate its ability to solve the intended problem but also indicate a gain in efficiency over [4] even when applied to generate optimal GRs. An application example in wireless localization is also given, in which a Cramér-Rao lower bounds (CRLBs) analysis of range-based target localization is used to illustrate the remarkable gains that can be achieved by employing orthogonal Golomb rulers to perform efficient multipoint ranging.