Near-Field Source Localization With Two-Level Nested Arrays

The concept of the nested array has been used widely for underdetermined far-field source localization. In this case, the enhanced degrees-of-freedom (DOFs) is often achieved by using spatial smoothing because the difference co-array of a two-level nested array behaves like a uniformly-spaced linear array (ULA). This ingenious operation cannot be used for near-field localization because the ULA behavior of the co-array is violated by the near-field’s curved wavefronts and range-dependent attenuation. Thus, the application of nested arrays for near-field localization becomes challenging. In this letter, we propose to concatenate the vectorization of multiple fourth-order cumulant matrices to increase the DOFs offered by the nested arrays. We also show that when the sources are in the near-field, the maximum DOFs provided by a two-level nested array with <inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> physical sensors can mathematically be up to exactly <inline-formula> <tex-math notation="LaTeX">$L^{2}$ </tex-math></inline-formula>. The well-posed identification conditions are discussed as well. Numerical examples are conducted to verify our analysis. Comparisons with existing ULA-based methods are also provided.