Costas array: Difference between revisions

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In mathematics, a '''Costas array''' can be regarded [[geometry|geometrically]] as a set of ''n'' points lyingcentered on the [[square]]s of aan ''n''×''n'' [[arraysquare tiling]], such that each row or column contains only one point, and that all of the ''n''(''n'' − 1)/2 [[displacement (vector)|displacement]] [[Euclidean vector|vectors]] between each pair of dots are distinct. This results in an ideal "thumbtack" auto-[[ambiguity function]], making the arrays useful in applications such as [[sonar]] and [[radar]]. Costas arrays can be regarded as two-dimensional cousins of the one-dimensional [[Golomb ruler]] construction, and, as well as being of mathematical interest, have similar applications in [[experimental design]] and [[phased array]] radar engineering.

Costas arrays are named after [[John P. Costas (engineer)|John P. Costas]], who first wrote about them in a 1965 technical report. Independently, [[Edgar Gilbert]] also wrote about them in the same year, publishing what is now known as the logarithmic Welch method of constructing Costas arrays.<ref>{{harvtxt|Costas|1965}}; {{harvtxt|Gilbert|1965}}; [http://nanoexplanations.wordpress.com/2011/10/09/an-independent-discovery-of-costas-arrays/ An independent discovery of Costas arrays], Aaron Sterling, October 9, 2011.</ref>