Joint Sparse Support Recovery for Direction of Arrival Estimation Using Rational Arrays

In array signal processing, integer linear arrays with sensors placed at multiples of the half-wavelength are standard. In this work, we overcome aperture constraints that often lead to under-utilized sensor resources by using rational arrays that position sensors at rational locations. By formulating direction-of-arrival (DOA) estimation as a joint sparse support recovery (JSSR) problem, we demonstrate that rational arrays can achieve superior performance compared to conventional integer arrays. Notably, rational non-uniform arrays can resolve <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{O}\left(M^{2}\right)$</tex> uncorrelated sources using only <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M$</tex> sensors, even when the available aperture is limited, a feat that integer non-uniform arrays like nested and coprime configurations cannot attain without large apertures. We derive the performance of these arrays using a sufficient JSSR condition and validate our findings through extensive simulations covering both overdetermined and underdetermined DOA estimation scenarios.