2-D Direction Finding with Pair-Matching Operation for L-Shaped Nested Array

In this letter, we devise a new approach for two-dimensional (2-D) direction finding using an L-shaped array structured by two nested arrays. By vectorizing the covariance matrices of the nested array outputs, the elevation and azimuth angles of the sources are firstly estimated separately. The pair-matching of the elevation and azimuth angle estimates is then achieved employing a permutation matrix which is obtained by solving an optimization problem with the array manifold matrices, cross-covariance matrix, and the source covariance matrix. Unlike the existing schemes, the proposed approach reconstructs the source covariance matrix in the coarray domain. Therefore, it can deal with more sources than the number of sensors in each nested array. Numerical results demonstrate the advantage of the proposed approach over the existing algorithms.