New Constructions of Extended Sonar Sequences From Sidon Sets

A (m,n) sonar sequence is an m\times n array with exactly one dot in each column and where all lines connecting two dots in the array are distinct as vectors. These arrays are known to have many applications such as sonar and radar detection and these are studied as a particular case of Golomb r...

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Bibliographic Details
Published in:IEEE access 2022, Vol.10, p.3343-3350
Main Authors: Ordonez, Luis Miguel Delgado, Ojeda, Carlos Andres Martos, Trujillo, Carlos A.
Format: Article
Language:English
Subjects:
extended sonar sequences
Mathematical analysis
Radar detection
Rectangles
Sidon set
Sonar
Sonar detection
Sonar sequences
Time-frequency analysis
Upper bound
Vectors (mathematics)
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Summary:A (m,n) sonar sequence is an m\times n array with exactly one dot in each column and where all lines connecting two dots in the array are distinct as vectors. These arrays are known to have many applications such as sonar and radar detection and these are studied as a particular case of Golomb rectangles or two-dimensional Sidon sets. The main open problem for sonar sequences is: for fixed m , find the largest n for which there is an (m,n) sonar sequence, these sequences are called the best sonar sequences. The extended sonar sequences are generalizations of sonar sequences where each column has at most one dot, the motivation to study these arrays are the best results obtained when applied to radar and sonar detection. In this paper, we give the best sonar sequences with m\leq 100 obtained from an exhaustive computational search based on the Caicedo, Ruiz and Trujillo constructions and we present new constructions of extended sonar sequences that use Sidon sets.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2021.3139564