Interpolation for Weight-Constrained Nested Arrays Having Non-Central ULA Segments in the Coarray

Abstract

Recently, we proposed weight-constrained nested arrays (WCNA) that have holes in the difference coarray at lags 1 and 2. While this helps in reducing the impact of mutual coupling, the ULA segment in the coarray is ‘one-sided’ from lag L<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> to L<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> where 0 < L<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> < L<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>. In this work, we propose to use covariance interpolation to effectively utilize such arrays having ‘central’ holes in the coarray. After interpolation, a larger Toeplitz matrix is generated, which is used to estimate directions of arrivals (DOAs) using root-MUSIC. We demonstrate that using this approach, we can accurately identify up to twice as many DOAs as what is possible using only the one-sided ULA segment in coarray. Even when the number of DOAs is small, the DOA estimation error after interpolation is over an order of magnitude smaller than that using only the one-sided ULA segment in coarray. Thus, we can mitigate the disadvantage of having central holes in the coarray while maintaining the advantage of WCNAs in reducing the impact of mutual coupling on DOA estimation. This interpolation approach can also be used for other arrays from the literature that have central holes in the coarray, such as CADiS.