Weight-Constrained Sparse Arrays For Direction of Arrival Estimation Under High Mutual Coupling

• Published in: IEEE transactions on signal processing 2024, Vol.72, p.4444-4462
• Main Authors: Kulkarni, Pranav, Vaidyanathan, P. P.
• Format: Article
• Language: English
• Subjects: <inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX"> mathcal{O}(N)</tex-math> </inline-formula> aperture arrays; Apertures; Array signal processing; Arrays; Closed-form solutions; Degrees of freedom; difference coarray; Direction of arrival; Direction-of-arrival estimation; DOA estimation; Estimation; Linear arrays; Monte Carlo simulation; Mutual coupling; Sensor arrays; Sensors; Sparse arrays; weight-constrained nested arrays; weight-constrained sparse arrays
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2024.3461720

In recent years, following the development of nested arrays and coprime arrays, several improved array constructions have been proposed to identify \mathcal{O}(N^{2}) directions with N sensors and to reduce the impact of mutual coupling on the direction of arrival (DOA) estimation. However, having \mathcal{O}(N^{2}) degrees of freedom may not be of interest, especially for large N. Also, a large aperture of such arrays may not be suitable when limited space is available to place the sensors. This paper presents two types of sparse array designs that can effectively handle high mutual coupling by ensuring that the coarray weights satisfy either w(1)=0 or w(1)=w(2)=0, where w(l) is the number of occurrences of the difference l in the set \{n_{i}-n_{j}\}_{i,j=1}^{N}, and n_{i} are sensors locations. In addition, several other coarray weights are small constants that do not increase with the number of sensors N. The arrays of the first type have an aperture of \mathcal{O}(N) length, making them suitable when the available aperture is restricted and the number of DOAs is also \mathcal{O}(N). These arrays are constructed by appropriately dilating a uniform linear array (ULA) and augmenting a few additional sensors. Despite having an aperture of \mathcal{O}(N) length, these arrays can still identify more than N DOAs. The arrays of the second type have \mathcal{O}(N^{2})