Efficient Use of Non-Central ULA Segments in the Coarrays of Weight-Constrained Sparse Arrays

Recently, we proposed weight-constrained sparse arrays (WCSAs) that have holes in the difference coarray at locations 1 and 2. CADiS arrays and constrained MRAs from the literature also have such central holes in their difference coarrays. Coarrays of these arrays have a one-sided ULA segment on the positive side and a corresponding ULA segment on the negative side. However, the coarray-domain direction of arrival (DOA) estimation for such arrays only uses the one-sided ULA segment in coarray. To take advantage of both ULA segments present in the coarray, we propose augmented root-MUSIC and augmented ESPRIT. These methods are based on the SVD of an augmented coarray matrix formed by stacking the Toeplitz matrices based on the two ULA segments. These methods can still provably identify up to | <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L$</tex> /2 | DOAs, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L$</tex> is the length of a one-sided ULA segment in coarray. Our numerical simulations show that augmented root-MUSIC has a smaller MSE than root-MUSIC based only on the one-sided ULA segment from the difference coarray. We also compare the proposed algorithms with other ways of efficiently using the non-central ULA segments in the coarray, including dictionary-based DOA estimation and coarray interpolation. The computation time of the proposed algorithms is observed to be much smaller than other optimization-based approaches.