Symmetry-Imposed Rectangular Coprime and Nested Arrays for Direction of Arrival Estimation With Multiple Signal Classification

Linear sparse arrays (coprime and nested arrays) have been studied extensively as a means of performing direction of arrival (DoA) estimation while bypassing Nyquist sampling theorem. However, rectangular sparse arrays have few studies, most of which are based in lattice theory. Although the multiple signal classification (MUSIC) alogrithm can be applied to lattice theory-based sparse arrays, fewer DoAs can be estimated for these arrays than for a full array with the same aperture. One contribution of this paper is the formulation of symmetry-imposed rectangular coprime and nested array designs that have wider contiguous lags than lattice-based arrays. Also, existing algorithms for rectangular arrays employ the direct sample covariance matrix estimate, which has low accuracy. Another contribution of this paper is an alternate method for estimating the covariance matrix that ensures the matrix is block-Toeplitz. Using the proposed covariance matrix estimate, we integrate a MUSIC-based DoA estimation method that applies to both full arrays and sparse arrays. The results show that the covariance estimates produced by the proposed method have higher accuracy than the traditional sample covariance estimates. The results also demonstrate that symmetry-imposed sparse arrays have higher resolution than full rectangular arrays with the same number of sensors.