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

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 $\mathcal{O}(N^{2})$ degrees of freedom and are suitable when the aperture is not restricted. These arrays are constructed by appropriately dilating a nested array and augmenting it with several additional sensors. We compare the proposed arrays with those in the literature by analyzing their coarray properties and conducting several Monte-Carlo simulations. Unlike ULA and nested array, any sensor pair in the proposed arrays has a spacing of at least 2 units, because of the coarray hole at lag 1. In the presence of high mutual coupling, the proposed arrays can estimate DOAs with significantly smaller errors when compared to other arrays because of the reduction of coarray weight at critical small-valued lags.