Weight-Constrained Nested Arrays With w(1) = w(2)=0 For Reduced Mutual Coupling

It is well-known that appropriately designed sparse arrays can identify O(N-2) directions of arrivals (DOAs) using N sensors through the difference coarray domain. Many sparse arrays have been proposed in the past decade that also reduce the impact of mutual coupling by reducing the coarray weights at small lags. In this paper, we propose weight-constrained nested arrays (WCNA) that have coarray weights satisfying either w(1) = 0 or w(1) = w (2) = 0. These arrays are obtained by appropriately expanding a nested array and augmenting it with several additional sensors. We prove that the proposed arrays contain O(N-2) contiguous lags in their difference coarrays. Although the uniform segment in the coarray is not centered around 0, appropriately modified coarray-MUSIC can be applied to estimate the DOAs. We demonstrate through Monte-Carlo simulations that such arrays are robust to the presence of strong mutual coupling and can perform better than many other sparse arrays proposed in the literature when the mutual coupling is present. The proposed arrays are also observed to have longer uniform segments in the difference coarray than that of CADiS arrays (having w(1) = 0) and thus can identify more DOAs than CADiS arrays using coarray-MUSIC.