Improved arithmetic for generating Costas arrays using welch construction method

On the symmetry of Welch- and Golomb-constructed Costas arrays

We prove that Welch Costas arrays are in general not symmetric and that there exist two special families of symmetric Golomb Costas arrays: one is the well-known Lempel family, while the other, although less well known, leads actually to the construction of dense Golomb rulers. © 2008 Elsevier B.V. All rights reserved.

Algebraic Constructions for Costas Arrays

Thus, if ai,,j, = ail,il= ajl,j, = aiJqj4 = 1 in the matrix, we must not have ii2 1 il 3jjL;$) = (i4 4 ,.i, -jd, nor may we have (iz i,,j, -j,)= . ,. . 13 ‘2, 3 Such matri& have been called either Costas Arrays or constellations in Ref. [2], which explores constructions as well as applications for these patterns. It is convenient to represent these arrays on an n X n grid, using dots for the l’...

A Recursive Method for Enumeration of Costas Arrays

In this paper, we propose a recursive method for finding Costas arrays that relies on a particular formation of Costas arrays from similar patterns of smaller size. By using such an idea, the proposed algorithm is able to dramatically reduce the computational burden (when compared to the exhaustive search), and at the same time, still can find all possible Costas arrays of given size. Similar t...

Construction of Baumert-Hall-Welch arrays and T-matrices

A Review of Costas Arrays

Costas arrays are not only useful in radar engineering, but they also present many interesting, and still open, mathematical problems. This work collects in it all important knowledge about them available today: some history of the subjects, density results, construction methods, construction algorithms with full proofs, and open questions. At the same time all the necessary mathematical backgr...