Rational Arrays for DOA Estimation

Abstract

Linear arrays used in array processing usually have sensor positions r <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</inf> λ/2 where λ is the wavelength of the impinging signals and r <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</inf> are integers. This paper considers rational arrays, where r <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</inf> are rational numbers. In particular, sparse rational arrays such as coprime rational arrays are introduced. In order to do this, some rational extensions of integer number theoretic concepts such as greatest common divisor and coprime numbers are required, which are introduced as well. The advantages of rational arrays are demonstrated with the help of rational coprime arrays. For example, they improve the accuracy of DOA estimation when the sensors have to be distributed with a fixed aperture constraint.