Sparse, Weight-Constrained Arrays With O(N) Aperture for Reduced Mutual Coupling

Recently, several sparse array constructions have been proposed to reduce the effect of mutual coupling on the direction of arrival (DOA) estimation, by reducing the number of sensor pairs with small separations. For a large number of sensors N and under aperture constraint, $\mathcal{O}\left( {{N^2}} \right)$ degrees of freedom and $\mathcal{O}\left( {{N^2}} \right)$ aperture may not be of interest, or desirable. In this paper, we consider sparse arrays with $\mathcal{O}(N)$ aperture and enforce the coarray weights at smaller lags to be zero. This helps reduce the effect of mutual coupling while maintaining $\mathcal{O}(N)$ aperture, which is desirable when there is an aperture constraint. We describe several specific ways in which such arrays can be generated by appropriately dilating uniform linear arrays and augmenting them with a few additional sensors. We perform Monte-Carlo simulations to demonstrate that the proposed arrays perform well in the presence of strong mutual coupling, unlike the uniform linear array. They can also perform better compared to $\mathcal{O}\left( {{N^2}} \right)$ aperture sparse arrays when the array aperture is constrained.