Generalized Constructions of Weight-Constrained Sparse Arrays

To reduce the impact of mutual coupling on the direction of arrival (DOA) estimation, we recently proposed weight-constrained sparse arrays (WCSAs) that have holes in the difference coarray at lag 1. Furthermore, for the situations where the available aperture can be limited, WCSAs with N sensors are designed to have an aperture with $\mathcal{O}\left( N \right)$ length, unlike the traditional sparse arrays with a large aperture of $\mathcal{O}\left( {{N^2}} \right)$ length. In this paper, we propose a generalized construction of WCSAs with w(1) = 0 that additionally satisfies the property that for a given integer P, w(l) for 2 ≤ l ≤ P are constants that do not increase with the number of sensors N. Here the coarray weights w(l) denote the number of occurrences of the difference l in the difference coarray $\left\{ {{n_i} - {n_j}} \right\}_{i,j = 1}^N$, and n<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</inf> are sensors locations. We prove that the difference coarrays of the proposed arrays contain a large one-sided ULA segment of $\mathcal{O}\left( N \right)$ length starting from lag 2. The effect of P on coarray properties and coupling leakage values is analyzed. Numerical simulations demonstrate that the proposed arrays can be more robust to mutual coupling than previously proposed WCSAs. Furthermore, the proposed arrays can also have smaller DOA estimation errors compared to the well-known sparse arrays from the literature, especially under high mutual coupling and aperture constraints.